CU-MBA-SEM-IV-Marketing Analytics

Understanding psychology: purchase hierarchies Choice-based conjoint analysis is also used to identify which attributes people regard as being most important (i.e., purchase hierarchies), which is useful to know for a wide variety of marketing planning purposes (e.g., new product design, store layout, communications messaging). Understanding psychology: preferences for attribute levels One of the key outputs of a choice-based conjoint analysis study is an estimate of the utility of different attribute levels. For example, in a study of chewing gum, the study will estimate the relative appeal of different flavors (spearmint, peppermint, apple, etc.). This is useful in planning future products and product modifications. Product optimization Where detailed information is known about the cost of different attribute levels, products can be optimized to maximize the net overall benefit. For example, working out the optimal structure of employment benefits (e.g., salary, versus lunch, versus health benefits). Computing brand equity Where brand is used as an attribute in a choice-based conjoint analysis study, the utility estimated for each brand becomes an estimate of brand equity, which is defined in this case as the relative strengths of brands when their features are at parity. Market segmentation Choice models are routinely used for market segmentation, as it leads to segments which different in terms of purchase hierarchies and preferences for attribute levels, which usually ensures that the segments are actionable in terms of marketing planning. Want to read more about choice-based conjoint analysis? Check out Writing a Questionnaire for a Choice-Based Conjoint Analysis Study! As such, conjoint analysis is an excellent means of understanding what product attributes determine a customer’s ability to pay & willingness to pay. It’s a method of learning what features a customer is willing to pay for and whether they’d be willing to pay more. Conjoint Analysis in Business operation, Sales & Marketing Conjoint analysis can inform more than just a company’s pricing strategy to inform how it markets and sells its offerings. When a company knows which features its customers value most, it can lean into them in its advertisements, marketing copy, and promotions. For example, an online store selling chocolate may find through conjoint analysis that its customers primarily value two features: Quality and the fact that a portion of each sale goes toward funding environmental sustainability efforts. The company can then use that input 201 CU IDOL SELF LEARNING MATERIAL (SLM)

&data information to number of different messaging and appeal to each segment's specific value. Conjoint Analysis in Research & Development Conjoint analysis can also inform a company’s research and development pipeline. For example, consider a smartphone manufacturer that conducts a conjoint analysis and discovers its customers value larger screens over all other features. With this information, the company might logically conclude that the best use of its product development budget and resources would be to develop larger screens. If, however, future analyses reveal that customer value has shifted to a different feature—for example, audio quality—the company may use that information to pivot its product development plans. Additionally, a company may use conjoint analysis to narrow down its product or service’s features. Returning to the smartphone example: There’s only so much space within a smartphone for components. How a phone manufacturer’s customers value different features can inform which components make it into the end product—and which are cut. 13.8 SUMMARY  What is Cluster Analysis? • Cluster is a collection of information , inputs & data objects – Similar to one another within the same cluster – Dissimilar to the objects in other clusters • Cluster analysis – Grouping a set of data objects into clusters • Clustering is unsupervised classification: no predefined classes  Cluster analysis is a statistical classification technique in which a set of objects or points with similar characteristics are grouped together in clusters. It encompasses a number of different algorithms and methods that are all used for grouping objects of similar kinds into respective categories. The aim of cluster analysis is to organize observed data into meaningful structures in order to gain further insight from them.  Conjoint analysis is an advanced market research technique that gets under the skin of how people make decisions and quantifies what customers really value in products and services. Conjoint analysis, also known as Discrete Choice Estimation, or stated preference research, involves presenting people with realistic product choices and then analyzing what features most drive purchasing decisions.  Reports & Outputs from conjoint analysis are measurements of customer value called utility scores or part-worth. Utility scores can be combined to build market models and forecasts to answer questions such as \"we should be building in more features, or bring our prices down?\" or \"Which of these changes will hurt our competitors most?\" to allow the business to better optimize product and service design to customer needs.  See conjoint analysis in action via our interactive Conjoint Demonstration, our simple conjoint in Excel to see how conjoint analysis works numerically, or use our Conjoint Explorer to design your own conjoint experiment. 202 CU IDOL SELF LEARNING MATERIAL (SLM)

