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Discriminant Analysis – Methods, Types and Examples

Table of Contents

Discriminant Analysis

Discriminant analysis is a statistical technique used in research that aims to classify or predict a categorical dependent variable based on one or more continuous or binary independent variables . It is often used when the dependent variable is non-metric (categorical) and the independent variables are metric (continuous or binary).

Discriminant Analysis Methodology

Here are the basic steps in the discriminant analysis methodology:

Define the Problem and Collect the Data

Firstly, clearly define the problem and the objectives of the analysis. Following this, collect the data for the dependent variable (the groups you want to predict or classify) and the independent variables (the predictors). The dependent variable should be categorical, and the independent variables are usually continuous.

Data Preprocessing

Clean and preprocess the data. This includes dealing with missing values, outliers, and ensuring that the data meets the assumptions of discriminant analysis. These assumptions include the independence of observations, normal distribution of predictor variables within each group of the dependent variable, and homogeneity of variances across groups.

Estimate Discriminant Functions

The next step is to estimate the discriminant functions, which are linear combinations of the predictor variables. These functions will differentiate the groups in the dependent variable. If there are two groups, only one discriminant function is created. If there are more than two groups, there can be more than one discriminant function.

Evaluate the Discriminant Functions

Check the significance of the discriminant functions using a Wilks’ lambda test. This test will tell you whether the discriminant functions significantly differentiate between the groups in your dependent variable.

Classification of Cases

Use the discriminant functions to classify the cases into groups. This is usually done by assigning a case to the group for which it has the highest discriminant score.

The final step is to validate the model by testing its classification accuracy. This can be done by splitting your data into a training set (to develop the discriminant functions) and a validation set (to test the accuracy of the classification). Alternatively, cross-validation or other out-of-sample validation techniques can be used.

Interpretation

Based on the discriminant function(s), interpret the results. The weights or coefficients of the predictor variables in the discriminant function can indicate which variables are most important for discriminating between the groups.

Once the discriminant analysis model is built and validated, it can be used to predict group membership for new cases

Types of Discriminant Analysis

Types of Discriminant Analysis are as follows:

Linear Discriminant Analysis (LDA)

This type of discriminant analysis is used when all the predictor variables are continuous and normally distributed, and the groups have equal covariance matrices. LDA seeks to find a linear combination of the predictors that separates the groups as much as possible.

Quadratic Discriminant Analysis (QDA)

QDA is similar to LDA, but it does not assume that the groups have equal covariance matrices. This means that it can model more complex group boundaries, but it also requires estimating more parameters than LDA and can be more prone to overfitting.

Regularized Discriminant Analysis (RDA)

This is a compromise between LDA and QDA that allows for the modeling of more complex group boundaries than LDA but is less prone to overfitting than QDA. It does this by “shrinking” the group-specific covariance matrices towards a common covariance matrix, with the degree of shrinkage determined by a tuning parameter.

Flexible Discriminant Analysis (FDA)

This is an extension of LDA that uses basis expansion methods to model non-linear boundaries between groups. It essentially applies LDA in a transformed space of the predictors.

Multinomial Discriminant Analysis (MDA)

This is used when you have more than two groups and you want to model the probability of group membership as a function of the predictors. MDA extends LDA and QDA to more than two groups.

Canonical Discriminant Analysis (CDA)

This type of discriminant analysis is used to identify and measure the associations among a set of variables and between that set of variables and a set of dummy variables that represent membership in the groups.

Discriminant Analysis Formulas

Discriminant analysis involves several important formulas. I’ll describe the general form of these formulas for Linear Discriminant Analysis (LDA) as it is one of the most commonly used forms of discriminant analysis.

The goal of LDA is to project a feature space (a dataset n-dimensional sample) onto a smaller subspace k (where k ≤ n-1) while maintaining the class-discriminatory information. It does this by maximizing the ratio of between-class variance to the within-class variance in any particular data dataset to guarantee maximal separability.

1. Within-Class Scatter Matrix (Sw)

The within-class scatter matrix Sw is computed as:

where: Si = Σ (x – mi)(x – mi)^T

and x runs over all N data points xi in class i, mi is the mean vector of class i, and the caret (^) indicates transposition.

2. Between-Class Scatter Matrix (Sb)

The between-class scatter matrix Sb is computed as:

Sb = Σ Ni (mi – m)(mi – m)^T

where: Ni is the number of samples in each class, mi is the mean vector of class i, and m is the overall mean.

3. Linear Discriminants

The linear discriminants for the new subspace are the eigenvectors of Sw^-1 * Sb. That is, we want to solve the generalized eigenvalue problem for (Sw^-1 * Sb) * v = λv, where v are the eigenvectors we are looking for.

The discriminant function, which is used to classify a given new sample x into a class, is given by:

D(x) = x * W

where W is the matrix of eigenvectors.

