what is factor analysis in marketing research

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What is factor analysis and how does it simplify research findings.

17 min read There are many forms of data analysis used to report on and study survey data. Factor analysis is best when used to simplify complex data sets with many variables.

What is factor analysis?

Factor analysis is the practice of condensing many variables into just a few, so that your research data is easier to work with.

For example, a retail business trying to understand customer buying behaviours might consider variables such as ‘did the product meet your expectations?’, ‘how would you rate the value for money?’ and ‘did you find the product easily?’. Factor analysis can help condense these variables into a single factor, such as ‘customer purchase satisfaction’.

The theory is that there are deeper factors driving the underlying concepts in your data, and that you can uncover and work with them instead of dealing with the lower-level variables that cascade from them. Know that these deeper concepts aren’t necessarily immediately obvious – they might represent traits or tendencies that are hard to measure, such as extraversion or IQ.

Factor analysis is also sometimes called “dimension reduction”: you can reduce the “dimensions” of your data into one or more “super-variables,” also known as unobserved variables or latent variables. This process involves creating a factor model and often yields a factor matrix that organises the relationship between observed variables and the factors they’re associated with.

As with any kind of process that simplifies complexity, there is a trade-off between the accuracy of the data and how easy it is to work with. With factor analysis, the best solution is the one that yields a simplification that represents the true nature of your data, with minimum loss of precision. This often means finding a balance between achieving the variance explained by the model and using fewer factors to keep the model simple.

Factor analysis isn’t a single technique, but a family of statistical methods that can be used to identify the latent factors driving observable variables. Factor analysis is commonly used in  market research , as well as other disciplines like technology, medicine, sociology, field biology, education, psychology and many more.

What is a factor?

In the context of factor analysis, a factor is a hidden or underlying variable that we infer from a set of directly measurable variables.

Take ‘customer purchase satisfaction’ as an example again. This isn’t a variable you can directly ask a customer to rate, but it can be determined from the responses to correlated questions like ‘did the product meet your expectations?’, ‘how would you rate the value for money?’ and ‘did you find the product easily?’.

While not directly observable, factors are essential for providing a clearer, more streamlined understanding of data. They enable us to capture the essence of our data’s complexity, making it simpler and more manageable to work with, and without losing lots of information.

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Key concepts in factor analysis

These concepts are the foundational pillars that guide the application and interpretation of factor analysis.

Central to factor analysis, variance measures how much numerical values differ from the average. In factor analysis, you’re essentially trying to understand how underlying factors influence this variance among your variables. Some factors will explain more variance than others, meaning they more accurately represent the variables they consist of.

The eigenvalue expresses the amount of variance a factor explains. If a factor solution (unobserved or latent variables) has an eigenvalue of 1 or above, it indicates that a factor explains more variance than a single observed variable, which can be useful in reducing the number of variables in your analysis. Factors with eigenvalues less than 1 account for less variability than a single variable and are generally not included in the analysis.

Factor score

A factor score is a numeric representation that tells us how strongly each variable from the original data is related to a specific factor. Also called the component score, it can help determine which variables are most influenced by each factor and are most important for each underlying concept.

Factor loading

Factor loading is the correlation coefficient for the variable and factor. Like the factor score, factor loadings give an indication of how much of the variance in an observed variable can be explained by the factor. High factor loadings (close to 1 or -1) mean the factor strongly influences the variable.

When to use factor analysis

Factor analysis is a powerful tool when you want to simplify complex data, find hidden patterns, and set the stage for deeper, more focused analysis.

It’s typically used when you’re dealing with a large number of interconnected variables, and you want to understand the underlying structure or patterns within this data. It’s particularly useful when you suspect that these observed variables could be influenced by some hidden factors.

For example, consider a business that has collected extensive  customer feedback through surveys . The survey covers a wide range of questions about product quality, pricing, customer service and more. This huge volume of data can be overwhelming, and this is where factor analysis comes in. It can help condense these numerous variables into a few meaningful factors, such as ‘product satisfaction’, ‘customer service experience’ and ‘value for money’.

Factor analysis doesn’t operate in isolation – it’s often used as a stepping stone for further analysis. For example, once you’ve identified key factors through factor analysis, you might then proceed to a  cluster analysis  – a method that groups your customers based on their responses to these factors. The result is a clearer understanding of different customer segments, which can then guide targeted marketing and product development strategies.

By combining factor analysis with other methodologies, you can not only make sense of your data but also gain valuable insights to drive your business decisions.

Factor analysis assumptions

Factor analysis relies on several assumptions for accurate results. Violating these assumptions may lead to factors that are hard to interpret or misleading.

Linear relationships between variables

This ensures that changes in the values of your variables are consistent.

Sufficient variables for each factor

Because if only a few variables represent a factor, it might not be identified accurately.

Adequate sample size

The larger the ratio of cases (respondents, for instance) to variables, the more reliable the analysis.

No perfect multicollinearity and singularity

No variable is a perfect linear combination of other variables, and no variable is a duplicate of another.

Relevance of the variables

There should be some correlation between variables to make a factor analysis feasible.

Types of factor analysis

There are two main factor analysis methods: exploratory and confirmatory. Here’s how they are used to add value to your research process.

Confirmatory factor analysis

In this type of analysis, the researcher starts out with a hypothesis about their data that they are looking to prove or disprove. Factor analysis will confirm – or not – where the latent variables are and how much variance they account for.

Principal component analysis (PCA) is a popular form of confirmatory factor analysis. Using this method, the researcher will run the analysis to obtain multiple possible solutions that split their data among a number of factors. Items that load onto a single particular factor are more strongly related to one another and can be grouped together by the researcher using their conceptual knowledge or pre-existing research.

Using PCA will generate a range of solutions with different numbers of factors, from simplified 1-factor solutions to higher levels of complexity. However, the fewer number of factors employed, the less variance will be accounted for in the solution.

Exploratory factor analysis

As the name suggests, exploratory factor analysis is undertaken without a hypothesis in mind. It’s an investigatory process that helps researchers understand whether associations exist between the initial variables, and if so, where they lie and how they are grouped.

How to perform factor analysis: A step-by-step guide

Performing a factor analysis involves a series of steps, often facilitated by statistical software packages like SPSS, Stata and the  R programming language . Here’s a simplified overview of the process.

Prepare your data

Start with a dataset where each row represents a case (for example, a survey respondent), and each column is a variable you’re interested in. Ensure your data meets the assumptions necessary for factor analysis.

Create an initial hypothesis

If you have a theory about the underlying factors and their relationships with your variables, make a note of this. This hypothesis can guide your analysis, but keep in mind that the beauty of factor analysis is its ability to uncover unexpected relationships.

Choose the type of factor analysis

The most common type is exploratory factor analysis, which is used when you’re not sure what to expect. If you have a specific hypothesis about the factors, you might use confirmatory factor analysis.

Form your correlation matrix

After you’ve chosen the type of factor analysis, you’ll need to create the correlation matrix of your variables. This matrix, which shows the correlation coefficients between each pair of variables, forms the basis for the extraction of factors. This is a key step in building your factor analysis model.

Decide on the extraction method

Principal component analysis is the most commonly used extraction method. If you believe your factors are correlated, you might opt for principal axis factoring, a type of factor analysis that identifies factors based on shared variance.

Determine the number of factors

Various criteria can be used here, such as Kaiser’s criterion (eigenvalues greater than 1), the scree plot method or parallel analysis. The choice depends on your data and your goals.

Interpret and validate your results

Each factor will be associated with a set of your original variables, so label each factor based on how you interpret these associations. These labels should represent the underlying concept that ties the associated variables together.

Validation can be done through a variety of methods, like splitting your data in half and checking if both halves produce the same factors.

How factor analysis can help you

As well as giving you fewer variables to navigate, factor analysis can help you understand grouping and clustering in your input variables, since they’ll be grouped according to the latent variables.

Say you ask several questions all designed to explore different, but closely related, aspects of customer satisfaction:

• How satisfied are you with our product?
• Would you recommend our product to a friend or family member?
• How likely are you to purchase our product in the future?

But you only want one variable to represent a customer satisfaction score. One option would be to average the three question responses. Another option would be to create a factor dependent variable. This can be done by running a principal component analysis (PCA) and keeping the first principal component (also known as a factor). The advantage of a PCA over an average is that it automatically weights each of the variables in the calculation.

Say you have a list of questions and you don’t know exactly which responses will move together and which will move differently; for example, purchase barriers of potential customers. The following are possible barriers to purchase:

• Price is prohibitive
• Overall implementation costs
• We can’t reach a consensus in our organisation
• Product is not consistent with our business strategy
• I need to develop an ROI, but cannot or have not
• We are locked into a contract with another product
• The product benefits don’t outweigh the cost
• We have no reason to switch
• Our IT department cannot support your product
• We do not have sufficient technical resources
• Your product does not have a feature we require
• Other (please specify)

Factor analysis can uncover the trends of how these questions will move together. The following are loadings for 3 factors for each of the variables.

Notice how each of the principal components have high weights for a subset of the variables. Weight is used interchangeably with loading, and high weight indicates the variables that are most influential for each principal component. +0.30 is generally considered to be a heavy weight.

The first component displays heavy weights for variables related to cost, the second weights variables related to IT, and the third weights variables related to organisational factors. We can give our new super variables clever names.

If we were to cluster the customers based on these three components, we can see some trends. Customers tend to be high in cost barriers or organisational barriers, but not both.

The red dots represent respondents who indicated they had higher organisational barriers; the green dots represent respondents who indicated they had higher cost barriers

Considerations when using factor analysis

Factor analysis is a tool, and like any tool its effectiveness depends on how you use it. When employing factor analysis, it’s essential to keep a few key considerations in mind.

Oversimplification

While factor analysis is great for simplifying complex data sets, there’s a risk of oversimplification when grouping variables into factors. To avoid this you should ensure the reduced factors still accurately represent the complexities of your variables.

Subjectivity

Interpreting the factors can sometimes be subjective, and requires a good understanding of the variables and the context. Be mindful that multiple analysts may come up with different names for the same factor.

Supplementary techniques

Factor analysis is often just the first step. Consider how it fits into your broader research strategy and which other techniques you’ll use alongside it.

Examples of factor analysis studies

Factor analysis, including PCA, is often used in tandem with  segmentation studies . It might be an intermediary step to reduce variables before using KMeans to make the segments.

