Multivariate Tests Types of Multivariate Tests Multiple Regression

Multivariate Tests

Types of Multivariate Tests • • • Multiple Regression Factor Analysis Discriminant Analysis Cluster Analysis Conjoint Analysis Multidimensional Scaling

Multiple Regression • Multiple Regression involves developing mathematical relationship between single dependent variable and two or more independent variables. For Example • How much of the variations in sales can be explained by advertising expenditures, prices and level of distribution • How much of the variations in market shares can be explained by the size of the sales force, advertising expenditure and sales promotion budget

Simple vs. Multiple Regression • One dependent variable Y predicted from one independent variable X • One regression coefficient • r 2: proportion of variation in dependent variable Y predictable from X • One dependent variable Y predicted from a set of independent variables (X 1, X 2 …. Xk) • One regression coefficient for each independent variable • R 2: proportion of variation in dependent variable Y predictable by set of independent variables (X’s)

Multiple Regression The test you choose depends on level of measurement: Independent Variable Dependent Variable Test Dichotomous Interval-Ratio Dichotomous Independent Samples t-test Nominal Dichotomous Cross Tabs Nominal Dichotomous Interval-Ratio Dichotomous ANOVA Interval-Ratio Dichotomous Interval-Ratio Bivariate Regression/Correlation Interval-Ratio Multiple Regression Two or More… Interval-Ratio Dichotomous

Multiple Regression allows us to: n Use several variables at once to explain the variation in a continuous dependent variable. n Isolate the unique effect of one variable on the continuous dependent variable while taking into consideration that other variables are affecting it too. n Write a mathematical equation that tells us the overall effects of several variables together and the unique effects of each on a continuous dependent variable. n Control for other variables to demonstrate whether bivariate relationships are spurious

The Multiple Regression Model building Idea: Examine the linear relationship between 1 dependent (Y) & 2 or more independent variables (Xi) Multiple Regression Model with k Independent Variables: Y-intercept Population slopes Random Error

• The coefficients of the multiple regression model are estimated using sample data with k independent variables Estimated (or predicted) value of Y Estimated intercept Estimated slope coefficients • Interpretation of the Slopes: (referred to as a Net Regression Coefficient) – b 1=The change in the mean of Y per unit change in X 1, taking into account the effect of X 2 (or net of X 2) – b 0 Y intercept. It is the same as simple regression.

Terminologies • Regression Co-efficient β : shows the amount of partial impact created by each of all independent variables on single dependent variable, means impact of each variable in overall impact of all variables • Co-efficient of Multiple Determination R 2: Shows the amount of variations that all independent variables have on single dependent variable • Adjusted R 2: shows the amount of variations that all independent variables have on single dependent variable after removing error from R 2 • Anova (F) Test: Used to confirm that the regression equation is valid

• Topic: Call Center Executive’s Listening Behaviour and Customer Responses Objectives: • To know the relationships among variables of Listening behaviour (Attentiveness, Perceptiveness and Responsiveness) and Customer Responses (Satisfaction, Trust and Call Intention) • To know the Impact of Variables of Listening behaviour on Customer Responses

Regression of attentiveness, perceptiveness and responsiveness on Trust Variables Entered/Removed Model 1 Variables Entered Variables Removed resp, atten, perc Method. Enter a. All requested variables entered. b. Dependent Variable: trust Model 1 R R Square. 186 a Adjusted R Square . 035 a. Predictors: (Constant), resp, atten, perc b. Dependent Variable: trust . 015 Std. Error of the Estimate. 58545

Regression of attentiveness, perceptiveness and responsiveness on Trust Unstandardized Coefficients Model 1 B Standardized Coefficients Std. Error (Constant) 2. 986 . 438 Atten -. 012 . 074 Perc . 169 Resp -. 032 a. Dependent Variable: trust Beta t Sig. 6. 820 . 000 -. 013 -. 158 . 875 . 074 . 186 2. 277 . 024 . 079 -. 032 -. 399 . 690

Factor Analysis • In factor analysis, there is no distinction between dependent and independent variables • It is a data reduction method. • It is very useful method to reduce a large number of variables resulting in data complexity to a few manageable factors. • These factors explain most part of the variations of the original set of data.