4. Score of a Case for a Group

Once the discriminant functions have been calculated, the discriminant score of a case for a group is given by substituting the case’s values for the predictors into the discriminant function for that group.

5. QDA Formula

The discriminant function used in QDA is given by:

D_k(x) = -0.5 * log|Σ_k| – 0.5 * (x – μ_k)^T * Σ_k^-1 * (x – μ_k) + log(P(C_k))

• D_k(x) is the discriminant function for class k.
• x is the feature vector of a sample.
• Σ_k is the covariance matrix for class k.
• μ_k is the mean vector for class k.
• (x – μ_k)^T is the transpose of the difference between the feature vector and the mean vector.
• Σ_k^-1 is the inverse of the covariance matrix for class k.
• |Σ_k| is the determinant of the covariance matrix for class k.
• P(C_k) is the prior probability of class k.

This function measures the distance from a sample to the center of a class, taking into account the spread or dispersion of the class. When a new sample is classified, it is assigned to the class that gives the highest value of the discriminant function. Note that in contrast to LDA, the quadratic term (x – μ_k)^T * Σ_k^-1 * (x – μ_k) allows QDA to model a more complex (i.e., non-linear) relationship between the features and the class labels.

Examples of Discriminant Analysis

Discriminant analysis is often used in various fields such as marketing, finance, and medicine. Here are a few practical examples of its applications:

• Marketing Research : Suppose a company wants to know what factors influence whether customers buy their product or a competitor’s. They may conduct a survey and ask respondents about their age, income, gender, and education. They can then use discriminant analysis to determine which of these variables are the best predictors of the brand of product purchased. The results may reveal, for example, that income and education level are significant discriminants, which can help the company target its marketing more effectively.
• Finance and Credit Scoring : A bank might use discriminant analysis to predict whether or not a loan applicant will default. The bank would use data from past customers, such as loan amount, income, credit score, and employment status, as predictor variables. The dependent variable would be whether the customer defaulted or not. The discriminant analysis can then help the bank make more informed loan approval decisions.
• Medical Diagnostics : Discriminant analysis can be used to classify patients into different categories based on symptoms or test results. For example, a researcher might use discriminant analysis to classify patients into those with and without a particular disease based on a range of symptoms or biomarkers.
• Human Resource Management : In HR, discriminant analysis can be used to predict job success based on a set of predictors like years of education, experience, skill level, and personality test scores. The dependent variable could be a binary measure of job success (successful or not) or a multi-category measure (like low, medium, or high performer).
• Psychology : A psychological study could use discriminant analysis to predict the success of therapy methods. For example, the dependent variable could be the type of therapy (e.g., cognitive-behavioral, psychodynamic, person-centered), and the independent variables could include demographic variables (like age or gender), psychometric scores, symptom severity, and the presence of any comorbid disorders.
• Education : Discriminant analysis could be used in educational research to predict the likelihood of students dropping out based on variables like attendance, grade point average, engagement in extracurricular activities, and socioeconomic status.

When to use Discriminant Analysis

Here are several situations when discriminant analysis can be particularly useful:

Multiclass Classification

Discriminant analysis is often used when the dependent variable is categorical and has more than two categories. While other techniques like logistic regression can handle binary outcomes, discriminant analysis is particularly suitable for multiclass classification problems.

Predictive Modeling

f you are interested in predicting group membership based on a set of predictors, discriminant analysis can be a good choice. For example, it can be used to predict whether a loan applicant will default or not based on their financial characteristics.

Understanding Group Differences

Discriminant analysis can also be used when you are interested in understanding which variables discriminate between two or more naturally occurring groups. For instance, a company might use discriminant analysis to understand which characteristics differentiate customers who make a repeat purchase from those who do not.

Assumption Fulfillment

Discriminant analysis assumes that the predictors are normally distributed and that the groups have equal covariance matrices. If your data meet these assumptions, discriminant analysis can be a particularly effective method.

Dimensionality Reduction

Linear Discriminant Analysis (LDA), a type of discriminant analysis, can also be used for dimensionality reduction. That is, it can be used to reduce the number of variables in a dataset while preserving as much information as possible.