 Every customer making choices between products and services is faced with trade- offs (see our conjoint demonstration). Is high quality more important than a low price and quick delivery for instance? Or is good service more important than design and looks?  For businesses, understanding precisely how customers value different elements of a product or service means product development can be optimized to give the best balance of features or quality for the prices the customer is willing to pay. Across a market as a whole, this can be used to define the best product range for different segments or market needs, balancing features, value and price across a product set in order to maximize customer value and market returns. 13.9 KEYWORDS  Conjoint analysis:With on-going development and improvements since it was invented in the 1970.  Cluster analysis or clustering: is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).  K-Means Cluster: This method is used to quickly cluster large datasets. Here, researchers define the number of clusters prior to performing the actual study  Two-Step Cluster: This method uses a cluster algorithm to identify groupings by performing pre-clustering first, and then performing hierarchical methods  Discrete choice-based conjoint (CBC) analysis:This type of conjoint study is the most popular because it asks consumers to imitate the real market’s purchasing behavior: which products they would choose, given specific criteria on price and features. 13.10 LEARNING ACTIVITY 1. What is Cluster Analysis? ___________________________________________________________________________ _____________________________________________________________________ 2. What are the benefits of Cluster Analysis in Marketing? ___________________________________________________________________________ _______________________________________________________________ 3. Define the concept of Conjoint Analysis? ___________________________________________________________________________ _______________________________________________________________ 203 CU IDOL SELF LEARNING MATERIAL (SLM)

13.11 UNIT END QUESTIONS A. Descriptive Questions Short Questions 1. Define Web Analytics 2. What is purpose of Web Analytics? 3. What is thepurpose of Web Analytics? 4. Define the concept of Sentiment Analysis 5. Explain importance of Sentiment Analysis in Marketing Long Questions 1. What is importance of Web Analytics? 2. Explain the steps of Web Analytics 3. How Does Web Analytics work? 4. What reports can be analysed through Web Analytics? 5. What is the scope of Sentiment Analysis? 6. Explain the different types of Sentiment Analysis? 7. Define the steps in Sentiment Analysis? 8. What are the benefits of Sentiment Analysis? 9. What are the various challenges that Sentiment Analysis has to handle with? B. Multiple choice Questions 1. Web Analytics is part of ________ a. Product b. Customer Data Analysis c. Customer Meet d. Test Marketing 2. Web analytics is very useful in ___________ 204 a. Google Analytics b. Market Survey c. Customer & Data Analysis d. Marketing Analytics CU IDOL SELF LEARNING MATERIAL (SLM)

3. Important elements of web analytics are _________& ____________ a. Each Lead & Website visit b. Direct Sales Report & Sales Forecast c. Marketing Feedback & Customer Response d. Exit Rate & Bounce Rate 4. Sentiment Analysis is a connection with ________ a. Sales Analysis b. Digital Marketing c. Consumer Behaviours d. Product Development 5. The Sentiment Analysis has a huge impact with _____________ a. Customer Purchases b. Customer & Competition c. Distribution d. Sales Reports Answers 1-b, 2-d, 3-d, 4-c, 5-a. 13.12 REFERENCES Textbooks  T1 Grigsby, M. 2115. Marketing Analytics: A practical guide to real marketing science, Its Ed., Kogan Page, India, ISBN: 978-0749474171.  T2 Winston, W. 2114.Marketing Analytics: Data Driven Technique using MS. Excel. Ist Ed. John Wiley & Sons, India, ISBN: 978-1118373439. Reference Books:  R1 Grigsby, M. 2116. Advanced Customer Analytics: Targeting, Valuing, Segmenting and Loyalty Techniques (Marketing Science). Ist Ed. Kogan Page. India. ISBN: 978-0749477158. Websites 205 CU IDOL SELF LEARNING MATERIAL (SLM)