Uses of Factor Analysis Scale Construction • Useful to develop concise multiple item scales for measuring various constructs • This study is exploratory in nature where large number of variables are reduced to newer, relevant and important/critical variables. Establish Antecedents • Reduces multiple input variables into grouped factors • Variables in one group are similar and related to common theme/concept

Uses of Factor Analysis Psychographic Profiling • Different independent variables are grouped to measure independent factors • Each group suggests different theme and all the groups together measure the same concept Segmentation Analysis • Variables having grater importance are selected and then grouped in one of the groups • Helpful to identify varying levels of importance to different factors

Example of Factor Analysis – Measuring Services Quality of Transporter Quick Response Flexibility Cost Consideration Correct Delivery Quality of Services Customization of Services Handling of Customer Complaints Use of Technology Shipments in terms of value/volume Total Order Cycle Time On Time Delivery Fill Rates Inventory Accuracy Sensitive Information Sharing Communication System Strategy Building

Variable Name Variation in overall measure Quick Response 0. 847 Flexibility 0. 784 Handling of Customer Complaints 0. 667 Total Order Cycle Time 0. 615 Cost Consideration 0. 843 On Time Delivery 0. 657 Use of Technology 0. 616 Correct Delivery 0. 549 Quality of Services 0. 843 Customization of Services 0. 730 Inventory Accuracy 0. 814 Shipments in terms of 0. 812 value/volume Fill Rates 0. 654 Communication System 0. 866 Sensitive Information Sharing 0. 625 Factor Name Responsiveness Accuracy Customization Inventory Information Sharing

Discriminant Analysis • A technique for analyzing marketing research data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature.

Objectives of Discriminant Analysis • Develop Discriminant functions which will best discriminate between the categories of the dependent variable • Examination of whether significant differences exist among the groups, in terms of the predictor variable • Determination of which independent variables contribute to most of the intergroup differences • Classification of cases to one of the groups based on the values of the independent variables • Evaluation of the accuracy of classification results

Uses of Discriminant Analysis • In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not? • Do heavy, medium and light users of soft drinks differ in terms of their consumption of baked food? • What psychographic characteristics help differentiate between price-sensitive and non-price-sensitive buyers of home loans? • Do the various levels of employees differ in terms of their preferences towards compensations schemes?

Example of Discriminant Analysis Problem Definition (Dependent variable) • A travel company wants to know the reasons why customers prefer to go for travel (group 1) and customers do not prefer to go for travel (group 2) Factors to consider for decision making (Independent) • Income (high -1, medium – 2 and low – 3) • Family size (three – 1, three to five – 2, more than five -3 ) • Price (Premium– 1, value for money– 2, reasonable– 3) • Incentives (high -1, medium – 2 and low – 3) • Attitude ( 1 – 7, from 1 - low to 7 – high)

Example of Discriminant Analysis Factors affecting decision to prefer travel (Group 1) Factors affecting decision not to prefer travel (Group 2) Income ( + 0. 78) Prize ( + 0. 79) Incentive ( + 0. 98) Family Size ( + 0. 67) Attitude ( + 0. 56)

Cluster Analysis • In cluster analysis, the whole population sample is undifferentiated and the attempts to assess similarity in response to variables and the grouping happens post the clustering • The basic objective is to group objects based on the characteristics they possess. • Cluster analysis groups objects (respondents), while factor analysis groups variables • Grouping of objects are based on distance among responses.

Cluster Analysis • Classifies objects so that each object is similar to others in the cluster based on a set of selected characteristics. • The resulting clusters of objects should exhibit high internal homogeneity and high external heterogeneity. • The cluster variate is required, which is the set of variables representing the characteristics used to compare objects in the cluster analysis • The focus is on the comparison of objects, not the estimation of it.