Applications of Discriminant Analysis

Applications of Discriminant Analysis area s follows:

• Medical Research : Discriminant Analysis can be used to classify patients into different groups based on their symptoms, medical history, or response to treatments. For instance, it can help distinguish between different types of diseases or predict patient outcomes.
• Psychological Research : In the field of psychology, Discriminant Analysis can be employed to identify which factors (such as personality traits, environmental factors, or genetic factors) predict different outcomes, such as the success of different therapeutic approaches or the development of certain behavioral patterns.
• Educational Research : Researchers in education may use Discriminant Analysis to predict academic success based on variables like previous academic achievement, socioeconomic status, and learning strategies.
• Marketing : Discriminant Analysis can be used to identify the most important factors that influence the choice of a particular product over another, allowing businesses to more effectively target their marketing strategies.
• Medical Diagnostics : It’s often used in medical fields to classify patients’ conditions based on symptoms or test results. This could include differentiating between different types of tumors, stages of a disease, or responses to different treatments.
• Finance : In the banking sector, Discriminant Analysis is used in credit scoring models to predict the probability of a borrower defaulting on a loan based on their financial information.
• Human Resources : It can be used to predict job performance or success in job applicants based on characteristics such as education level, years of experience, or personality test scores.
• Ecology : Discriminant Analysis can be used to classify different environments based on a set of features, such as climate conditions, soil properties, or vegetation types. This is especially useful in determining the habitats of various species or predicting the impact of climate change.
• Customer Segmentation : Businesses can use Discriminant Analysis to classify customers into different segments based on their buying behavior, demographic characteristics, and other attributes. This helps businesses understand their customers better and deliver more personalized offerings.
• Face Recognition : In computer vision, Linear Discriminant Analysis (LDA) is often used to enhance facial recognition technology by reducing dimensionality and improving classification accuracy.

Advantages of Discriminant Analysis

Discriminant analysis offers several advantages that make it a valuable tool in a researcher’s statistical toolkit:

• Multiclass Classification : Discriminant analysis can handle situations where there are more than two classes in the dependent variable, which is a limitation for some other methods such as logistic regression.
• Understanding Group Differences : Discriminant analysis does not just predict group membership; it also provides information on which variables are important discriminators between groups. This makes it a useful tool for exploratory research to understand the differences between groups.
• Efficient with Large Variables : Discriminant analysis can handle a large number of predictor variables efficiently. It becomes useful when the number of variables is very large, potentially exceeding the number of observations.
• Dimensionality Reduction : Linear Discriminant Analysis (LDA) can be used for dimensionality reduction – it can reduce the number of variables in a dataset while preserving as much information as possible.
• Prior Probabilities : Discriminant analysis allows for the inclusion of prior probabilities, meaning that researchers can incorporate prior knowledge about the proportions of observations in each group.
• Model Interpretability : The model produced by discriminant analysis is relatively interpretable compared to some other machine learning models, such as neural networks. The weights of the features in the model can provide an indication of their relative importance.

Disadvantages of Discriminant Analysis

While discriminant analysis offers numerous benefits, there are also some limitations and disadvantages associated with its use:

• Assumption of Normality : Discriminant analysis assumes that the predictors are normally distributed. If this assumption is violated, the performance of the model may be affected.
• Assumption of Equal Covariance Matrices : Discriminant analysis, particularly Linear Discriminant Analysis (LDA), assumes that the groups being compared have equal covariance matrices. If this assumption is not met, it may lead to inaccuracies in classification.
• Multicollinearity : Discriminant analysis may not work well if there is high multicollinearity among the predictor variables. This situation can lead to unstable estimates of the coefficients and difficulties in interpreting the results.
• Outliers : Discriminant analysis is sensitive to outliers, which can have a large influence on the classification function.
• Overfitting : Like many statistical techniques, discriminant analysis can result in overfitting if the model is too complex. Overfitting happens when the model fits the training data very well but performs poorly on new, unseen data.
• Limited to Linear Relationships : Linear Discriminant Analysis (LDA) assumes a linear relationship between predictor variables and the log-odds of the dependent variable. This limits its utility in scenarios where relationships are complex or nonlinear. In such cases, Quadratic Discriminant Analysis (QDA) or other non-linear methods might be more appropriate.

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Discriminant Analysis: Meaning, Purpose, and Applications

Table of Contents

Discriminant Analysis is a multivariate statistical technique used to classify data into distinct groups based on a set of independent variables. It is a predictive modeling technique that helps identify the variables that contribute most to the differences between groups.

The primary goal of Discriminant Analysis is to find the linear combination of independent variables that maximizes the separation between groups. This separation is measured by the distance between the means of the groups and their variance.

Applications of Discriminant Analysis

Discriminant Analysis has various applications in research and business, such as:

• Customer segmentation: Discriminant Analysis helps identify the characteristics of customers who buy a particular product or service, which can aid in segmenting the market and targeting specific customer groups.
• Credit scoring: Discriminant Analysis is used to evaluate the creditworthiness of individuals based on their financial and demographic data.
• Medical research: Discriminant Analysis can help identify the factors that differentiate between healthy and diseased individuals or between different stages of a disease.
• Quality control: Discriminant Analysis can help identify the factors that affect the quality of a product and ensure that it meets the required standards.

How Discriminant Analysis Works

Discriminant Analysis works by identifying a set of discriminant functions that separate the groups based on their means and variances. These functions are derived from a set of independent variables that are used to predict the group membership of a new observation.