Factor analysis provides simplicity after reducing variables. For long studies with large blocks of  Matrix Likert scale  questions, the number of variables can become unwieldy. Simplifying the data using factor analysis helps analysts focus and clarify the results, while also reducing the number of dimensions they’re clustering on.

Sample questions for factor analysis

Choosing exactly which questions to perform factor analysis on is both an art and a science. Choosing which variables to reduce takes some experimentation, patience and creativity. Factor analysis works well on Likert scale questions and Sum to 100 question types.

Factor analysis works well on matrix blocks of the following question genres:

Psychographics (Agree/Disagree):

• I value family
• I believe brand represents value

Behavioural (Agree/Disagree):

• I purchase the cheapest option
• I am a bargain shopper

Attitudinal (Agree/Disagree):

• The economy is not improving
• I am pleased with the product

Activity-Based (Agree/Disagree):

• I love sports
• I sometimes shop online during work hours

Behavioural and psychographic questions are especially suited for factor analysis.

Sample output reports

Factor analysis simply produces weights (called loadings) for each respondent. These loadings can be used like other responses in the survey.

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Factor Analysis in Marketing Research

• Home > What We Do > Research Methods > Statistical Techniques > Factor Analysis in Marketing Research

Factor analysis in marketing research aims to describe a large number of variables or questions by using a reduced set of underlying variables, called factors.

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To find out more about factor analysis and how it can help your business

What is factor analysis in marketing research?

Factor analysis explains a pattern of similarity between observed variables. Questions which belong to one factor are highly correlated with each other; unlike cluster analysis, which classifies respondents, factor analysis groups variables.

There are two types of factor analysis in marketing research: exploratory and confirmatory. Exploratory factor analysis is driven by the data, i.e. the data determines the factors. Confirmatory factor analysis, used in structural equation modelling, tests and confirms hypotheses.

Factor analysis in market research is often used in customer satisfaction studies to identify underlying service dimensions, and in profiling studies to determine core attitudes. For example, as part of a national survey on political opinions, respondents may answer three separate questions regarding environmental policy, reflecting issues at the local, regional and national level. Factor analysis can be used to establish whether the three measures do, in fact, measure the same thing.

It can also prove to be useful when a lengthy questionnaire needs to be shortened, but still retain key questions. Factor analysis indicates which questions can be omitted without losing too much information.

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Factor Analysis: Types & Applications

• Soumyaa Rawat
• Sep 14, 2021

What is Factor Analysis ?

Data is everywhere. From data research to artificial intelligence technology, data has become an essential commodity that is being perceived as a link between our past and future. Is an organization willing to collect its past records? 

Data is the key solution to this problem. Is any programmer willing to formulate a Machine Learning algorithm ? Data is what s/he needs to begin with. 

While the world has moved on to technology, it still is unaware of the fact that data is the building block of all these technological advancements that have together made the world so advanced. 

When it comes to data, a number of tools and techniques are put to work to arrange, organize, and accumulate data the way one wants to. Factor Analysis is one of them. A data reduction technique, Factor Analysis is a statistical method used to reduce the number of observed factors for a much better insight into a given dataset. 

But first, we shall understand what is a factor. A factor is a set of observed variables that have similar responses to an action. Since variables in a given dataset can be too much to deal with, Factor Analysis condenses these factors or variables into fewer variables that are actionable and substantial to work upon. 

A technique of dimensionality reduction in data mining, Factor Analysis works on narrowing the availability of variables in a given data set, allowing deeper insights and better visibility of patterns for data research. 

Most commonly used to identify the relationship between various variables in statistics , Factor Analysis can be thought of as a compressor that compresses the size of variables and produces a much enhanced, insightful, and accurate variable set. 

“FA is considered an extension of principal component analysis since the ultimate objective for both techniques is a data reduction.” Factor Analysis in Data Reduction  

Types of Factor Analysis

Developed in 1904 by Spearman, Factor Analysis is broadly divided into various types based upon the approach to detect underlying variables and establish a relationship between them. 

While there are a variety of techniques to conduct factor analysis like Principal Component Analysis or Independent Component Analysis , Factor Analysis can be divided into 2 types which we will discuss below. Let us get started. 

Confirmatory Factor Analysis

As the name of this concept suggests, Confirmatory Factor Analysis (CFA) lets one determine whether a relationship between factors or a set of overserved variables and their underlying components exists. 

It helps one confirm whether there is a connection between two components of variables in a given dataset. Usually, the purpose of CFA is to test whether certain data fit the requirements of a particular hypothesis. 

The process begins with a researcher formulating a hypothesis that is made to fit along the lines of a certain theory. If the constraints imposed on a model do not fit well with the data, then the model is rejected, and it is confirmed that no relationship exists between a factor and its underlying construct. Perhaps hypothetical testing also finds a space in the world of Factor Analysis.  

Exploratory Factor Analysis

In the case of Exploratory Factor Statistical Analysis , the purpose is to determine/explore the underlying latent structure of a large set of variables. EFA, unlike CFA, tends to uncover the relationship, if any, between measured variables of an entity (for example - height, weight, etc. in a human figure). 

While CFA works on finding a relationship between a set of observed variables and their underlying structure, this works to uncover a relationship between various variables within a given dataset. 

Conducting Exploratory Factor Analysis involves figuring the total number of factors involved in a dataset. 

“EFA is generally considered to be more of a theory-generating procedure than a theory-testing procedure. In contrast, confirmatory factor analysis (CFA) is generally based on a strong theoretical and/or empirical foundation that allows the researcher to specify an exact factor model in advance.” EFA in Hypothesis Testing  

Applications of Factor Analysis

With immense use in various fields in real life, this segment presents a list of applications of Factor Analysis and the way FA is used in day-to-day operations. 

Applications of factor analysis

Marketing is defined as the act of promoting a good or a service or even a brand. When it comes to Factor Analysis in marketing, one can benefit immensely from this statistical method. 

In order to boost marketing campaigns and accelerate success, in the long run, companies employ Factor Analysis techniques that help to find a correlation between various variables or factors of a marketing campaign. 

Moreover, FA also helps to establish connections with customer satisfaction and consequent feedback after a marketing campaign in order to check its efficacy and impact on the audiences. 

That said, the realm of marketing can largely benefit from Factor Analysis and trigger sales with respect to much-enhanced feedback and customer satisfaction reports. 

(Must read: Marketing management guide )

Data Mining

In data mining, Factor Analysis can play a role as important as that of artificial intelligence. Owing to its ability to transform a complex and vast dataset into a group of filtered out variables that are related to each other in some way or the other, FA eases out the process of data mining. 

For data scientists, the tedious task of finding relationships and establishing correlation among various variables has always been full of obstacles and errors. 

However, with the help of this statistical method, data mining has become much more advanced. 

(Also read: Data mining tools )

Machine Learning

Machine Learning and data mining tools go hand in hand. Perhaps this is the reason why Factor Analysis finds a place among Machine Learning tools and techniques.

As Factor Analysis in machine learning helps in reducing the number of variables in a given dataset to procure a more accurate and enhanced set of observed factors, various machine learning algorithms are put to use to work accordingly. 

They are trained well with humongous data to rightly work in order to give way to other applications. An unsupervised machine learning algorithm, FA is largely used for dimensionality reduction in machine learning. 

Thereby, machine learning can very well collaborate with Factor Analysis to give rise to data mining techniques and make the task of data research massively efficient. 

(Recommended blog: Data mining software )

Nutritional Science

Nutritional Science is a prominent field of work in the contemporary scenario. By focusing on the dietary practices of a given population, Factor Analysis helps to establish a relationship between the consumption of nutrients in an adult’s diet and the nutritional health of that person. 

Furthermore, an individual’s nutrient intake and consequent health status have helped nutritionists to compute the appropriate quantity of nutrients one should intake in a given period of time. 

The application of Factor Analysis in business is rather surprising and satisfactory.

Remember the times when business firms had to employ professionals to dig out patterns from past records in order to lay a road ahead for strategic business plans?

Well, gone are the days when so much work had to be done. Thanks to Factor Analysis, the world of business can use it for eliminating the guesswork and formulating more accurate and straightforward decisions in various aspects like budgeting, marketing, production, and transport. 

Pros and Cons of Factor Analysis  

Having learned about Factor Analysis in detail, let us now move on to looking closely into the pros and cons of this statistical method. 

Pros of Factor Analysis

Measurable attributes.

The first and foremost pro of FA is that it is open to all measurable attributes. Be it subjective or objective, any kind of attribute can be worked upon when it comes to this statistical technique. 

Unlike some statistical models that only work on objective attributes, Factor Analysis goes well with both subjective and objective attributes. 

Cost-Effective

While data research and data mining algorithms can cost a lot due to the extraordinary charges, this statistical model is surprisingly cost-effective and does not take many resources to work with. 

That said, it can be incorporated by any beginner or an experienced professional in light of its cost-effective and easy approach towards data mining and data reduction. 

Flexible Approach

While many machine learning algorithms are rigid and constricted to a single approach, Factor Analysis does not work that way. 

Rather, this statistical model has a flexible approach towards multivariate datasets that let one obtain relationships or correlations between various variables and their underlying components. 

(Must read: AI algorithms )

Cons of Factor Analysis

Incomprehensive results.

While there are many pros of Factor Analysis, there are various cons of this method as well. Primarily, Factor Analysis can procure incompetent results due to incomprehensive datasets. 

While various data points can have similar traits, some other variables or factors can go unnoticed due to being isolated in a vast dataset. That said, the results of this method could be incomprehensive. 

Non-Identification of Complicated Factors

Another drawback of Factor Analysis is that it does not identify complicated factors that underlie a dataset. 

While some results could clearly indicate a correlation between two variables, some complicated correlations can go unnoticed in such a method. 

Perhaps the non-identification of complicated factors and their relationships could be an issue for data research. 

Reliant on Theory

Even though Factor Analysis skills can be imitated by machine learning algorithms, this method is still reliant on theory and thereby data researchers. 

While many components of a dataset can be handled by a computer, some other details are required to be looked into by humans. 

Thus, one of the major drawbacks of Factor Analysis is that it is somehow reliant on theory and cannot fully function without manual assistance. 

(Suggested reading: Deep learning algorithms )

Summing Up  

To sum up, Factor Analysis is an extensive statistical model that is used to reduce dimensions of a given dataset with the help of condensing observed variables in a smaller size. 