 https://springer.com  https://michaelpawlicki.com  https://statisticshowto.com  https://stattrek.com  https://slideshare.com 206 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT 14: MDS & DISCRIMINANT ANALYSIS STRUCTURE 14.0 Learning Objectives 14.1 Introduction of MDS 14.2 Concepts of MDS 14.3 Importance of MDS 14.4 Process of MDS 14.5 Concept of Discriminant Analysis 14.6 Various Steps in Discriminant Analysis 14.7 Summary 14.8 Keywords 14.9 Learning Activity 14.10 Unit End Questions 14.11 References 14.0 LEARNING OBJECTIVES After studying this unit, you will be able to  The Fundamental elements of multimedia.  It will provide an understanding of the fundamental elements in multimedia.  The emphasis will be on learning the representations, perceptions and applications of multimedia.  Software skills and hands on work on digital media in business. 14.1 INTRODUCTION OF MDS Multidimensional scaling (MDS), also called perceptual mapping, is based on the comparison of objects (persons, products, companies, services, ideas, etc.). The objectives of MDS are to identify the relationships between objects and to represent them in geometrical form. MDS is a set of various procedures that allows the manager to gauge distances between objects in a multidimensional space into a lower-dimensional space in order to show how the objects are related. MDS was introduced by Torgerson (1952). It has its origins in psychology where it was used to understand respondents’ opinions on similarities or dissimilarities between objects. MDS is also used in sale & marketing by top management, finance, sociology, information science, 207 CU IDOL SELF LEARNING MATERIAL (SLM)

political science, physics, biology, ecology, etc. For example, it will be beneficial to understand the perceptions of respondents, new customers to identify unrecognized dimensions, for segmentation analysis, to position these different brands, to position companies, and so on. It is a Multidimensional scaling is one of several multivariate techniques that aim to reveal the structure of a data set by plotting points in one or two dimensions. The basic idea can be motivated by a geographical example. Multidimensional scaling (MDS) is a very useful technique for market researchers because it produces an invaluable \"perceptual map\" revealing like and unlike products, thus making it useful in brand similarity studies, product positioning, and market segmentation. Multidimensional scaling (MDS) refers to a family of models in which the structure in a set of data is represented graphically by the relationships between a set of points in a space. MDS has many useful on a wide variety of data, using different models and allowing different assumptions about the level of measurement. It introduces how multimedia can be used in various application areas. It provides a solid foundation to the students so that they can identify the proper applications of multimedia, evaluate the appropriate multimedia systems and develop effective multimedia applications. What Is (MDS) Multidimensional Scaling? In simple words Multidimensional scaling is the visual representation of distances or dissimilarities between sets of objects. It can also be defined as a means of visualizing the level of similarity of individual cases of a dataset. Multidimensional scaling or MDS is a form of non-linear dimensionality reduction. The objects of the dimensional scale can be anything like colors, faces, map coordinates, political persuasion, or any real or conceptual stimuli. The term scaling comes from psychometrics and it benefits to measure the parity between the objects. For instance, you are looking for quantify a person's attitude to feminism. You could assign a ‘1' to ‘do believe in the ideology of feminism' a ‘10' to ‘firmly believe in feminism'. The scale of 2-9 will be used to interpret the parity in attitudes in between. Read on to know how multidimensional scaling is essential in marketing research. 14.2 CONCEPTS OF MDS Multidimensional scaling is a visual representation of distances or dissimilarities between sets of objects. “Objects” can be colours, logs, images face, map coordinates, political persuasion, or any kind of real or conceptual stimuli (Kruskal and Wish, 1978) Basic concepts in multidimensional scaling (MDS) Multidimensional Scaling (MDS) are a class of procedures for representing perception and preferences of respondents spatially by means of a visual display will be useful for Perceived or psychological relationships among 208 CU IDOL SELF LEARNING MATERIAL (SLM)