The discriminant functions are calculated based on the training data and can be used to predict the group membership of new data. The accuracy of the prediction can be measured using classification rates or cross-validation techniques.

Types of Discriminant Analysis

There are two types of Discriminant Analysis: linear and quadratic. Linear Discriminant Analysis (LDA) assumes that the groups have equal covariance matrices, while Quadratic Discriminant Analysis (QDA) assumes that each group has its own covariance matrix.

The choice of the type of Discriminant Analysis depends on the nature of the data and the research question. In general, LDA is preferred when the groups have similar variances and the sample size is small, while QDA is preferred when the groups have different variances or the sample size is large.

Discriminant Analysis is a powerful statistical tool that can help you classify your data into distinct groups based on a set of independent variables. It has various applications in research and business and can aid in customer segmentation, credit scoring, medical research, and quality control.

By understanding how Discriminant Analysis works and the types of Discriminant Analysis available, you can use this tool to make informed decisions and gain insights into your data.

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Research Methodology for Management Decisions

1 Research Methodology: An Overview

• Meaning of Research
• Research Methodology
• Research Method
• Business Research Method
• Types of Research
• Importance of business research
• Role of research in important areas

2 Steps for Research Process

• Research process
• Define research problems
• Research Problem as Hypothesis Testing
• Extensive literature review in research
• Development of working hypothesis
• Preparing the research design
• Collecting the data
• Analysis of data
• Preparation of the report or the thesis

3 Research Designs

• Functions and Goals of Research Design
• Characteristics of a Good Design
• Different Types of Research Designs
• Exploratory Research Design
• Descriptive Research Design
• Experimental Research Design
• Types of Experimental Designs

4 Methods and Techniques of Data Collection

• Primary and Secondary Data
• Methods of Collecting Primary Data
• Merits and Demerits of Different Methods of Collecting Primary Data
• Designing a Questionnaire
• Pretesting a Questionnaire
• Editing of Primary Data
• Technique of Interview
• Collection of Secondary Data
• Scrutiny of Secondary Data

5 Attitude Measurement and Scales

• Attitudes, Attributes and Beliefs
• Issues in Attitude Measurement
• Scaling of Attitudes
• Deterministic Attitude Measurement Models: The Guttman Scale
• Thurstone’s Equal-Appearing Interval Scale
• The Semantic Differential Scale
• Summative Models: The Likert Scale
• The Q-Sort Technique
• Multidimensional Scaling
• Selection of an Appropriate Attitude Measurement Scale
• Limitations of Attitude Measurement Scales

6 Questionnaire Designing

• Introductory decisions
• Contents of the questionnaire
• Format of the questionnaire
• Steps involved in the questionnaire
• Structure and Design of Questionnaire
• Management of Fieldwork
• Ambiguities in the Questionnaire Methods

7 Sampling and Sampling Design

• Advantage of Sampling Over Census
• Simple Random Sampling
• Sampling Frame
• Probabilistic As pects of Sampling
• Stratified Random Sampling
• Other Methods of Sampling
• Sampling Design
• Non-Probability Sampling Methods

8 Data Processing

• Editing of Data
• Coding of Data
• Classification of Data
• Statistical Series
• Tables as Data Presentation Devices
• Graphical Presentation of Data

9 Statistical Analysis and Interpretation of Data: Nonparametric Tests

• One Sample Tests
• Two Sample Tests
• K Sample Tests

10 Multivariate Analysis of Data

• Regression Analysis
• Discriminant Analysis
• Factor Analysis

11 Ethics in Research

• Principles of research ethics
• Advantages of research ethics
• Limitations of the research ethics
• Steps involved in ethics
• What are research misconducts?

12 Substance of Reports

• Research Proposal
• Categories of Report
• Reviewing the Draft

13 Formats of Reports

• Parts of a Report
• Cover and Title Page
• Introductory Pages
• Reference Section
• Typing Instructions
• Copy Reading
• Proof Reading

14 Presentation of a Report

• Communication Dimensions
• Presentation Package
• Audio-Visual Aids
• Presenter’s Poise

Marketing91

Discriminant Analysis: Significance, Objectives, Examples, and Types

June 10, 2023 | By Hitesh Bhasin | Filed Under: Marketing

Discriminant Analysis can be understood as a statistical method that analyses if the classification of data is adequate with respect to the research data. It is implemented by researchers for analyzing the data at the time when-

• Dependent variable or criterion is categorical
• Independent variable or predictor is an interval

Still confused about the actual significance of Discriminant Analysis? Let us understand this in a more in-depth fashion-

Table of Contents

Significance of Discriminant Analysis

There are many different times during a particular study when the researcher comes face to face with a lot of questions which need answers at best.

Well, these are some of the questions that we think might be the most common one for the researchers, and it is really important for them to find out the answers to these important questions.

Are some groups different than the others?

If they are different, then what are the variables which make them different?