(Top reading: Statistical data distribution models )

By arranging observed variables in groups of super-variables, Factor Analysis has immensely impacted the way data mining is done. With numerous fields relying on this technique for better performance, FA is the need of the hour. 

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Factor Analysis 101: The Basics

• Market Research , Survey Tips

What is Factor Analysis?

Factor analysis is a powerful data reduction technique that enables researchers to investigate concepts that cannot easily be measured directly. By boiling down a large number of variables into a handful of comprehensible underlying factors, factor analysis results in easy-to-understand, actionable data. 

By applying this method to your research, you can spot trends faster and see themes throughout your datasets, enabling you to learn what the data points have in common. 

Unlike statistical methods such as regression analysis , factor analysis does not require defined variables. 

Factor analysis is most commonly used to identify the relationship between all of the variables included in a given dataset.

The Objectives of Factor Analysis

 Think of factor analysis as shrink wrap. When applied to a large amount of data, it compresses the set into a smaller set that is far more manageable, and easier to understand. 

The overall objective of factor analysis can be broken down into four smaller objectives: 

• To definitively understand how many factors are needed to explain common themes amongst a given set of variables.
• To determine the extent to which each variable in the dataset is associated with a common theme or factor.
• To provide an interpretation of the common factors in the dataset.
• To determine the degree to which each observed data point represents each theme or factor.

When to Use Factor Analysis

Determining when to use particular statistical methods to get the most insight out of your data can be tricky.

When considering factor analysis, have your goal top-of-mind.

There are three main forms of factor analysis. If your goal aligns to any of these forms, then you should choose factor analysis as your statistical method of choice: 

Exploratory Factor Analysi s should be used when you need to develop a hypothesis about a relationship between variables. 

Confirmatory Factor Analysis should be used to test a hypothesis about the relationship between variables.

Construct Validity should be used to test the degree to which your survey actually measures what it is intended to measure.

How To Ensure Your Survey is Optimized for Factor Analysis

If you know that you’ll want to perform a factor analysis on response data from a survey, there are a few things you can do ahead of time to ensure that your analysis will be straightforward, informative, and actionable.

Identify and Target Enough Respondents

Large datasets are the lifeblood of factor analysis. You’ll need large groups of survey respondents, often found through panel services , for factor analysis to yield significant results. 

While variables such as population size and your topic of interest will influence how many respondents you need, it’s best to maintain a “more respondents the better” mindset. 

The More Questions, The Better

While designing your survey , load in as many specific questions as possible. Factor analysis will fall flat if your survey only has a few broad questions.  

The ultimate goal of factor analysis is to take a broad concept and simplify it by considering more granular, contextual information, so this approach will provide you the results you’re looking for. 

Aim for Quantitative Data

If you’re looking to perform a factor analysis, you’ll want to avoid having open-ended survey questions . 

By providing answer options in the form of scales (whether they be Likert Scales , numerical scales, or even ‘yes/no’ scales) you’ll save yourself a world of trouble when you begin conducting your factor analysis. Just make sure that you’re using the same scaled answer options as often as possible.

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Factor analysis: decipher complex data and make better decisions

Appinio Research · 05.12.2023 · 16min read

In today's fast-paced marketing world, making decisions based on data gives companies a real edge. But let's face it, collecting data is one thing, figuring out what it all means is another ball game. That's where factor analysis swoops in like a superhero for your complex data sets.

Imagine it like this: it's like a magic trick to make big, messy data sets simpler and spot the cool patterns. In this guide, we're going to chat about where factor analysis comes from, how it does its thing, the good stuff it brings to the table, and even its not-so-great sides. Plus, we'll spill the beans on the difference between exploratory and confirmatory factor analysis and a bunch more exciting tips.

What is factor analysis?

Factor analysis, a statistical method tailored for unraveling complex data sets, serves as a crucial analytical tool in modern decision-making processes. 

At its core, factor analysis strives to streamline extensive datasets by distilling them into a few essential factors. The ultimate goal is to enhance clarity and manageability in handling substantial amounts of data.

Additionally, factor analysis plays a pivotal role in unearthing concealed patterns and structures within datasets, shedding light on intricate phenomena and relationships. 

To appreciate the significance of this methodology, let's delve into a concise historical overview

A Historical Perspective

Originating in the late 19th century within the realm of psychology, factor analysis found its early roots during the endeavors of Francis Galton and Charles Spearman. Their pursuit revolved around developing tests to gauge intelligence. 

Spearman, in 1904, introduced the first mathematical approach to factor analysis, laying the groundwork for its subsequent applications across diverse disciplines such as statistics, social sciences, economics, and market research.

Advancements in technology, coupled with the advent of sophisticated data analysis software, have propelled factor analysis into a more accessible and precise realm. 

Far from a relic of the past, this methodology stands as a contemporary powerhouse for pattern recognition and information extraction from intricate data sets.

What is factor analysis used for?

Whether deployed in a confirmatory or exploratory manner, factor analysis proves instrumental in simplifying market segmentation, devising targeted marketing strategies, and optimizing products and services. 

Its ability to facilitate data-driven decision-making processes positions factor analysis as a catalyst for organizations seeking a competitive advantage.

By distilling complex data sets, factor analysis provides valuable insights into consumer behavior and preferences. 

Market researchers leverage this methodology to identify patterns and structures in surveys and customer evaluations, offering a deeper understanding of purchasing behavior.

Ultimately, the reduction of factors and variables to their core elements enhances comprehension of the needs and preferences of target groups .

When is a factor analysis useful?

Factor analysis proves its worth in various scenarios, offering a multifaceted approach to data exploration. Let's break down its utility:

• Streamlining variables In instances where datasets boast an extensive array of variables, factor analysis steps in to categorize and simplify the data. By doing so, it transforms a potentially overwhelming set into a clearer and more interpretable format.
• Unveiling patterns Factor analysis, particularly in its explorative form, plays the role of a detective, unveiling concealed patterns and structures within the data. This process brings hidden connections to light, providing a richer understanding of the underlying dynamics.

Variable classification Ever wondered which factors carry the most weight in a dataset? Factor analysis shines a light on the variance within datasets, elucidating the influence each factor wields. This classification proves invaluable in discerning the pivotal elements within complex data structures.

• Testing theories and hypotheses For situations where concrete assumptions or hypotheses already exist regarding data content and structure, confirmatory factor analysis steps in. It systematically checks these assumptions, serving as a validation tool that either affirms or challenges existing theories.
• Segmentation mastery Factor analysis serves as a keen observer in the realm of customer profiles. By scrutinizing similarities and differences among these profiles, it becomes a linchpin in the definition of distinct customer segments. This segmentation approach provides nuanced insights into diverse consumer behaviors.

In essence, factor analysis transcends the mere simplification of data; it acts as a versatile analytical ally, unveiling the intricacies of datasets and offering a structured lens through which to understand, validate, and strategically utilize information.

Where does factor analysis reach its limits?

While factor analysis stands as a formidable tool, it's imperative to acknowledge its limits and exercise discretion based on specific objectives and data quality. This method, powerful as it may be, isn't a one-size-fits-all solution. Let's explore the situations where factor analysis might take a backseat:

• Not a panacea Factor analysis excels at reducing variables and exploring relationships within a dataset. However, when the goal is to pinpoint and form groups of similar data for a more specific segmentation, cluster analysis takes the lead. It's tailored for the task of identifying distinct groups and segments within a dataset, surpassing factor analysis in this particular arena.
• The power of regression When the emphasis shifts to understanding the relationship between variables, regression analysis often emerges as the more fitting choice. Unlike factor analysis, which hones in on complex patterns and hidden structures, regression analysis specifically delves into the influence of one or more independent variables on a dependent variable.
• Navigating customer preferences Factor analysis encounters its limitations when the focus zeroes in on discerning customer preferences or specific values tied to various product characteristics and features. In such cases, where a detailed understanding of customer preferences is key, conjoint analysis is a more tailored alternative.

In essence, while factor analysis stands as a robust methodology, its effectiveness is context-dependent. 

Recognizing the unique strengths of other analytical tools, such as cluster analysis and regression analysis, ensures a comprehensive approach to data exploration and interpretation. The selection of the most suitable method hinges on a nuanced understanding of the specific objectives and the intricacies of the dataset at hand.

Where is factor analysis used?

Despite its roots in psychology, factor analysis has evolved into a versatile tool, finding applications across a spectrum of disciplines.

• Market research insights In the realm of market research , factor analysis takes center stage. Its primary role involves segmenting target and buyer groups, offering a nuanced understanding of product preferences. By deciphering these preferences, businesses can craft targeted marketing strategies that resonate with specific consumer segments.
• Economic and financial analysis Factor analysis extends its reach into the economic and financial sectors. Here, it delves into variables such as interest rates, inflation, and share prices. The objective is clear: to analyze and determine the risk-return profiles of investment portfolios. By identifying and understanding these key factors, financial analysts can make informed decisions, optimizing investment strategies.
• Healthcare insights The medical and healthcare domains leverage factor analysis for a different purpose. Here, it plays a crucial role in identifying associated symptoms or risk factors for diseases, particularly in fields like cardiovascular health. By discerning these factors, medical professionals can enhance diagnostic accuracy and refine treatment approaches.
• Tech-driven advancements Beyond traditional sectors, factor analysis steps into the realms of image and speech processing. In image processing, it excels at extracting features from large datasets, contributing to advancements in facial recognition technology. Similarly, in speech processing, factor analysis aids in enhancing the extraction of key features, refining the capabilities of speech recognition systems.

Exploratory vs. confirmatory factor analysis

Factor analysis adapts to the specific needs of research objectives and data scenarios, presenting two distinct methodologies: exploratory and confirmatory factor analysis.

• Exploratory Factor Analysis (EFA) Positioned at the inception of research endeavors, exploratory factor analysis shines when the terrain is uncharted or information is incomplete. It becomes the investigator's tool, delving into large datasets to unearth latent patterns that were previously unknown. In this phase, exploratory factor analysis not only simplifies data but also acts as a catalyst for generating new hypotheses, providing a solid foundation for subsequent stages of research.
• Confirmatory Factor Analysis (CFA) As research progresses into more advanced stages, confirmatory factor analysis takes the spotlight. This method is tailor-made for situations where existing hypotheses need validation. To employ confirmatory factor analysis effectively, a well-defined model is crucial, built upon established theoretical frameworks or previous studies. It operates as a precision tool, rigorously testing specific relationships between variables, aligning research outcomes with pre-existing theories.