points in a multidimensional space. These geometric representations are often called spatial maps. The axes of the spatial map are assumed to denote the psychological bases or underlying dimensions respondents use to form perceptions and preferences for stimuli.  Places, Channel decisions. Judgments on compatibility of brands with different retail outlets could lead to spatial maps useful for making channel decisions.  Attitude scale construction. MDS techniques can be used to develop the appropriate dimensionality and configuration of the attitude space 14.3 IMPORTANCE OF MDS Multidimensional scaling (MDS) is a technique that creates a map displaying the relative positions of a number of objects, given only a table of the distances between them. The map may consist of one, two, three, or even more dimensions. The program calculates either the metric. In marketing, Multidimensional scaling (MDS) is a statistical technique for taking the preferences and perceptions of respondents and representing them on a visual grid. These grids, called perceptual maps are usually two-dimensional, but they can represent more than two or the non-metric solution.  MDS has been used in sales & marketing to review:  The number and nature of dimensions consumers use to perceive different brands in the marketplace  The positioning of current brands on these dimensions  The positioning of consumers ideal brand on these dimensions.  Information by MDS has been used for a variety of marketing applications, including:  Image measurement. Compare the customers’ and noncustomers’ perceptions of the firm with the firm’s perceptions of it and thus identify perceptual gaps.  Market segmentation. Position brands and consumers in the same space and thus identify groups of consumers with relatively homogeneous perceptions.  New product development. To look for gaps in the spatial map, which indicate potential opportunities for positioning new products? Also, to evaluate new product concepts and existing brands on attest basis to determine how consumers perceive the new concepts. The proportion of preferences for each new product is one indicator of its success.  Assessing advertising effectiveness. Spatial maps can be used to determine whether advertising has been successful in achieving the desired brand positioning.  Pricing analysis. Spatial maps developed with and without pricing information can be compared to determine the impact of pricing. 14.4 PROCESS OF MDS The basic steps in a non-metric MDS algorithm are: 209 CU IDOL SELF LEARNING MATERIAL (SLM)

1. Find a random configuration of points, e. g. by sampling from a normal distribution. 2. Calculate the distances d between the points. 3. Find the optimal monotonic transformation of the proximities, in order to obtain optimally scaled data How Multidimensional Scaling Works? The process that multidimensional scaling follows while working is simple. Multidimensional scaling has problems that can deliver improper results. It is applied by using a square that is known as a symmetric matrix for input. The matrix shows the relationship between the items in the scale. Here are some of the basic steps that you need to follow while using a multidimensional scale.  Please assign a number of points to coordinates in n-dimensional space: The ‘N’ space in the scale is the central dimension. The ‘N’ dimensional space of the symmetric matrix can be 2-dimensional or 3-dimensional at the same time. There are specific coordination axes that work to measure the scale. These axes work to find out the proximity among various scales in the multidimensional sphere.  Calculating Euclidean distance for all pairs of points: The straight line between the two ‘X' of the scale is the Euclidean space. It helps to measure the distance and calculate the time to cover the distance. This is the simple process in which multidimensional scaling works. Methods for Multidimensional Scaling In the simplest problems, one matrix is used and the dissimilarities are symmetric. An example of such a matrix is the matrix of intercity mileages often found on road maps, where the distance among two cities is the dissimilarity measure. Often one matrix is observed. For example, several different mapmakers' estimations of the distances between cities may be observed. Since each mapmaker may use different methods for measuring distance, different distance matrices will result. Regardless of the number of matrices observed, the MDS problem is to locate the stimuli (cities) in a multidimensional space of known dimension based upon the observed dissimilarities. 1. The Distance Measures A dissimilarity matrix may not be a symmetric. A of multidimensional scaling data with asymmetric dissimilarity matrices is given in Table 1. The stimuli are seven stores and the observed dissimilarity is the rank of the distance of the column store from the row store. In other words, for each row, the column store with rank 1 is near to row store, the column store with rank 2 is second closest, etc. This matrix is clearly not symmetric since the dissimilarity measures dij≠djidij≠dji. Moreover, due of the method used for data collection, comparison of ranks in row ii with ranks in row jj should not be made. 210 CU IDOL SELF LEARNING MATERIAL (SLM)