Is a person able to decide which group will someone belong to based on these variables?

While these questions might seem a little bit difficult to answer, there are some methods that one can use to answer these questions in the best way.

Here we are going to discuss one such method, and it is known as Discriminant analysis.

Have you never heard of the term before? Would you like to know more about it?

Well, if the answer is a Yes, then you have come to the right place because we are going to tell you all about Discriminant analysis and how it can help the researchers in the best way.

Defining Discriminant Analysis: What is It?

Before we move into the details of the subject right here, it is important to get the basics right. First of all, you need to know all about the definition of Discriminant analysis and then will you be able to understand the whole concept of it.

So, let us be your guide as we tell you all about this concept so that you can have a clear idea of what we are talking about.

Discriminant analysis is a particular technique which can be used by all the researchers during their research where they will be able properly to analyze the data of research for understanding the relationship between a dependent variable and different independent variables.

Now, what does the term categorical mean in the first place? Let us explain.

When we say categorical, we mean that the dependent variable will be divided easily into different categories.

Let us provide you with an example to help you understand better. Suppose there are three different computer brands , namely A, B, and C. These three brands can actually be the categorically dependent variables in the study here.

When research uses the values of independent variables for predicting a variable, then that predicted variable is the Dependent Variable.

The objective of Discriminant Analysis

Now that you know a little bit about the definition of Discriminant analysis let us focus on some other things that you need to know about. One of the most important parts for the person to know would be the objective of using Discriminant analysis.

So, in this part of the post, we are going to provide you with an explanation of it in the best way.

The main objective of using Discriminant analysis is the developing of different Discriminant functions which are just nothing but some linear combinations of the independent variables and something which can be used to completely discriminate between these categories of dependent variables in the best way.

With the help of Discriminant analysis, the researcher will be able to examine certain difference which always exists amongst the different groups and that too in terms of the prediction variables.

Apart from that, this method can also help in establishing the accuracy when it comes to the classification between these two groups.

So there is simply not a single speck of doubt about the fact that having the Discriminant analysis as a technique for research is going to be a great help to the researcher in the process. So, why wouldn’t anyone want to use it in the first place?

Discriminant analysis can be easily described by the different categories and the numbers which are possessed by the variable which is dependent in nature. In the case of statistics, the summation of everything happens until a point of infinity.

So, when it comes to the Discriminant analysis, the dependent variable will definitely have two different categories for sure. The type which is used will be the 2-group Discriminant analysis. There are also some cases where the variable which is dependent has got about three or more categories in total.

In those cases, the type which is used will be the multiple Discriminant analysis. So, what is the major point of distinction in such cases?

Well, in the case of the two group example, there is a possibility of just one Discriminant function, and in the other cases, there can be more than one function in case of the Discriminant analysis.

So, this is all you need to know about the objectives of the Discriminant analysis method. Let us move on to something else now.

Here we are going to provide you with some of the examples which will then explain the use and the fitting of Discriminant analysis in the best way.

So, are you all set for the explanation?

We are pretty sure that you are and hence you will get all the information that you want to have.

The examples of Discriminant analysis can be used in order to find out whether the light, heavy, and the medium drinkers of the cold drinks are different on the basis of the consumption or not.

Apart from that, the Discriminant analysis method is also useful in the field of psychology too.

This method can be used to find out the certain differences between the non-price and the price-sensitive consumers of the groceries and that too based on their psychology as well as their characteristics too.

Not just that but this technique also has its importance in the field of business too. In the business field, this can be used so that the company can understand the attributes of particular customers and the store loyalty that they have.

Types of Discriminant Analysis

There are four types of Discriminant analysis that comes into play-

#1. Linear Discriminant Analysis

This one is mainly used in statistics, machine learning , and stats recognition for analyzing a linear combination for the specifications that differentiate 2 or 2+ objects or events.

#2. Multiple Discriminant Analysis

It is used for compressing the multivariate signal so that a low dimensional signal which is open to classification can be produced.

#3. Quadratic Discriminant Analysis

In this type of analysis, your observation will be classified in the forms of the group that has the least squared distance. However, in this, the squared distance will never be reduced to the linear functions.

#4. Canonical Discriminant Analysis

In this type of analysis, dimension reduction occurs through the canonical correlation and Principal Component Analysis.

There are many different benefits which might come with the Discriminant analysis process, and most of them are something that can be mentioned from a statistical point of view.

For those who want to have a little bit more information about the benefits of Discriminant analysis, this part is certainly one of the most important ones as they will be able to understand how this technique is able to help each and every single aspect.

We are here to tell you that this technique is a pretty great tool for statistical research and that it is pretty similar to the technique of regression analysis.

Discriminant analysis has its uses in determining the predictor variables which can be related easily to the dependent variables in the first place.