Uses of Cluster Analysis • Data Reduction – rather than gathering data from entire population, with the help of cluster analysis, required information can be gathered from more concise and small number of groups. • Data Simplification – by defining structure among the objects, it develops a simple structure by grouping observations differently • Hypothesis Generation – useful when a researcher wishes to develop hypothesis concerning the nature of the data or to examine previously stated hypothesis

Uses of Cluster Analysis • Segmentation – objects included in cluster analysis can be grouped differently based on their attitude towards the defined criteria, thus useful to segments the objects • Construct identification – exploratory in nature and find new constructs based on classification of objects • Relationship Identification – with clusters defined, the researcher has a means of revealing relationships among the observations like similarities and differences.

Example of Cluster Analysis Objective • On the basis of 100 firms employees transporters, company wants to know the characteristics (reasons for) of firms with respect to selection of transporters. Factors to consider • Responsiveness • Accuracy • Customization • Inventory • Information Sharing

Example of Cluster Analysis Customer Orientation (Cluster 1) Service Orientation (Cluster 2) Responsiveness (20) Accuracy (22) Customization (18) Inventory (25) Information Sharing (25)

Conjoint Analysis • Multivariate technique helpful to understand how respondents develop preferences for any type of object (product, service or ideas) • It is based on the simple premise that consumers evaluate the value of an object by combining the separate amounts of value provided by each attribute • Consumers can best provide their estimates of preference by judging objects formed by combinations of attributes.

Conjoint Analysis -Utility • Judgment of preference unique to each individual • Utility encompasses all features of the object, both tangible and intangible • Utility is assumed to be based on the value placed on each of the levels of the attributes in different combinations • Utility is expressed by a relationship reflecting the manner in which the utility is formulated for any combination of attributes

Uses Conjoint Analysis • Can determine possible different combinations of attributes for a given stimuli • Can define consumer preferences towards unique combination of different attributes • Can determine the best combination of different attributes that majority of the consumers prefer • Can determine the relative importance of each attribute in relation to other attributes

Multi Dimensional Scaling • Multidimensional scaling (MDS) is a series of techniques that helps the analyst to identify key dimensions underlying respondents’ evaluations of objects. Once the data is in hand, multidimensional scaling can help determine: • what dimensions respondents use when evaluating objects • how many dimensions they may use in a particular situation • the relative importance of each dimension, and • how the objects are related perceptually

Purpose of MDS • The purpose of MDS is to transform consumer judgments of similarity or preference (eg. preference for stores or brands) into distances represented in multidimensional space. The resulting perceptual maps show the relative positioning of all objects. • Multidimensional scaling is based on the comparison of objects. Any object (product, service, image, etc. ) can be thought of as having both perceived and objective dimensions.

Purpose of MDS [cont…] • For example, a firm may see their new model of lawnmower as having two color options (red versus green) and a 24 -inch blade. These are the objective dimensions. Customers may or may not see these attributes. Customers may also perceive the lawnmower as expensive-looking or fragile, and these are the perceived dimensions.

Example • Let’s take an example of understanding consumer’s perceptions of 6 candy bars [A, B, C, D, E, & F] in the market. • Instead of trying to gather information about consumers’ evaluation of the candy bars on a number of attributes, the researcher will instead gather only perceptions of overall similarities or dissimilarities. • The data are typically gathered by having respondents give simple global responses to statements such as these: ü Rate the similarity of products A and B on a 10 -point scale ü Product A is more similar to B than to C ü I like product A better than product C

Example [cont…. ] • The data are gathered by first creating a set of 15 unique pairs of the six candy bars (6 C 2). Respondents are then asked to rank the following 15 candy bar pairs, where a rank of 1 is assigned to the pair of candy bars that is most similar and a rank of 15 indicates the pair is least alike. The results for all pairs of candy bars for one respondent are shown below: Candy Bar A B C D E F A _ B C 2 13 _ 12 D _ E F 4 3 8 6 5 7 9 _ 10 11 1 14 _ 15 _

Example [cont…. ] • If we want to illustrate the similarity among candy bars graphically, a first attempt would be to draw a single similarity scale. We can do this for bars A, B and C as shown • Although a one-dimensional map can be accomplished with three objects, the task becomes increasingly difficult as the number of objects increases. Because one-dimensional scaling does not fit the data well, a two-dimensional solution should be attempted. This would allow for another scale (dimension) to be used in configuring the six candy bars, as shown:

Example [cont…. ]