Fig. 14.1 Historically, there are four types of dissimilarity data have most often been considered as input in multidimensional scaling problems:  Nominal data using categories for distance. (Distances corresponding to dissimilarities within the said category are assumed identical).  Ordinal data, as in the example above, using the rank of the distance.  Interval data, using distance plus a constant.  Ratio data, using distance. Models involving ratio or interval data are called metric scaling models, while models with nominal or ordinal data are called non-metric scaling models. Distance need not be Euclidean. For example, r2pqrpq2 could be used as the distance measure between stimuli pp and qq, where r2pqrpq2 is the correlation coefficient between variables pp and qq. 2. The Sampling/Measurement Method Another common consideration in multidimensional scaling is the sampling/measurement scheme used in collecting the required data. In the above example, because the rankings were made within each row, comparisons of ranks between rows are not meaningful. If instead a dissimilarity matrix is provided by each of two judges, then the dissimilarities between the two matrices cannot be compared unless it can be verified that the two judges used the same scale and judging criteria. In general, the sampling/measurement scheme used to obtain the data determines strata (or conditionality groups) within which dissimilarities can be compared, while comparison of dissimilarities between strata does not make sense. Three sampling/measurement schemes are as below: 211 CU IDOL SELF LEARNING MATERIAL (SLM)

 If sampling/measurement is such that all dissimilarity measures can be compared, then the required data come from a single stratum and are said to be unconditional data.  If only dissimilarity measures within a matrix can be compared, then each matrix is a stratum, and the data are said to be matrix conditional.  If sampling is such that only dissimilarity measures within a row of each dissimilarity matrix can be compared, then each row of each matrix is a stratum, and the data are said to be row conditional. 3. A Distance Model Generally, the stimuli are located in an ττ-dimensional Euclidean space, τ≥1τ≥1, in such a manner that the agreement between the observed dissimilarities (whether ordinal, ratio, etc.) and the predicted distances is in some sense optimal. In order to locate the stimuli, some model for the distance between stimuli must be specified. In this example, the model is Euclidean and is given by: δij= ⎷ τ∑k=1(Xik−Xjk)2 δij=∑k=1τ(Xik−Xjk)2 Where XikXik is the coordinate of the ithith stimulus in the kthkth of ττ dimensions in the Euclidean space and the matrix XX is called the configuration matrix. For a given XX, the model gives the distances between all stimuli. Since the distance between stimuli is translation invariant, the location of the origin is arbitrary. In the following, the origin is assumed to be zero, so that ∑iXik=0∑iXik=0. Also, the Euclidean model, unlike other distance models, is rotation invariant (i.e., multiplying XX by an orthogonal matrix T,X=XTT,X=XT yields the same distance measures). This means that the configuration obtained is not unique rotationally. Usually, no attempt is made for the Euclidean model to obtain a unique solution with respect to rotation, although any of the orthogonal rotations in factor analysis could be used for this purpose. 4. A Criterion Function In order to estimate parameters, a criterion function, usually called the stress function, may be minimized. In this example, the stress function is given as: q=∑ni=1∑nj=1(~δij−δij)2∑ni=1∑nj=1(~δij)2=ωn∑i=1n∑j=1(~δij−δij)2q=∑i=1n∑j=1n(δ~ij −δij)2∑i=1n∑j=1n(δ~ij)2=ω∑i=1n∑j=1n(δ~ij−δij)2 Where nn is the number of stimuli and ~δδ~ denotes the optimal dissimilarities, called the disparities. In metric data, qq is optimized with respect to δδ only, whereas in non-metric data, q is optimized with respect to both δδ and the disparities ~δijδ~ij. Let ^δδ^ denote predicted 212 CU IDOL SELF LEARNING MATERIAL (SLM)

values of δδ. Disparities in non-metric data are found from the predicted distances ^δδ^, such that the rank requirements of ordinal data or the equivalence requirements of nominal data are satisfied and an optimal criterion function is obtained. With the stress qq above, ordinal data disparities are optimal when they are taken as the monotonic regression of ^δδ^ on the observed ranks within each stratum. In categorical data, the disparities ~δδ~ are optimal when they are estimated as the average of all ^δδ^ within the same category and stratum. The numerator in the above criterion function is a least squares criterion, whereas the denominator (or ωω ) is a scaling factor. Scaling is required in non-metric data to prevent the solution from becoming degenerate. If the denominator were not present, qq could be made as small as desired by simultaneously scaling both ^δδ^ and ~δδ~ downward. Different criterion functions are often used in metric data, which do not have this scaling requirement. 5. Monotonic Regression A good example of the monotonic regression used in optimizing ~δδ~ in ordinal data, consider the following table in which the data corresponds to the store example discussed above. Fig. 14.2 In this table, the rank of the distance between each store and store 7 is given in the second row. Using the estimated configuration matrix ^XX^, the predicted distances ^δδ^ are computed in the third row of the table, while the disparities ~δδ~ are given in the fourth row. Note in the third row that the predicted distances (.69, .65, and .44) for stores 1, 3, and 6 are not in the order required by the observed ranks. Because the disparities must preserve the observed ranks, the order in the estimated disparities must be reversed from the order obtained from ^δδ^. In order to accomplish this, the monotonic regression averages adjacent elements of ^δδ^ as required to obtain ~δδ~. (See Barlow, Bartholomew, Brunk, and Bremmer (1972) for a discussion of how to determine when averaging is “required.” ) This results in the disparities given in the fourth row, in which the first three predicted distances are averaged, as are predicted distances 4 and 5. The resulting ~δδ~ preserves the rank requirements of the observed data and is as close as possible to ^δδ^, in the least squares sense. 213 CU IDOL SELF LEARNING MATERIAL (SLM)