Also, it can be used in order to predict the certain value which is provided to the dependent variable. Apart from that, another one of the benefits of the process is that it can be used in the creation of perpetual mapping, which is done by marketers.

This has some benefits over some of the other methods which involve the use of perceived distances. We are talking about the options which are used in the tests of significance for checking the dissimilarities that products might have with one another.

Not just that but the distance between the two products can also be found with the help of this.

There are some other practical applications of Discriminant analysis that one needs to know about, and here we are going to shed some light on that topic as well.

With the help of Discriminant analysis, one can use it in combination with the cluster analysis process as well. Let us provide you with an example right here.

Say a bank has proper loans depart and it wants to figure out the worthiness of credit when it comes to the applicants before they provide the loans to them. The technique of Discriminant analysis can be used to determine whether the applicant in question has a good risk of credit or a bad one.

So, it can prove to be a great factor when it comes to the screening of these applicants who are here to look for loans. As a result of that, banks all over can actually avoid having the issue of bad debt, which is one of the most common problems that they face.

Apart from that, retail chains can conduct the segmentation of the market to find out the service attributes of the customers. There can be a survey which is conducted to find out the ratings of the respondents of the desirable attributes of services.

Then it can be easily combined with Discriminant analysis and cluster analysis, which will then allow the companies to segment the market in the best way and assign certain customers to their desirable segments .

A result of it will be that the retailer will be able to find out easily about the preferences of the customers.

Wrapping it up!

So, that is all we have for you today. We hope that this article was a bit informative for you in understanding the concepts of Discriminant analysis.

What do you think most important about Discriminant analysis? Do you have any other example where you had to implement this method to discriminate between variables? Share with us in the comments.

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About Hitesh Bhasin

Hitesh Bhasin is the CEO of Marketing91 and has over a decade of experience in the marketing field. He is an accomplished author of thousands of insightful articles, including in-depth analyses of brands and companies. Holding an MBA in Marketing, Hitesh manages several offline ventures, where he applies all the concepts of Marketing that he writes about.

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dear Hitesh, this article is really helpful to a non-mathematical student../ if you can send me an email on ‘service quality and customer value’ in the Retail industry and the application of Discriminant analysis in comprehending these attributes, I would be grateful to you../ I am inspired by your ‘practical’ approach to this ‘sophisticated-looking’ technique../ regards, ravi../

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The Benefits of Performing Discriminant Analysis on Survey Data

• Survey Tips

What is Discriminant Analysis?

Discriminant analysis is a versatile statistical method often used by market researchers to classify observations into two or more groups or categories. In other words, discriminant analysis is used to assign objects to one group among a number of known groups.

In order to perform any kind of discriminant analysis, you must first have a sample within these known groups. 

When To Use Discriminant Analysis

By performing discriminant analysis, researchers are able to address classification problems in which two or more groups, clusters, or populations are known up front, and one or more new observations are placed into one of the known classifications based on measured characteristics. 

Discriminant analysis is also used to investigate how variables contribute to group separation, and to what degree. For this reason, it’s often leveraged to compliment the findings of cluster analysis .

Market researchers are continuously faced with situations in which their goal is to obtain a better understanding of how groups (customers, age cohorts, etc.) or items (brands, ideas, etc.), differ in terms of a set of explanatory or independent variables. 

These situations are where discriminant analysis serves as a powerful research and analysis tool. 

Descriptive vs. Predictive Discriminant Analysis

Discriminant analysis can be used for descriptive or predictive objectives.

Descriptive discriminant analysis is used when researchers want to assess the adequacy of classification, given the group memberships of the object under study.

Predictive discriminant analysis is used when researchers want to assign objects to one of a number of known groups of objects. 

It’s essential to remember that in both of these cases, some group assignments must be known before conducting the statistical procedure. Due to the fact that these group assignments can be obtained in any way, discriminant analysis is often performed alongside cluster analysis .

Further, if the objective of a researcher is to understand how the groups or items at hand differ, the researcher could conduct a one-way analysis of variance (ANOVA) on each independent variable, such as a brand attribute rating scale, across the group means. 

Oftentimes, in practical market research, the independent variables — in this case the brand-rating scales — are correlated to some extent. This means that there’s a possibility that a series of one-way ANOVA’s will show that many of the independent variables maintain group means that are significantly different, when in actuality only one or two non-redundant independent variables do.

If there’s a large number of independent variables, there may be differences between groups that are a result of chance where there really are no differences. This is due to Type I error.

Discriminant analysis helps researchers overcome Type I error.

In discriminant analysis, the intercorrelation of variables is addressed by partitioning correlations between independent variables. 

When discriminant analysis uses one independent variable to rationalize differences between the groups, the remaining variables are amended so that any difference that is apparent between groups is not due to correlation that the other independent variables have with the first variable. 

For this reason, discriminant analysis only addresses the unduplicated variance between groups. 