In essence, the choice between exploratory and confirmatory factor analysis hinges on the stage of research and the clarity of existing hypotheses . 

Exploratory factor analysis pioneers the exploration of unknown territories, unraveling patterns and generating new insights. 

On the flip side, confirmatory factor analysis stands as the sentinel of validation, ensuring that research findings align with established theoretical constructs. 

Together, these dual approaches empower researchers to navigate the intricate landscape of data analysis with precision and purpose.

What are the advantages and disadvantages of factor analysis?

Factor analysis, like any analytical tool, comes with a set of advantages and drawbacks, shaping its utility in various contexts.

• Data simplification and focus Factor analysis excels in simplifying intricate datasets, distilling them to their essential components. By highlighting the most crucial points, it transforms data complexity into a more manageable and insightful form.
• Unearthing hidden patterns The method serves as a detective, uncovering latent patterns that might otherwise slip through the cracks. This capability brings valuable insights, contributing to a more comprehensive understanding of the data.
• Clarity amidst complexity In the midst of the data jungle, factor analysis brings clarity. It acts as a guide, simplifying interpretation and making the data more accessible, aiding in effective decision-making.
• Testing ideas and theories Factor analysis provides a robust platform for hypothesis testing. By comparing data and checking for plausibility, it becomes a reliable tool for scrutinizing ideas and theories against empirical evidence.

Disadvantages

• Dependency on data quality The reliability of factor analysis is contingent upon the quality and comprehensiveness of the input data. In cases where data is lacking in these aspects, the results may be compromised.
• Assumption sensitivity The outcomes of factor analysis are sensitive to the clarity of data summaries and the assumptions underlying them. Ambiguities in these aspects can introduce uncertainties into the results.
• Incompatibility with poor data Factor analysis is not the go-to approach when dealing with incomplete or poor-quality data. Its effectiveness is contingent upon a robust dataset, and deviations from this standard may undermine its validity.
• Human judgment in factor selection The method relies on human judgment for factor selection, introducing an element of subjectivity. This reliance on interpretation can lead to errors, impacting the accuracy of the analysis.
• Risk of over-extraction Factor analysis, in its quest for patterns, runs the risk of extracting excessive detail from the data. This unintended consequence may increase complexity, potentially hindering rather than aiding understanding.

7 steps to optimal factor analysis

Wie funktioniert eine Faktorenanalyse in der Marktforschung? Dazu braucht es lediglich sieben Schritte – ohne dabei zu sehr ins Detail zu gehen:

The integration of factor analysis into market research involves a systematic process, encompassing seven key steps that pave the way for valuable insights:

Data preparation Begin by collecting comprehensive datasets, ensuring that the data is normalized for effective comparison. The choice between exploratory and confirmatory factor analysis is a critical decision at this stage and sets the tone for the subsequent analytical journey.

Determining factors The next step involves determining the number of factors to be extracted. This decision is driven by research objectives or can be guided by statistical methods, aligning the analysis with the specific goals of the study.

Implementation Employing statistical software, such as SPSS, becomes essential in this phase. These tools perform intricate mathematical calculations to extract factors, unveiling the underlying patterns within the datasets.

Factor rotation Factor rotation, while not altering the data's content, enhances interpretability. This step simplifies the factors' interpretation, making the results more accessible without modifying the intrinsic meaning of the data.

Interpretation of factors and factor loadings With factors in hand, attention turns to interpreting factor loadings. This analysis unveils the relationships between factors and original variables, paving the way to name and interpret these factors. It's the bridge to understanding the intricate interplay within the data.

Interpretation of results Delving into the interpreted factors provides insights into the underlying structures and correlations of data and variables. This critical phase aids in forming a cohesive narrative around the relationships discovered during factor analysis.

Use of results The derived factors, beyond merely simplifying datasets, become powerful tools. They serve as a foundation for developing hypotheses or, in the context of market research, segmenting target groups. The insights gained from factor analysis become integral to shaping strategic decisions and refining marketing approaches.

Example of a factor analysis: Reasons for buying a car 

Let's shift from theory to the real-world application of factor analysis, exemplified in the automotive industry where understanding the factors influencing car buyers becomes paramount.

In this scenario, a company embarks on a data collection journey, gathering insights from hundreds of customers regarding various vehicle features. These features encompass a spectrum, ranging from engine performance and fuel efficiency to price, design, and safety features.

• Data collection The first step involves collecting a diverse dataset that encapsulates the multifaceted aspects of a car. Engine performance, fuel efficiency, price, design, and safety features are meticulously cataloged, forming the foundation for factor analysis.
• Factor identification Employing factor analysis, the company identifies the underlying factors exerting the most significant influence on the purchase decision. Through this analytical lens, factors like "environment" and "safety" emerge as the driving forces shaping customers' choices.
• Strategic decision-making Armed with these insights, the company gains a nuanced understanding of customer preferences. This clarity enables the development of targeted marketing strategies, tailoring messages to highlight the environmentally conscious and safety-oriented aspects of their vehicles.
• Product development Beyond marketing, the findings guide decisions in product development. Understanding that environmental concerns and safety features top the priority list, the company can focus on integrating and enhancing these elements in their vehicles, aligning their offerings with the genuine needs and desires of their customer base.

Conclusion: Understanding customers and target groups better with factor analysis

In the contemporary landscape of data-driven decision-making, factor analysis stands out as an invaluable asset for companies and market researchers alike. 

Its ability in distilling clarity from complex data sets, unearthing concealed patterns, and facilitating informed decision-making positions it as an indispensable tool. By simplifying data and enhancing its structural organization, factor analysis empowers companies to decipher customer preferences, fine-tune marketing strategies, and align products with market needs. 

The insights garnered extend beyond mere statistical analysis , delving into the intricate realm of consumer behaviors and preferences.

Factor analysis emerges not just as a methodology but as a powerful ally in navigating the competitive terrain, enabling businesses to not only survive but thrive by better serving the evolving needs of their customers.

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Factor analysis is a powerful statistical technique used by data professionals in various business domains to uncover underlying data structures or latent variables. Factor analysis is sometimes confused with Fact Analysis of Information Risk, or FAIR, but they are not the same—factor analysis encompasses statistical methods for data reduction and identifying underlying patterns in various fields, while FAIR is a specific framework and methodology used for analyzing and quantifying information security and cybersecurity risks.

This article examines factor analysis and its role in business, explores its definitions, various types, and provides real-world examples to illustrate its applications and benefits. With a clear understanding of what factor analysis is and how it works, you’ll be well-equipped to leverage this essential data analysis tool in making connections in your data for strategic decision-making.

Table of Contents

The Importance of Factor Analysis

In data science , factor analysis enables the identification of extra-dimensionality and hidden patterns in data and can be used to simplify data to select relevant variables for analysis.

Finding Hidden Patterns and Identifying Extra-Dimensionality 

A primary purpose of factor analysis is dataset dimensionality reduction. This is accomplished by identifying latent variables, known as factors, that explain the common variance in a set of observed variables.

In essence, it helps data professionals sift through a large amount of data and extract the key dimensions that underlie the complexity. Factor analysis also allows data professionals to uncover hidden patterns or relationships within data, revealing the underlying structure that might not be apparent when looking at individual variables in isolation.

Simplifying Data and Selecting Variables

Factor analysis simplifies data interpretation. Instead of dealing with a multitude of variables, researchers can work with a smaller set of factors that capture the essential information. This simplification aids in creating more concise models and facilitates clearer communication of research findings.

Data professionals working with large datasets must routinely select a subset of variables most relevant or representative of the phenomenon under analysis or investigation. Factor analysis helps in this process by identifying the key variables that contribute to the factors, which can be used for further analysis.

How Does Factor Analysis Work? 

Factor analysis is based on the idea that the observed variables in a dataset can be represented as linear combinations of a smaller number of unobserved, underlying factors. These factors are not directly measurable but are inferred from the patterns of correlations or covariances among the observed variables. Factor analysis typically consists of several fundamental steps.

1. Data Collection

The first step in factor analysis involves collecting data on a set of variables. These variables should be related in some way, and it’s assumed that they are influenced by a smaller number of underlying factors.

2. Covariance/Correlation Matrix

The next step is to compute the correlation matrix (if working with standardized variables) or covariance matrix (if working with non-standardized variables). These matrices help quantify the relationships between all pairs of variables, providing a basis for subsequent factor analysis steps.

Covariance Matrix

A covariance matrix is a mathematical construct that plays a critical role in statistics and multivariate analysis, particularly in the fields of linear algebra and probability theory. It provides a concise representation of the relationships between pairs of variables within a dataset.

Specifically, a covariance matrix is a square matrix in which each entry represents the covariance between two corresponding variables. Covariance measures how two variables change together; a positive covariance indicates that they tend to increase or decrease together, while a negative covariance suggests they move in opposite directions.

A covariance matrix is symmetric, meaning that the covariance between variable X and variable Y is the same as the covariance between Y and X. Additionally, the diagonal entries of the matrix represent the variances of individual variables, as the covariance of a variable with itself is its variance.

Correlation Matrix

A correlation matrix is a statistical tool used to quantify and represent the relationships between pairs of variables in a dataset. Unlike the covariance matrix, which measures the co-variability of variables, a correlation matrix standardizes this measure to a range between -1 and 1, providing a dimensionless value that indicates the strength and direction of the linear relationship between variables.

A correlation of 1 indicates a perfect positive linear relationship, while -1 signifies a perfect negative linear relationship. A correlation of 0 suggests no linear relationship. The diagonal of the correlation matrix always contains ones because each variable is perfectly correlated with itself.

Correlation matrices are particularly valuable for identifying and understanding the degree of association between variables, helping to reveal patterns and dependencies that might not be immediately apparent in raw data.

3. Factor Extraction

Factor extraction involves identifying the underlying factors that explain the common variance in the dataset. Various methods are used for factor extraction, including principal component analysis (PCA) and maximum likelihood estimation (MLE). These methods seek to identify the linear combinations of variables that capture the most variance in the data.

PCA is a dimensionality reduction and data transformation technique used in statistics, machine learning , and data analysis . Its primary goal is to simplify complex, high-dimensional data while preserving as much relevant information as possible.