Examples of Multidimensional Scaling Multidimensional scaling (MDS) is an essential tool in finding out and determining the strategy of product positioning. According to many market researchers, MDS can create ‘perceptual maps' that will help the companies to assess the market position and sell their products. There are many technical examples of MDS that students may find to be challenging. Here is a practical example that shows how MDS is necessary for every market researcher when they plan to boost the business with appropriate positioning of the product. Here is an example: A spirits manufacturer planned the optimal positioning of one of his products – herb liqueur – within the competitive environment. With this in mind, a tracking study was put in place to monitor specific changes in the product over a long period. 9 items were defined related to the objective. It was checked by identifying the key dimensions. The factor analysis showed that the items could be classified into the three key rating dimensions, \"taste, contents and effect\". Three dimensions were used accordingly to create a graphical presentation. Dimension 1 Dimension 2 Dimension 3 Taste of the herbs Contents of the products Effect · Pleasant taste · High alcohol content · Easily digestible · Please aroma · Musty substances · Strong aftertaste · Fresh taste · Bitter herbs · Well-tolerated · Savory Taste Table 1: Example of the usage of multidimensional scaling In the example shown above, you can understand how the scaling works to find out the value of the product. Accordingly, the manufacturer can implement changes in the product (if needed) and position it in the market. 14.5 CONCEPTS OF DISCRIMINANT ANALYSIS Discriminant analysis is a technique that is used by the researcher to analyze the research data when the criterion or the dependent variable is categorical and the predictor or the independent variable is interval in nature. The term categorical variable means that the dependent variable is divided into a number of categories. For example, three brands of computers, Computer A, Computer B and Computer C can be the categorical dependent variable. 214 CU IDOL SELF LEARNING MATERIAL (SLM)

The objective of discriminant analysis is to develop discriminant functions that are nothing but the linear combination of independent variables that will discriminate between the categories of the dependent variable in a perfect manner. It enables the researcher to examine whether significant differences exist among the groups, in terms of the predictor variables. It also evaluates the accuracy of the classification. 14.6 VARIOUS STEPS IN DISCRIMINANT ANALYSIS Process of conducting Discriminant analysis (DA) Discriminant analysis (DA) is to predict group membership (DV – Categorical variable) from a set of predictors (IV – Continuous variables). Thus, DA is MANOVA turned around. Research question: Do PERF, INFO, VERBEXP permit he classification of students by types of learning disabilities? DV: Types of learning disabilities (3 groups)  Memory: Children whose major difficulty seems to be with tasks related to memory;  Perception: Children who show difficulty in visual perception;  Communication: Children with language difficulty. IVs (predictors):  PERF: Performance Scale IQ of the WISC;  INFO: Information subtest of the WISC;  VERBEXP: Verbal Expression subtest of the ITPA; Discriminant analysis is a 7-step procedure. Step 1: Collect training data Training data are data with known group memberships. Here, we actually know which population contains each subject. For example, in the Swiss Bank Notes, we actually know which of these genuine notes are and which others are counterfeit examples. Step 2: Prior Probabilities The prior probability pi represents the expected portion of the community that belongs to population πi. There are three common choices: 1. Equal priors: p^i=1g This is useful if we believe that all of the population sizes are equal 2. Arbitrary priors selected according to the investigator’s beliefs regarding the relative population sizes. Note! We require: p^1+p^2+⋯+p^g=1 3. Estimated priors: 215 CU IDOL SELF LEARNING MATERIAL (SLM)