The Benefits of Discriminant Analysis

Discriminant analysis provides various benefits. 

Ultimately, it aims to answer the following questions:

• Where do the expected and observed classifications differ?
• How statistically significant is the deviation of observed from expected classification?

Discriminant analysis can be closely compared to regression analysis for the ways in which it identifies the degree to which objects adhere to the specifications of certain groups.

As discussed above, discriminant analysis can be leveraged to determine which predictor variables are related to the dependant variable, as well as to predict the value of the dependent variable based on the values of the predictor variables. 

Discriminant analysis is also commonly used by marketers to develop perceptual maps .

There are seemingly endless ways to implement discriminant analysis for market research and business purposes. 

By conducting this method of data analysis, researchers are able to obtain a much stronger grasp on the products and services they provide, and how these offerings stack up against varying topics and areas of interest.

Have you conducted discriminant analysis for business research purposes? If so, we’d love to hear from you. Drop us a line in the comments below!

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Discriminant validity testing in marketing: an analysis, causes for concern, and proposed remedies

• Methodological Paper
• Published: 07 July 2015
• Volume 44 , pages 119–134, ( 2016 )

Cite this article

• Clay M. Voorhees 1 ,
• Michael K. Brady 2 ,
• Roger Calantone 1 &
• Edward Ramirez 3  

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The results of this research suggest a new mandate for discriminant validity testing in marketing. Specifically, the authors demonstrate that the AVE-SV comparison (Fornell and Larcker 1981) and HTMT ratio (Henseler et al. 2015) with 0.85 cutoff provide the best assessment of discriminant validity and should be the standard for publication in marketing. These conclusions are based on a thorough assessment of the literature and the results of a Monte Carlo simulation. First, based on a content analysis of articles published in seven leading marketing journals from 1996 to 2012, the authors demonstrate that three tests—the constrained phi (Jöreskog 1971), AVE-SV (Fornell and Larcker 1981), and overlapping confidence intervals (Anderson and Gerbing 1988)—are by far most common. Further review reveals that (1) more than 20% of survey-based and over 80% of non-survey-based marketing studies fail to document tests for discriminant validity, (2) there is wide variance across journals and research streams in terms of whether discriminant validity tests are performed, (3) conclusions have already been drawn about the relative stringency of the three most common methods, and (4) the method that is generally perceived to be most generous is being consistently misapplied in a way that erodes its stringency. Second, a Monte Carlo simulation is conducted to assess the relative rigor of the three most common tests, as well as an emerging technique (HTMT). Results reveal that (1) on average, the four discriminant validity testing methods detect violations approximately 50% of the time, (2) the constrained phi and overlapping confidence interval approaches perform very poorly in detecting violations whereas the AVE-SV test and HTMT (with a ratio cutoff of 0.85) methods perform well, and (3) the HTMT .85 method offers the best balance between high detection and low arbitrary violation (i.e., false positive) rates.

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Anderson, J. C., & Gerbing, D. W. (1988). Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach. Psychological Bulletin, 103 (3), 411–423.

Bacharach, S. B. (1989). Organizational theories: Some criteria for evaluation. Academy of Management Review, 14 (4), 496–515.

Baggozi, R. P., & Philips, L. W. (1982). Representing and Testing Organizational Theories: A Holistic Construal. Administrative Science Quarterly, 27 (3), 459–489.

Bagozzi, R. P. (1981). Evaluating Structural equation models with unobservable variables and measurement error: a comment. Journal of Marketing Research, 18 (3), 375–381.

Batra, R., & Sinha, I. (2000). Consumer-Level Factors Moderating the Success of Private Label Brands. Journal of Retailing, 76 (2), 175–191.

Burton, S., Liechenstein, D. R., Netemeyer, R. G., & Garreston, J. A. (1998). A Scale for Measuring Attitude Toward Private Label Products and Examination of Its Psychological and Behavioral Correlates. Journal of the Academy of Marketing Science, 26 (4), 293–306.

Campbell, D. T., & Fiske, D. W. (1959). Convergent and Discriminant Validity by the Multitrait-Multimethod Matrix. Psychological Bulletin, 56 (2), 81–105.

Cannon, J. P., & Homburg, C. (2001). Buyer–supplier Relationships and Firm Costs. Journal of Marketing, 65 (1), 29–43.

Churchill, G. A. (1979). A paradigm for developing better measures of marketing constructs. Journal of Marketing Research, 16 (1), 64–73.

Article   Google Scholar  

Farrell, A. M. (2010). Insufficient discriminant validity: A comment on Bove, Pervan, Beatty, and Shiu (2009). Journal of Business Research, 63 (3), 324–327.

Finn, J. D. (1974). A general model for multivariate analysis. New York: Holt, Rinehart, & Winston.

Folger, R. (1989). Significance Tests and the Duplicity of Binary Decisions. Psychological Bulletin, 106 (1), 155–160.