PCA accomplishes this by identifying and extracting a set of orthogonal axes, known as principal components, that capture the maximum variance in the data. These principal components are linear combinations of the original variables and are ordered in terms of the amount of variance they explain, with the first component explaining the most variance, the second component explaining the second most, and so on. By projecting the data onto these principal components, you can reduce the dimensionality of the data while minimizing information loss.

As a powerful way to condense and simplify data, PCA is an invaluable tool for improving data interpretation and modeling efficiency, and is widely used for various purposes, including data visualization, noise reduction, and feature selection. It is particularly valuable in exploratory data analysis, where it helps researchers uncover underlying patterns and structures in high-dimensional datasets. In addition to dimensionality reduction, PCA can also aid in removing multicollinearity among variables, which is beneficial in regression analysis.

MLE is a fundamental statistical method used to estimate the parameters of a statistical model. The core premise behind MLE is to find the parameter values that maximize the likelihood function, which measures how well the model explains the observed data. In other words, MLE seeks to identify the parameter values that make the observed data the most probable under the assumed statistical model.

To perform MLE, one typically starts with a probability distribution or statistical model that relates the parameters to the observed data. The likelihood function is then constructed based on this model, and it quantifies the probability of observing the given data for different parameter values. MLE involves finding the values of the parameters that maximize this likelihood function.

In practice, this is often achieved through numerical optimization techniques, such as gradient descent or the Newton-Raphson method . MLE is highly regarded for its desirable properties, such as asymptotic efficiency and consistency, making it a widely used and respected method for parameter estimation in statistical modeling and data analysis.

4. Factor Rotation

Once factors are extracted, they are often rotated to achieve a simpler, more interpretable factor structure. Rotation methods like Varimax and Promax aim to make the factors more orthogonal or uncorrelated, which enhances their interpretability.

5. Factor Loadings

Factor loadings represent the strength and direction of the relationship between each variable and the underlying factors. These loadings indicate how much each variable contributes to a given factor and are used to interpret and label the factors.

6. Interpretation

The final step of factor analysis involves interpreting the factors and assigning meaning to them. Data professionals examine the factor loadings and consider the variables that are most strongly associated with each factor. This interpretation is a critical aspect of factor analysis, as it helps in understanding the latent structure of the data.

Types of Factor Analysis

Factor analysis comes in several variations, depending on the assumptions and constraints applied to the analysis. The two primary types are exploratory factor analysis (EFA) and confirmatory factor analysis (CFA).

Exploratory Factor Analysis (EFA)

EFA is used to explore and uncover the underlying structure of data. It is an open-ended approach that does not impose any specific structure on the factors. Instead, it allows the factors to emerge from the data. EFA is often used in the early stages of research when there is little prior knowledge about the relationships between variables.

Confirmatory Factor Analysis (CFA)

CFA, on the other hand, is a more hypothesis-driven approach—it starts with a predefined factor structure. The data is then tested to see if it fits that structure. This type of analysis is used when there is a theoretical model or prior knowledge about the expected relationships between variables and factors.

Benefits of Factor Analysis

Factor analysis offers several advantages to data professionals working a wide range of business/enterprise settings:

• Data reduction and enhanced interpretability. By reducing the dimensionality of data, you can more easily analyze and interpret complex datasets. This results in enhanced data interpretation and explainability—by identifying latent factors, factor analysis provides a more meaningful interpretation of the relationships among variables, making it easier to understand complex phenomena.
• Multivariable selection and analysis. Factor analysis aids in variable selection by identifying the most important variables that contribute to the factors. This is especially valuable when working with large datasets. Crucially, factor analysis is a form of multivariate analysis, which is essential in use cases that require examining relationships between multiple variables simultaneously.

Factor Analysis Examples

Organizations can use factor analysis in a wide range of applications to identify underlying factors or latent variables that explain patterns in data.

Market Research

Market researchers often use factor analysis to identify the key factors that influence consumer preferences. For example, a survey may collect data on various product attributes like price, brand reputation, quality, and customer service. Factor analysis can help determine which factors have the most significant impact on consumers’ product choices. By identifying underlying factors, businesses can tailor their product development and marketing strategies to meet consumer needs more effectively.

Financial Risk Analysis

Factor analysis is commonly used in finance to analyze and manage financial risk. By examining various economic indicators, asset returns, and market conditions, factor analysis helps investors and portfolio managers understand how different factors contribute to the overall risk and return of an investment portfolio.

Customer Segmentation

Businesses often use factor analysis to identify customer segments based on their purchasing behavior, preferences, and demographic information. By analyzing these factors, companies can create better targeted marketing strategies and product offerings.

Employee Engagement

Factor analysis can be used to identify the underlying factors that contribute to employee engagement and job satisfaction. This information helps businesses improve workplace conditions and increase employee retention.

Brand Perception

Companies may employ factor analysis to understand how customers perceive their brand. By analyzing factors like brand image, trust, and quality, businesses can make informed decisions to strengthen their brand and reputation.

Product Quality Controls

In manufacturing, factor analysis can help identify the key factors affecting product quality. This analysis can lead to process improvements and quality control measures, ultimately reducing defects and enhancing customer satisfaction.

These examples are just a handful of use cases that demonstrate how factor analysis can be applied in business. As a versatile statistical tool, it can be adapted to various data-driven decision-making processes for helping organizations gain deeper insights and make informed choices.

Factor Analysis vs. FAIR

Factor analysis is different from Fact Analysis of Information Risk, or FAIR. Factor analysis encompasses statistical methods for data reduction and identifying underlying patterns in various fields, while FAIR is a specific framework and methodology used for analyzing and quantifying information security and cybersecurity risks. Unlike traditional factor analysis, which deals strictly with data patterns, FAIR focuses specifically on information and cyber risk factors to help organizations prioritize and manage their cybersecurity efforts effectively.

Bottom Line

With factor analysis in their cachet of tools, data professionals and business researchers have a powerful and battle-tested statistical technique for simplifying data, identifying latent structures, and understanding complex relationships among variables. Through these discoveries, organizations can better explain observed relationships among a set of variables by reducing complex data into a more manageable form, making it easier to understand, interpret, and draw meaningful conclusions.

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Factor Analysis: A Short Introduction, Part 1

by guest contributer   97 Comments

Why use factor analysis?

It allows researchers to investigate concepts they cannot measure directly. It does this by using a large number of variables to esimate a few interpretable underlying factors.

What is a factor?

The key concept of factor analysis is that multiple observed variables have similar patterns of responses because they are all associated with a latent variable (i.e. not directly measured). their association with an underlying latent variable, the factor, which cannot easily be measured.

For example, people may respond similarly to questions about income, education, and occupation, which are all associated with the latent variable socioeconomic status.

In every factor analysis, there are one fewer factors than there are variables.  Each factor captures a certain amount of the overall variance in the observed variables, and the factors are always listed in order of how much variation they explain.

The eigenvalue is a measure of how much of the common variance of the observed variables a factor explains.  Any factor with an eigenvalue ≥1 explains more variance than a single observed variable.

So if the factor for socioeconomic status had an eigenvalue of 2.3 it would explain as much variance as 2.3 of the three variables.  This factor, which captures most of the variance in those three variables, could then be used in other analyses.

The factors that explain the least amount of variance are generally discarded.  Deciding how many factors are useful to retain will be the subject of another post.

What are factor loadings?

The factor loadings express the relationship of each variable to the underlying factor. Here is an example of the output of a simple factor analysis looking at indicators of wealth, with just six variables and two resulting factors.

The variable with the strongest association to the underlying latent variable. Factor 1, is income, with a factor loading of 0.65.

Since factor loadings can be interpreted like standardized regression coefficients , one could also say that the variable income has a correlation of 0.65 with Factor 1. Most research fields consider this a strong association for a factor analysis.

Two other variables, education and occupation, are also associated with Factor 1. Based on the variables loading highly onto Factor 1, we could call it “Individual socioeconomic status.”

House value, number of public parks, and number of violent crimes per year, however, have high factor loadings on the other factor, Factor 2. They seem to indicate the overall wealth within the neighborhood, so we may want to call Factor 2 “Neighborhood socioeconomic status.”

Notice that the variable house value also is marginally important in Factor 1 (loading = 0.38). This makes sense, since the value of a person’s house should be associated with his or her income.

About the Author: Maike Rahn is a health scientist with a strong background in data analysis.   Maike has a Ph.D. in Nutrition from Cornell University.

Reader Interactions

August 29, 2021 at 12:11 am

this is what i was searching. the interpretation.

March 16, 2021 at 2:44 am

Thanks for posting the best information and the blog is very informative seku .

November 16, 2020 at 9:34 am

Nice explanation thanks for the good work

July 30, 2020 at 3:37 am

Explained nicely. Now the meaning of factor loading is clear. But, there is still a confusion. What is eigen value. If eigen value is greater than 1, so what does it mean???

May 29, 2020 at 1:51 am

Thank you so much for my first understanding on FA

May 27, 2020 at 2:36 pm

Very nice presentation. I have two questions: 1)on the SPSS output which of the analyses do you prefer-component, pattern or structure? and 2)how do you interpret negative sign loadings? Thanks so much. Tiffany

April 20, 2020 at 7:27 am

Hi, I am still confused about the factor analysis. If have 6 factors in my analysis table, is it necessary to reduce it to say only 2 factors only? Thanks

August 22, 2019 at 7:42 pm

Thank you sir for this explanation.my question here can I add principal component analysis and factor analysis to make an analysis?

June 23, 2019 at 12:16 pm

Dear, In my study,l have selected some municipalities with their different indicators viz. Demographic, education, amenities, health. Here,my quarries is -by which analysis I am going to confirm that the situation of this or that municipality are good or bad. Pls reply.

May 30, 2019 at 6:50 am

Helpful thank you for help

April 13, 2019 at 2:44 am

please help me

how many variables minimum we need to run factor analysis? I saw some researchers use at least 15. Is it the rule of thumb?

I have 3 varible and for evry vaible 150 observation can I use factor analysis?

April 1, 2019 at 11:11 am

Well Explained, I found it very helpful and useful as described in the easiest way to understand it. Thank u.