p^i=niN where ni is the number observations from population πi in the training data and N=n1+n2+…+ng Step 3: Bartlett's test Use Bartlett’s test to determine if the variance-covariance matrices are homogeneous for all populations involved. The result of this test will determine whether to use Linear or Quadratic Discriminant Analysis.: Case 1: Linear Linear discriminant analysis is for homogeneous variance-covariance matrices: Σ1=Σ2=⋯=Σg=Σ In this case the variance-covariance matrix does not depend on the population. Case 2: Quadratic Quadratic discriminant analysis is used for heterogeneous variance-covariance matrices: Σi≠Σj for some i≠j This allows the variance-covariance matrices to depend on the population. Note! We do not discuss testing whether the means of the populations are different. If they are not, there is no case for DA Step 4: Estimate the parameters of the conditional probability density functions f (X|πi). Here, we shall make the following standard assumptions: 1. The data from group i has common mean vector μi 2. The data from group i has common variance-covariance matrix Σ. 3. Independence: The subjects are independently sampled. 4. Normality: The data are multivariate normally distributed. Step 5: Compute discriminant functions. This is the rule to classify the new object into one of the known populations. Step 6: Use cross validation to estimate misclassification probabilities. As in all statistical procedures, it is helpful to use diagnostic procedures to assess the efficacy of the discriminant analysis. We use cross-validation to assess the classification probability. Typically, you are going to have some prior rule as to what is an acceptable misclassification rate. Those rules might involve things like, \"what is the cost of misclassification?\" This could come up in a medical study where you might be able to diagnose cancer. There are really two alternative costs. The cost of misclassifying someone as having cancer when they don't. This 216 CU IDOL SELF LEARNING MATERIAL (SLM)

could cause a certain amount of emotional grief! There is also the alternative cost of misclassifying someone as not having cancer when in fact they do have it. The cost here is obviously greater if early diagnosis improves cure rates. Step 7: Classify observations with unknown group memberships. The procedure described above assumes that the unit or subject being classified actually belongs to one of the considered populations. If you have a study where you look at two species of insects, A and B, and the insect to classify actually belongs to species C, then it will obviously be misclassified as to belonging to either A or B. 14.7 SUMMARY  There are many examples that can explain when discriminant analysis fits. It can be used to know whether heavy, medium and light users of soft drinks are different in terms of their consumption of frozen foods. In the field of psychology, it can be used to differentiate between the price sensitive and non-price sensitive buyers of groceries in terms of their psychological attributes or characteristics. In the field of business, it can be used to understand the characteristics or the attributes of a customer possessing store loyalty and a customer who does not have store loyalty.  Discriminant analysis requires the researcher to have measures of the dependent variable and all of the independent variables for a large number of cases. In regression analysis and ANOVA, the dependent variable must be a \"continuous variable.\" A numeric variable indicates the degree to which a subject possesses some characteristic, so that the higher the value of the variable, the greater the level of the characteristic. A good example of a continuous variable is a person's income.  Variable Selection Method. In addition to the direct-entry method, you can specify any of several stepwise methods for entering variables into the discriminant analysis using the METHOD subcommand. You can set the values for the statistical criteria used to enter variables into the equation usingthe TOLERANCE, FIN, PIN, FOUT, POUT, and VIN subcommands, and you can specify inclusion levels on the ANALYSIS subcommand. You can also specify the maximum number of steps in a stepwise analysis using the MAXSTEPS subcommand.  Case Selection. You can select a subset of cases for the analysis phase using the SELECT subcommand.  Prior Probabilities. You can specify prior probabilities for membership in a group using the PRIORS subcommand. Prior probabilities are used in classifying cases.  New Variables. You can add new variables to the active dataset containing the predicted group membership, the probability of membership in each group, and discriminant function scores using the SAVE subcommand. 217 CU IDOL SELF LEARNING MATERIAL (SLM)

