Chapter 17 Overview of Multivariate Analysis Methods

Multivariate Analysis These techniques are important in marketing research because most business problems are multidimensional and can only be understood when multivariate techniques are used. statistical techniques used when there are multiple measurements of each element/concept and the variables are analyzed simultaneously. 17-2

Classification of Multivariate Methods We’ve already discussed ANOVA, MANOVA, Correlation, Multiple Regression, and Perceptual Mapping. 17-3

Summary of Multivariate Methods 17-4

Dependence VS INTERDEPENDENCE Methods Examples: multiple regression analysis, discriminant analysis, ANOVA and MANOVA Dependence – multivariate techniques appropriate when one or more of the variables can be identified as dependent variables and the remaining as independent variables. Examples: factor analysis, cluster analysis, and multidimensional scaling. Interdependence – multivariate statistical techniques in which a set of interdependent relationships is examined – The goal is grouping variables in some way. 17-5

Purpose – to simplify the data. Factor Analysis Purpose – to simplify the data. Dependent and independent variables are analyzed separately, not together. . . . used to summarize information contained in a large number of variables into a smaller number of subsets or factors. All variables being examined are analyzed together – to identify underlying factors. 17-6

Factor Analysis Process Steps Examine factor loadings & percentage of variance Interpret & name factors Decide on number of factors Notes: Some of the future predictions of trends in retailing are: The use of entertainment to lure customers. A shift toward providing greater convenience. The emergency of customer management programs to foster loyalty and enhance communications with a retailer’s best customers. 17-7

These are the starting point for interpreting factor analysis. Factor loadings are calculated between all factors and each of the original variables. These are the starting point for interpreting factor analysis. Factor Loadings are correlations between the variables and the new composite factor. They measure the importance of each variable relative to each composite factor. Like correlations, factor loadings range from +1.0 to –1.0 17-8

Cluster Analysis classifies or segments objects into groups that are similar within groups and as different as possible across groups. classifies objects into relatively homogeneous groups based on the set of variables analyzed. identifies natural groupings or segments among many variables, does NOT include a dependent variable. 17-9

Cluster Analysis 17-10

SPSS Dialog box for Cluster Analysis 17-11

Cluster Analysis COefficients 17-12

New Cluster variable New cluster variable 17-13

Discriminant Analysis Dependent variable – nonmetric or categorical (nominal or ordinal). It’s a dependence technique used for predicting group membership on the basis of two or more independent variables. Independent variables – metric (interval or ratio), but non-metric (nominal) dummy variables are possible. 17-14

Discriminant Analysis Characteristics Discriminant function – a linear combination of independent variables that bests discriminates between the dependent variable groups. Develops a linear combination of independent variables and uses it to predict group membership. Predicts categorical dependent variable based on group differences using a combination of independent variables. 17-15

Discriminant Analysis Multipliers of variables in the discriminant function when variables are in the original units of measurement. Estimates of the discriminatory power of a particular independent variable. Discriminant Function Coefficients 17-16

Discriminant Analysis . The prediction is referred to as the hit ratio. . Shows the number of correctly and incorrectly classified cases . Classification (Prediction) Matrix – shows whether the estimated discriminant function is a good predictor. 17-17

Discriminant Analysis scatter plot 17-18

SPSS Dialog box for Discriminant Analysis 17-19

Spss Discriminant Analysis output 17-20

Spss Discriminant Analysis output continued 17-21

Sample Conjoint Survey Profiles 17-22

Importance Calculations for Restaurant Data 17-23

Conjoint Part-Worth Estimates for Restaurant Survey 17-24