March 29, 2019 at 7:01 am

Very clear example and useful coverage to the FA concept

November 20, 2018 at 4:45 am

Dear Mr Rahn,

I would like to ask for your piece of advice on the following questions in relation to factor analysis: 1) How do you decide how many factors should be extracted? For instance, I have 44 variables in my survey and data is mainly categorical. 2) Do you conduct the factor analysis for all of variables at once or it is best to first prepare a bunch of variables and conduct the analysis. In my case, should I make like for instance 4 bunches of 11 variables and on a separate case run the factor analysis for each of the bunches. Does this mean that I should in advance make a descriptive statistic for each variable? 3) Once conducting a principle factor analysis for all variables, I see that the highest correlations have value 0,252 or 0,314 (in the correlation matrix). Does this mean that the model is insignificant?

Thank you in advance for your kind guidance.

Kind regards, Mariya Zheleva PhD student at Sofia University “St. Kliment Ohridski”, Bulgaria and at UVSQ in Paris, France

October 11, 2019 at 6:57 am

can someone respond to this question please.

I am facing the same problem

October 30, 2018 at 6:16 am

Easy to understand. thank you.

August 31, 2018 at 5:31 pm

Really nice summary! Precise and comprehensive! Much appreciated,

July 11, 2018 at 11:18 pm

easy to understand.thks

May 4, 2018 at 10:54 am

Clear, precise, simple to understand!

May 4, 2018 at 2:47 am

Hi, how are the factors obtained?

April 24, 2018 at 8:05 am

How you get factor 1 and Factor 2 ??

February 5, 2018 at 3:00 pm

You are happy evening I would like to ask you about your effective position on whether it is possible to use counting variables with factor analysis thanks Best wishes from IRAQ

February 14, 2018 at 11:23 am

It’s possible. The assumption is that all variables are normally distributed. Count variables are often skewed, but not always. So check your distributions.

January 19, 2018 at 6:17 am

Dear Maike,

thank you so much for your clear and useful explanation. I totally understand how to apply it well.

Best wishes from Germany

November 16, 2017 at 1:52 am

Thank you. It was easy to understand.

November 13, 2017 at 10:10 am

thanks a lot for the information

October 21, 2017 at 3:02 pm

The article states “In every factor analysis, there are the same number of factors as there are variables”. However the table used in the example shows 6 variables and 2 factors. Why are the two numbers not equal? Does “variable” have different meanings in the statement and the table?

Thanks in advance for any clarification.

January 29, 2018 at 12:18 pm

Mark, Because although there are as many factors as variables, they aren’t all useful. So part of the job of the data analyst is to decide how many factors are useful and therefore retained.

September 30, 2017 at 1:44 pm

This is a clear and straight forward explanation.

September 30, 2017 at 1:42 pm

This clear and straight forward explanation. Thank you

September 14, 2017 at 5:25 am

Thank you for the clear explanation!

September 4, 2017 at 7:50 am

Thanks for the simplicity and clear info 🙂

August 17, 2017 at 7:22 pm

Thanks. It was explained very well.

June 29, 2017 at 2:04 am

June 21, 2017 at 10:13 am

It is a well written article. If I understood correctly, we may use many questionnaire to assess some construct like Motivation. For this, I may include questions related to Work environment, Supervisor relationship, pay and other benefits, job satisfaction, training facilities etc., So there are five subcategories under which I have framed the questions. A factor analysis, if done properly should result at least in five factors. So, a factor analysis tries to stratify the questions included in the survey to homogeneous sub groups. Whether my understanding is correct?

May 30, 2017 at 9:59 am

commendable . best explanation so far

April 5, 2017 at 6:59 pm

so if i understood it well, the FA can be used to analyse a data on “barroriers” to effective communication. That is when i have about 20 factors of the barriers to analyse. Thank you

March 29, 2017 at 1:46 am

God Bless you. it was an interesting, simple and understandable. it was well written and to the point. helped me a lot

January 15, 2017 at 3:22 am

Thanks for your contribution of FA. It’s is helping but need a hypothesis to support it

October 16, 2016 at 3:58 am

Dr Maike Rahn, Thanks so much for the short explanation of what factor analysis is all about. I fully understand how to apply. I wish one day you read my piece of work. Kindest regards from Queenstown in Eastern Cape-South Africa

October 14, 2016 at 2:42 pm

Hey, could you please name 4 psychological tests based on factor analysis, such as 16 PF and NEO, any other tests that you have come across? Thanks.

September 29, 2016 at 6:27 pm

I have read several articles trying to explain factor analysis. This one is the easiest to understand because it is clear and concise.

July 26, 2016 at 3:07 am

Is it safe to say that factor analysis is the the analysis done in seeking the relationship of demographic and the variables (dependent, mediator, moderator) in the study? or Or is it the analysis done on every items under a construct? to see the loading among the items that represent the construct. Do help me as I still cant figure out what factor analysis is. Kindly assist. Many thanks.

October 14, 2016 at 11:47 am

Hi Mike, No, FA isn’t done to seek relationship between different variables in a relationship model.

Factor Analysis is a measurement model for an unmeasured variable (a construct). So it’s closer to your latter definition.

July 18, 2016 at 4:24 am

Thank you very much! The clearest explanation I ever read. Regards from Spain.

November 13, 2017 at 10:08 am

Thank you very much. I fully understand how to apply it.

July 17, 2016 at 12:34 pm

Thank you for easier explanation. It definitely will helpful for my next step of data analysis.

July 5, 2016 at 7:10 am

Excellent description, very helpful to build understanding of the topic.

June 29, 2016 at 5:10 am

Explained in the simplest way even a lay man can understand. Thanks a bunch.

June 26, 2016 at 1:57 pm

Simple and very clear explanation. It’s very clear for me now. Thank you.

June 18, 2016 at 6:20 pm

Very nice explained, as simple as lay mans language

June 6, 2016 at 3:08 am

I wish everything had such an easy to understand definition! Thank you

June 6, 2016 at 12:31 am

Very crisp, clear and concise explanation. Thanks a ton.

May 30, 2016 at 7:37 am

have been through many documents about factor analysis, yours is the most clear explanation. Thanks big time

May 19, 2016 at 4:02 pm

this is the best explanation that i have understand, keep on the standard Dr,,

May 19, 2016 at 9:56 am

I like it. kudos!

May 19, 2016 at 3:11 am

Very nice explanation of factor analysis. Keep up the nice work. A small request to you sir – please start small regular tutorials on statistics & data analysis.

April 14, 2016 at 5:42 pm

Just adding my thanks to the list so you keep the posts coming!

April 10, 2016 at 10:21 am

OMG ! As I have searched many of websites for factor analysis. This was the best and easiest explanation i found yet. Really helpful ! Great attempt ! Keep on doing social service !

March 11, 2016 at 6:44 pm

that is very nice explanation. you are so wonderful

March 9, 2016 at 6:56 am

Very lucid introduction on factors which would be useful to any novice to FA.

March 5, 2016 at 9:37 am

February 20, 2016 at 1:26 am

Simple but valuable explanation. Thanks.

December 30, 2015 at 2:08 pm

Thank you for your clear explanation of factor loading!

December 8, 2015 at 5:56 am

thanks for the introduction on factor analysis

November 27, 2015 at 11:28 pm

Excellent explanation of the basics, in my language there is a saying ( around 2000 years old) “Good teachings should have the quality of mothers milk,being good ,simple,digestable and sustaining) and I feel I have found it for Factor analysis. Keep up the good work!

September 30, 2015 at 7:40 am

Explained in one of the best ways possible!!! Helps you understand by just reading it once (quite the contrary for the definitions on the other websites)

September 29, 2015 at 4:57 am

Hi Maike, I have a survey with 15 q, 3 measure reading ability, 3 writing, 3 understanding, 3 measure monetary values and 3 measure literacy unrelated aspects. I am confused do I pick the read, write and understanding on the SPSS for factor analysis? how about the literacy unrelated q which are controls? Thanks for your help. Sat

September 19, 2015 at 6:27 am

Very simple and straight forward…Thanx

September 16, 2015 at 7:18 pm

Very clear explanation and useful examples. Thanks. I woudl liek to aks you somehting. I have a questionnaire of 52 items (I used it for Pilot Sutdy)and I have done FA obtaining 1O factors after reduction. I need to reduce the number of questions since 52 is too much and leave the most ‘powerful’ can I use the FA analysis to reduce the number of questions? Thank you

July 30, 2015 at 7:15 am

I would like to design a questionnaire using Likert scale that I can use for factor analysis. my challenge is should I mix positive statements and negative statements in my compilation of the questionnaire? e.g. Let us say I need to find out the view of a student if they have a negative attitude towards learning a subject. Should I say in my questionnaire, “I have a negative attitude towards Mathematics.” or I do not have a negative attitude towards Mathematics.”

June 2, 2015 at 8:36 pm

A very good work, thank you sir.

May 9, 2015 at 10:11 pm

It seems to me you have mixed up the difference between factor analysis and PCA (Principal Component Analysis). Where you talked about the amount of variance a factor captures and eigenvalue that measures that. it is principal components in PCA that tells you that because each principal component is orthogonal to the others and associated with an eigen-vector with a corresponding eigenvalue.

If not please let me know how eigenvalues of factors are calculated in factor anlysis

April 23, 2015 at 2:24 pm

Very simple and nice explainations

April 17, 2015 at 6:48 am

March 30, 2015 at 10:47 am

Thanks Doc This has been the most understandable explanation I have so far had. You mentioned something about your next post? about determination of number of factors. May you please also talk about factor analysis using R.

March 29, 2015 at 6:32 am

Good day to you. I have a question on factor analysis. I have a pool of 30 items for my construct, then I conducted the PCs, with nine items. After conducted the CFA, it only has three items. Does this acceptable ? Thank you.

March 26, 2015 at 10:31 am

Fantastic explanation!! Thank you

January 12, 2015 at 3:38 am

I have two kinds of questions: one with a 5-option response and another with a 7-option one. Can I run exploratory FA on both at the same time? When I run them with SPSS it lead to 8 factors that can explain 61% of the variance. But, mathematically, is it right?

December 31, 2014 at 11:28 am

Hi Rahn, Great Job.!!! How am I suppose to put citations to your web site?

December 11, 2014 at 10:16 pm

FACTOR ANALYSIS IS VERY USEFUL METHOD FOR ANALYSING SCIENTIFIC DATA PARTICULARLY FOR DATA RELATING TO BIOTECH AND FOOD TECNOLOGY AND ANIMAL BEHAVIOUR ALSO;Principal component analysis and exploratory factor analysis are both data reduction techniques — techniques to combine a group of correlated variables into fewer variables. You can then use those combination variables — indices or subscales — in other analyses.