 Classification Options. With the CLASSIFY subcommand, you can classify only those cases that were not selected for inclusion in the discriminant analysis, or only those cases whose value for the grouping variable was missing or fell outside the range analyzed. In addition, you can classify cases based on the separate-group covariance matrices of the functions instead of the pooled within-groups covariance matrix.  Statistical Display. You can request any of a variety of statistics on the STATISTICS subcommand. You can rotate the pattern or structure matrices using the ROTATE subcommand. You can compare actual with predicted group membership using a classification results table requested with the STATISTICS subcommand or compare any of several types of plots or histograms using the PLOT subcommand.  Basic Specification The basic specification requires two subcommands:  GROUPS specify the variable used to group cases.  VARIABLES specify the predictor variables. 14.8 KEYWORDS  Multidimensional scaling (MDS), also called perceptual mapping, is based on the comparison of objects (persons, products, companies, services, ideas, etc.).  Discriminant analysis is a technique that is used by the researcher to analyze the research data when the criterion or the dependent variable is categorical and the predictor or the independent variable is interval in nature.  Multidimensional scaling is a useful tool to help quantify the ubiquitous, but slippery, notion of similarity. Although we all know what it means for two things to share a sense of closeness, similarity is difficult to estimate empirically.  Variable Selection Method. In addition to the direct-entry method, you can specify any of several stepwise methods for entering variables into the discriminant analysis using the METHOD subcommand.  Statistical Display. You can request any of a variety of statistics on the STATISTICS subcommand. 14.9 LEARNING ACTIVITY 1. What are MDS? ___________________________________________________________________________ _____________________________________________________________________ 2. What are the benefits of MDS in Modern Marketing? 218 CU IDOL SELF LEARNING MATERIAL (SLM)

___________________________________________________________________________ _____________________________________________________________________ 3. Define the concept of Discriminant Analysis? ___________________________________________________________________________ _______________________________________________________________ 14.10 UNIT END QUESTIONS A. Descriptive Questions Short Questions 1. Explain the concept of MDS 2. What is purpose of MDS? 3. What are the objectives of MDS? 4. Explain the concept of Discriminant Analysis 5. Explain importance of Discriminant Analysis in Marketing Long Questions 1. What is importance of MDS? 2. Explain the steps of MDS 3. How Does MDS works? 4. What data you analyse through Discriminant Analysis? 5. What are the benefits of Discriminant Analysis? B. Multiple choice Questions 1. MDS is part of ________ a. Product b. Customer Data Analysis c. Customer Meet d. Sampling 2. MDS is very useful in ___________ 219 a. Google Analytics b. Market Survey c. Customer & Data Analysis CU IDOL SELF LEARNING MATERIAL (SLM)

d. Marketing Analytics 3 Important impacts of MDS are _________ a. Direct Sales Report & Sales Forecast b. Marketing Feedback & Customer Response c. New Market Analysis d. Business Research Methods 4. Discriminant Analysis is _________ a. Sales Analysis b. Versatile Statistical Method c. Consumer Behaviours d. Product Development 5. Discriminant Analysis classifies sets of measures in to group on the following _____________ a. Customer Purchases b. Customer & Competition c. Multiple Measure d. Sales Reports Answers 1-b, 2-d, 3-d, 4-b, 5-b. 14.11 REFERENCES Textbooks  T1 Grigsby, M. 2115. Marketing Analytics: A practical guide to real marketing science, Its Ed., Kogan Page, India, ISBN: 978-0749474171.  T2 Winston, W. 2114.Marketing Analytics: Data Driven Technique using MS. Excel. Ist Ed. John Wiley & Sons, India, ISBN: 978-1118373439. Reference Books: 220 CU IDOL SELF LEARNING MATERIAL (SLM)

 R1 Grigsby, M. 2116. Advanced Customer Analytics: Targeting, Valuing, Segmenting and Loyalty Techniques (Marketing Science). Ist Ed. Kogan Page. India. ISBN: 978-0749477158. Websites  https://springer.com  https://michaelpawlicki.com  https://statisticshowto.com  https://stattrek.com  https://slideshare.com 221 CU IDOL SELF LEARNING MATERIAL (SLM)