Fornell, C., & Larcker, D. F. (1981). Evaluating Structural Equation Models with unobservable variables and measurement error. Journal of Marketing Research, 18 (1), 39–50.

Frambach, R. T., Prabhu, J., & Verhallen, T. M. M. (2003). The Influence of Business Strategy on New Product Activity: The Role of Market Orientation. International Journal of Research in Marketing, 20 (4), 377–397.

Grewal, R., Cote, J. A., & Baumgartner, H. (2004). Multicollinearity and Measurement Error in Structural Equation Models: Implications for Theory Testing. Marketing Science, 23 (4), 519–529.

Harris, L. C., & Goode, M. M. H. (2004). The four levels of loyalty and the pivotal role of trust: a study of online service dynamics.  Journal of Retailing, 80 , 139–158.

Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43 , 115–135.

Hu, L., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3 (4), 424–453.

Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6 (1), 1–55.

Jap, S. D. (2001). “Pie Sharing” in Complex Collaboration Contexts. Journal of Marketing Research, 38 (1), 86–99.

Joreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 36 (4), 409–426.

Kohli, A. K., Shervani, T. A., & Challagalla, G. N. (1998). Learning and Performance Orientation of Salespeople: The Role of Supervisors. Journal of Marketing Research, 35 (2), 263–274.

Lord, F. M. (1957), A signif'icance test for the hypothesis that two variables measure the same trait except for errors of'measurement, Psychometrika , 207–220.

Low, G. S., & Mohr, J. J. (2001). Factors Affecting the Use of Information in the Evaluation of Marketing Communications Productivity. Journal of the Academy of Marketing Science, 29 (1), 70–88.

Lytle, R. S., Hom, P. W., & Mokwa, M. P. (1998). SERV*OR: A Managerial Measure of Service Orientation. Journal of Retailing, 74 (4), 455–589.

Mathwick, C., & Rigdon, E. (2004). Play, Flow, and the Online Search Experience. Journal of Consumer Research, 31 (2), 324–332.

Mathwick, C., Malhotra, N., & Rigdon, E. (2001). Experiential Value: Conceptualization, Measurement, and Application in the Catalog and Internet Shopping Environment. Journal of Retailing, 77 (1), 39–56.

Maxham, J. G., & Netemeyer, R. G. (2002). A Longitudinal Study of Complaining Customers’ Evaluations of Multiple Service Failures and Recovery Efforts. Journal of Marketing, 66 (4), 57–71.

Peter, J. P. (1981). Construct Validity: A Review of Basic Issues and Marketing Practices. Journal of Marketing Research, 18 (2), 133–145.

Pollard, P. (2014), How Significant is ‘Significance’? in A Handbook for Data Analysis in the Behaviorial Sciences, Volume 1: Methodological Issues Volume 2: Statistical Issues, 449

Rich, G. A. (1997). The Sales Manager as a Role Model: Effects on Trust, Job Satisfaction, and Performance of Salespeople. Journal of the Academy of Marketing Science, 25 (4), 319–328.

Spreng, R. A., MacKenzie, S. B., & Olshavsky, R. W. (1996). A Reexamination of the Determinants of Consumer Satisfaction. Journal of Marketing, 60 (3), 15–32.

Wang, G., & Netemeyer, R. G. (2002). The effects of job autonomy, customer demandingness, and trait competitiveness on salesperson learning, self-efficacy, and performance. Journal of the Academy of Marketing Science, 30 (3), 217–228.

Yilmaz, C., & Hunt, S. D. (2001). Salesperson Cooperation: The Influence of Relational, Task, Organizational, and Personal Factors. Journal of the Academy of Marketing Science, 29 (4), 335–357.

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Acknowledgments

The authors would like to thank Peter Bentler for his comments on an earlier version of the simulations used in this paper.

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Department of Marketing, The Eli Broad Graduate School of Management, Michigan State University, N370 North Business Complex, East Lansing, MI, 48824-1122, USA

Clay M. Voorhees & Roger Calantone

Department of Marketing, Florida State University, 821 Academic Way, Tallahassee, FL, 32306-1110, USA

Michael K. Brady

Department of Marketing and Management, College of Business Administration, University of Texas at El Paso, 500 West University Avenue, El Paso, TX, 79968-0539, USA

Edward Ramirez

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Correspondence to Clay M. Voorhees .

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Voorhees, C.M., Brady, M.K., Calantone, R. et al. Discriminant validity testing in marketing: an analysis, causes for concern, and proposed remedies. J. of the Acad. Mark. Sci. 44 , 119–134 (2016). https://doi.org/10.1007/s11747-015-0455-4

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Received : 11 February 2015

Accepted : 10 June 2015

Published : 07 July 2015

Issue Date : January 2016

DOI : https://doi.org/10.1007/s11747-015-0455-4

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