September 8, 2015 at 1:33 am

Dear sir, I am a new research student please help me about ”Comparatively study on data reduction method between factor analysis and principal component analysis”. Kindly guide me about this I will waiting for your answer.

October 25, 2014 at 5:57 pm

I am grateful to have little idea on how to apply factor analysis. But stil sir! How would I enter data on exel spreat sheet and how will I start running the analysis? I am ph.D student and one of my objective of the study has to do with factor analysis. I have identify four factors with twenty three variable in question. Pls explain step by step for me. Thanks and best regard. Looking forward to hear from you sir.

October 24, 2014 at 3:15 pm

October 7, 2014 at 6:25 am

Thank you very much Dr. Rahn. I have struggled 13 months to understand Factor Analysis, and this has been the simple and very helpful. Thank you again.

September 24, 2014 at 12:00 pm

Dear Dr Thanks very much for you explanation on factor analysis, even those who beginners in statistics like me can follow your elaborations. its so illuminating. have gone through several text on factor analysis but could hardly capture the concept, Thanks

September 23, 2014 at 3:55 pm

As i am using Factor analysis by SPSS in my master research, i got five factors related to my research. At the end of the results by spss there is a 5*5 matrix ( 5 are the factors ). What does this matrix endicated for? in the beginning i thought it is a correlation matrix of the factors, but then i’ve been told no it isn’t ( without giving me what it is exactly). Can you help please? p.s ; welcome to everybodys’ answer.

August 3, 2014 at 2:42 am

This was simple and clear with commonsense.

July 21, 2014 at 7:40 am

very usefull an understandable explanation.saved lit if time bcoz if this easy explationation..thank you…sir mikhe…

July 18, 2014 at 7:14 am

Thanks a lot this made my life a lot easier in the PHD Thanks again!!

July 13, 2014 at 8:33 pm

Dr. Rahn- I’ve been trying all afternoon to understand a research article that used this method and this was the first explanation that has helped me. Thank you very much for posting it!

June 30, 2014 at 11:01 am

Thanks, this was great. simple and to the point. many thanks.

March 11, 2014 at 4:54 am

very simple and informative.

November 10, 2013 at 10:53 am

the first one is correct. the Factor is a linear combination of the original variable. Hence, your first formula, represents the required info.

September 17, 2013 at 10:14 pm

Dear Dr. Rahn,

I would like to hear your opinion if this method is valid:

I have used a PLS model and created an ‘factor’ (lets called it “Loyalty”). To make that factor I’ve used four variables and the factor loadings are the following:

s1 factorloading: 0,934 s2 factorloading: 0,886 s3 factorloading: 0,913 s4 factorloading: 0,937

Next I would like to estimate the loyalty of a respondent, who has the following values:

s1 = 3 s2 = 4 s3 = 4 s4 = 2

How can I emerge these values to one value and group each respondent into e.g. two groups (e.g. high loyalty, low loyalty)

I have an idea: I use this formular:

Sum of (factorloading (si) * values(si))

(0.934 * 3) + (0.886 * 4) + (0.913 * 4) * (0.937 * 2) = 11.872

or maybe this formular:

Sum of (factorloadings(si) / (sum of factorloadings(s1,s2,s3,s4)) * values(si)

((0.934/(0.934+0.886+0.913+0.937)) * 3) + ((0.886/ (0.934+0.886+0.913+0.937)) * 4 + ((0.913 * (0.934+0.886+0.913+0.937)) * 4 + ((0.937 * (0.934+0.886+0.913+0.937)) * 2) = 3.23 Using this formular in this example would give the respondent a value of:

which formular is the right one (if any), and if either of them are the right one, what is?

p.s. Anyone is welcome to answer this question 🙂

September 12, 2013 at 9:04 am

Very clear and useful description, also understandable for non-mathematicians, e.g. linguists. Many thanks for posting this!

August 17, 2013 at 7:33 pm

Hello Dr. Rahn

This was the best and and easiest to understand explanation of Factor Analysis I have found. I will book mark your page as a future reference. Thanks

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Lesson 12: factor analysis, overview section  .

Factor Analysis is a method for modeling observed variables, and their covariance structure, in terms of a smaller number of underlying unobservable (latent) “factors.” The factors typically are viewed as broad concepts or ideas that may describe an observed phenomenon. For example, a basic desire of obtaining a certain social level might explain most consumption behavior. These unobserved factors are more interesting to the social scientist than the observed quantitative measurements.

Factor analysis is generally an exploratory/descriptive method that requires many subjective judgments. It is a widely used tool and often controversial because the models, methods, and subjectivity are so flexible that debates about interpretations can occur.

The method is similar to principal components although, as the textbook points out, factor analysis is more elaborate. In one sense, factor analysis is an inversion of principal components. In factor analysis, we model the observed variables as linear functions of the “factors.” In principal components, we create new variables that are linear combinations of the observed variables.  In both PCA and FA, the dimension of the data is reduced. Recall that in PCA, the interpretation of the principal components is often not very clean. A particular variable may, on occasion, contribute significantly to more than one of the components. Ideally, we like each variable to contribute significantly to only one component. A technique called factor rotation is employed toward that goal. Examples of fields where factor analysis is involved include physiology, health, intelligence, sociology, and sometimes ecology among others.

• Understand the terminology of factor analysis, including the interpretation of factor loadings, specific variances, and commonalities;
• Understand how to apply both principal component and maximum likelihood methods for estimating the parameters of a factor model;
• Understand factor rotation, and interpret rotated factor loadings.

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3 Types of Factor Analysis

Factor analysis is a statistical technique used to identify the underlying structure of a set of variables.

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Market research and analysis of large volumes of data are necessary when it comes to analyzing and determining the right market segment, potential demand, and potential areas of competition, product development requirements and all other facets of the business marketing portfolio. One of the most common tools used to deal with the vast amounts of data is Factor Analysis.

What is Factor Analysis?

Factor analysi s is a statistical technique used to identify the underlying structure of a set of variables. In layman’s terms, it is used to analyze the relationship between two observable variables and how it is affected by another smaller set of unobservable variables. For example, factor analysis can be used in market segmentation to identify the underlying variables according to which customers can be grouped.

Uses of factor analysis in market research and analysis

Factor analysis has proved to be very beneficial in market research and analysis of variables that determine consumer behavior:

• It helps to make sense of large data with interlinked relationships
• It may point out relationships that may not have been obvious
• It can point out to the underlying relationships with respect to consumer tastes, preferences, etc.
• It is easier to condense and correlate data through factor analysis and also to draw conclusions from the data gathered in market research and analysis.
• It can be used to form empirical clusters of variables and underlying factors that affect them

Types of factor analysis

A factor analysis is mainly used for interpretation of data and in analyzing the underlying relationships between variable and other underlying factors that may determine consumer behavior. Instead of grouping responses and response types, factor analysis segregates the variable and groups these according to their co relevance.There are mainly three types of factor analysis that are used for different kinds of market research and analysis.

• Exploratory factor analysis
• Confirmatory factor analysis
• Structural equation modeling

Exploratory factor analysis is used to measure the underlying factors that affect the variables in a data structure without setting any predefined structure to the outcome. Confirmatory factor analysis on the other hand is used as tool in market research and analysis to reconfirm the effects and correlation of an existing set of predetermined factors and variables that affect these factors. Structural equation modeling hypothesizes a relationship between a set of variables and factors and tests these casual relationships on the linear equation model.  Structural equation modeling can be used for exploratory and confirmatory modeling alike, and hence it can be used for confirming results as well as testing hypotheses.

Factor analysis will only yield accurate and useful results if done by a researcher who has adequate knowledge to select data and assign attributes. Selecting factors and variables so as to avoid too much similarity of characteristics is also important. Factor analysis, if done correctly, can allow for market research and analysis that helps in various areas of decision making like product features, product development, pricing, market segmentation, penetration and even with targeting.

Applications of Factor Analysis

Factor analysis has several applications in different fields, including:

• Market Research: it is widely used in market research to identify the underlying factors that influence customer preferences and behavior. For example, a market research study may use factor analysis to identify the key factors that influence consumers' purchasing decisions.
• Psychology: it is used in psychology to identify the underlying dimensions of personality traits, intelligence, and cognitive abilities. For example, a factor analysis of a personality test may identify factors such as extraversion, neuroticism, and openness to experience.
• Education: it is used in education to identify the underlying factors that contribute to academic achievement. For example, a factor analysis of academic test scores may identify factors such as verbal reasoning, mathematical ability, and spatial ability.

Factor analysis is a powerful statistical technique that can help in identifying the underlying factors that contribute to the patterns of the data. By reducing large amounts of data into a smaller number of factors, it can simplify the data and help in making meaningful conclusions. Whether you're conducting market research, psychological studies, or educational research, factor analysis can be a valuable tool for understanding the relationships between variables and identifying the underlying factors that explain the patterns in the data.

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In essence, factor analysis in marketing research is changing one marketing variable to see what affect, if any, the change has on the outcome. The change in sales also affects the bottom line of the company, so factor analysis in marketing helps companies determine which marketing efforts it should pursue, which efforts need work and which marketing efforts may meet the cutting room floor.

Importance of Factor Analysis

Factor analysis in marketing requires an evaluation of how changing one marketing point, such as price, changes the sales of the product. In order to measure how the factor changes the sales, it requires that only one marketing variable is changed at a time in order to measure the relationship between the variables and the outcome. In marketing, changing one variable can be significant because it may cause an increase or decrease the sales of the product.

Types of Marketing Variables

An infinite number of marketing variables can exist, which is why it is necessary to alter only one at a time. Marketing variables include the product, the product packaging, the size of the product and the color of the product. The price, distribution channels and marketing strategies may also be variables of the product that can be changed to see how the change makes a difference in the sales of the product.

Identifying What Customers Want

Marketing experts understand the importance of factor analysis in understanding the perception of the buyer of the product. By testing variables, it is possible for marketing professionals to determine what is important to the customers of the product. For example, if a product is only available in black and the sales reach $150,000 in one year, but when the company adds color options of red, blue and silver, and sales reach $300,000, then the company can conclude through factor analysis that color options are important to the customers of the product. Ultimately, it is imperative to use factor analysis in marketing to create the ideal product for customers, which in turn, increases the sales of the product.

Conducting Factor Analysis

Generally, companies test variables with factor analysis in marketing research using tools such as focus groups and surveys, according to Qualtrics . Since making changes to the product itself in order to test variables can be expensive, surveys and focus groups allows companies to gather pertinent information without increasing the cost to manufacture the product. Focus groups and surveys allow companies to gather perceptual information from current and potential customers of the product.

Consumer information is important because it allows the company to see the product from the vantage point of the customers and determine which factors in marketing are the most important to the customers. For example, a focus group may see four different package versions of a product and then ask the focus group participants to choose which package they like best and explain why. Companies can use this information to alter product packaging to attract more customers and sell more products.

Limitations of Factor Analysis

Factor analysis in marketing can inform the way a company sells its product, but factor analysis in marketing is primarily an exploratory approach, as explained by People & Co . Grand scale confirmation testing with analysis of how multiple variables work together is typically required to come to a fair conclusion on the relationship of the variables. It is wise to have a market research expert help to conduct the factor analysis and evaluate the test results to ensure it is not an incorrectly implied cause and effect relationship.

• Qualtrics: Your Ultimate Guide to Market Research and how to Conduct It Like a Pro
• People & Co.: Factor Analysis Using IBM SPSS

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What is factor analysis?

Factor analysis is a statistical technique that reduces a set of variables by extracting all their commonalities into a smaller number of factors. It can also be called data reduction.

When observing vast numbers of variables, some common patterns emerge, which are known as factors. These serve as an index of all the variables involved and can be utilized for later analysis.

Factor analysis uses several assumptions:

• The variables’ linear relationships
• Absence of multicollinearity
• Relevance of the variables
• The existence of a true correlation between factors and variables

Therefore, it becomes a statistical technique used to see how a group shares a common variance. While it is mostly used in psychological research, it can also be applied in areas like business and market study to understand customer satisfaction or employee job satisfaction and in finance, to study the fluctuation of stock prices.

Features of factor analysis

While studying customer satisfaction related to a product, a researcher will usually pose several questions about the product through a survey. These questions will consist of variables regarding the product’s features, ease of purchase, usability, pricing, visual appeal, and so forth. These are typically quantified on a numeric scale. But, what a researcher looks for is the underlying dimensions or “factors” regarding customer satisfaction. These are mostly psychological or emotional factors toward the product that cannot be directly measured. Factor analysis uses the variables from the survey to determine them indirectly.

When a researcher assumes these variables from the survey, they are condensed into one or more factors. Some of the methods used to extract these factors could include:

Principal component analysis

This is the most commonly used method. The first factor is extracted by determining the maximum variance. This variance is then removed and is replaced by the factor. The second factor is then determined by the next highest variance, and the process continues until there are no more variances.

Common factor analysis

In this method, the factors are extracted from commonly-occurring variances and do not include the unique variances of all the variables.

Image factoring

Based on the correlation matrix, this process uses predicted variables using the OLS regression method.

Once the factors are extracted, the questionnaire’s score is assumed to be related to the factors in a linear manner. The margin of error is also taken into consideration, along with all the factors to the equation.

Types of factor analysis

There are essentially two types of factor analysis:

• Exploratory Factor Analysis: In exploratory factor analysis, the researcher does not make any assumptions about prior relationships between factors. In this method, any variable can be related to any factor. This helps identify complex relationships among variables and group them based on common factors.
• Confirmatory Factor Analysis: The confirmatory factor analysis, on the other hand, assumes that variables are related to specific factors and uses pre-established theory to confirm its expectations of the model.

Assumptions of factor analysis

Factor analysis makes use of several assumptions in order to produce the outcomes:

• There will not be any  outliers  in the data.
• The sample size will be greater than the size of the factor.
• Since the method is interdependent, there will be no perfect multicollinearity between any of the variables.
• When in a sequence of random variables, all the variables have the same finite variance, known as being homoscedastic. Since factor analysis works as a linear function, it will not need homoscedasticity between variables.
• There is the assumption of linearity. This means that even non-linear variables can be used, but once transferred, they become linear variables.
• There is also the assumption of interval data.

How factor analysis is used

Business marketing.

In a business model, factor analysis is used to explain complex variables or data using the matrix of association. It studies the interdependencies of data and assumes that complex variables can be reduced to a few important dimensions. This is possible because of some of the relationships between variables and their dimensions. The attribute of one variable might sometimes be the result of the dimension of another. It breaks down the initial rating, using statistical algorithms on various components and uses these partial scores to extract various factors.

Automotive industry

The use of factor analysis in the automotive industry was mentioned as far back as 1997 in an article by Professor Emeritus Richard B. Darlington of Cornell University. He explained how a study could be used to identify all the variables that apply to the decision-making of purchasing a car—size, pricing, options, accessories, and more. The study could then be used to arrive at a few key variables that actually close a purchase decision. Automotive dealers can then tailor their offerings to cater to the market.

The key to a productive investment portfolio is diversification. To ensure a diverse portfolio, investment professionals use factor analysis to predict movement across a wide sector of industries and provide insights on factors that may be under the radar. For example, the average portfolio contains stocks of industries like technology and commodities. A look at the rise in stock prices of a related industry, like oil, will give investment professionals a good idea on what to sell and retain.

Human resources

There are many factors that go into a company’s hiring process. With statistics, human resource professionals will be able to create a comfortable and productive working environment. Several variables can be compared and analyzed to see which combination in terms of the number of team members, varied skill sets, and contractual or in-house talent works, improving the overall functioning of the organization.

Restaurants

For restaurants, factor analysis can be used to understand demographics and target diners in the creation of menus. A fast-food restaurant opening next to a university campus will have to plan its menu differently than if it was placed in a high-end shopping location. Factors such as surrounding competition, foot-traffic, age-groups, and location all determine success.

When hiring teachers and deciding on a curriculum for the school year, factor analysis plays a huge role. It is used to determine classroom sizes, staffing limits, salary distribution, and a wide range of other requirements necessary for the school year to run smoothly.

Challenges and solutions of factor analysis

While factor analysis is a useful tool for business research and analysis, there are a few challenges to keep in mind in order to ensure the right results. The result entirely depends on the ability of the researcher to gather the right set of variables associated with the business and the product. Neglecting even a small detail might result in the wrong value of the procedure.

If the observed variables for a particular item are similar to each other but distinct from other items, the algorithm might consider this as a single factor to those items, which could result in inaccurate analysis results. Knowledge of the item and its theory is important in naming factors accurately. Even dissimilar variables might have dependencies for no reason.

Gathering information using an accurate survey is the key. Besides the knowledge of the product and its theory, it is also important to know its market.

Research and developments in the field of factor analysis continue to contribute to making more informed decisions in various sectors. Continuous refinement in confirmatory factor analysis techniques makes this one of the most important decision-making tools for every industry in the future.

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Application of Factor Analysis: To Study the Factor Structure Among Variables

• First Online: 18 October 2012

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• J. P. Verma 2  

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Buying decision of an individual depends upon large number of product characteristics. But the market strategy cannot be developed on the basis of all those parameters of a product that affect the buying behavior of an individual. The factor analysis, a multivariate technique, comes to our rescue in solving such problems. The factor analysis technique reduces the large number of variables into few underlying factors to explain the variability of the group characteristics. The concept used in factor analysis technique is to investigate the relationship among the group of variables and segregate them in different factors on the basis of their relationship. Thus, each factor consists of those variables which are related among themselves and explain some portion of the group variability. For example, personality characteristics of an individual can be assessed by the large number of parameters. The factor analysis may group these variables into different factors where each factor measure some dimension of personality characteristics. Factors are so formed that the variables included in it are related with each other in some way. The significant factors are extracted to explain the maximum variability of the group under study.

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Verma, J.P. (2013). Application of Factor Analysis: To Study the Factor Structure Among Variables. In: Data Analysis in Management with SPSS Software. Springer, India. https://doi.org/10.1007/978-81-322-0786-3_11

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Title: Identifying the antecedents of voter behaviour: an empirical study on Indian electorates

Authors : Deepika; Shashank Vikram Pratap Singh; Santosh Kumar

Addresses : Sri Venkateswara College, University of Delhi, New Delhi, 110021, India ' Shri Ram College of Commerce, University of Delhi, New Delhi, 110007, India ' Shri Ram College of Commerce, University of Delhi, New Delhi, 110007, India

Abstract : Political parties adopt various means to reach and influence their targeted electoral base. Practices in India are not an exception to this. Political parties are devising various concepts of marketing for this purpose. Therefore, the aim of the present study is to find out factors that are considered by the voters while casting their vote. Thus, the study first establishes the concept of political marketing by collecting expert opinion from marketing experts, political scientists and journalists. Based on the results, data was collected from the voters from all over India to study their behaviour. The data collected was empirically tested using exploratory factor analysis and canonical correlation in SPSS to establish factors that contribute the most to studying voter behaviour. The result of the study provides useful insights for the political parties in India.

Keywords : voter behaviour; political marketing; electorates; political parties; election; democracy; India.

DOI : 10.1504/IJEG.2024.138458

International Journal of Electronic Governance, 2024 Vol.16 No.1, pp.74 - 109

Received: 07 Oct 2023 Accepted: 16 Jan 2024 Published online: 03 May 2024 *

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MARA Factor-Based Stock Analysis

May 01, 2024 — 09:06 am EDT

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MARATHON DIGITAL HOLDINGS INC ( MARA ) is a mid-cap growth stock in the Software & Programming industry. The rating using this strategy is 57% based on the firm’s underlying fundamentals and the stock’s valuation. A score of 80% or above typically indicates that the strategy has some interest in the stock and a score above 90% typically indicates strong interest.

The following table summarizes whether the stock meets each of this strategy's tests. Not all criteria in the below table receive equal weighting or are independent, but the table provides a brief overview of the strong and weak points of the security in the context of the strategy's criteria.

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About David Dreman : Dreman's Kemper-Dreman High Return Fund was one of the best-performing mutual funds ever, ranking as the best of 255 funds in its peer groups from 1988 to 1998, according to Lipper Analytical Services. At the time Dreman published Contrarian Investment Strategies: The Next Generation, the fund had been ranked number one in more time periods than any of the 3,175 funds in Lipper's database. In addition to managing money, Dreman is also a longtime Forbes magazine columnist.

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About Validea : Validea is an investment research service that follows the published strategies of investment legends. Validea offers both stock analysis and model portfolios based on gurus who have outperformed the market over the long-term, including Warren Buffett, Benjamin Graham, Peter Lynch and Martin Zweig. For more information about Validea, click here

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