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Multiple Discriminant Analysis

What is discriminant analysis?. The appropriate statistical technique when the dependent variable is categorical and the independent variables are metricTwo or more (multiple) groups

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Multiple Discriminant Analysis

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    1. Multiple Discriminant Analysis Dr. Milne

    2. What is discriminant analysis? The appropriate statistical technique when the dependent variable is categorical and the independent variables are metric Two or more (multiple) groupshence MDA Mathematically it is the reverse of MANOVA.

    12. Discriminant Analysis Decision Process

    13. Discriminant Function

    14. Objectives of Discriminant Analysis Inference Dimension reduction Prediction Interpretation

    15. INFERENCE Determine whether statistically significant differences exist between the average score profiles on a set of variables for two (or more) a priori defined groups. DIMENSION REDUCTION Determining which of the independent variables account for the most for the differences in the average score profiles of the two or more groups. PREDICTION Establishing procedures for classifying statistical units into groups on the basis of their scores on a set of independent variable INTERPRETATION Establishing the number and composition of the dimensions of discrimination between groups formed from the set of independent variables.

    16. Research Design Selection of Variables Groups must be mutually exclusive and exhaustive Artificial groups?, polar extremes? Independent variables picked based on theory and intuition Sample Size 20 observations per predictor variable Each group should at least have 20 observations Division of the Sample Analysis and holdout groups (60/40 or 75/25)

    17. Assumptions of Discriminant Analysis Multivariate normality of the independent variables and unknown (but equal) dispersion and covariance structure (matrices) for groups. Linearity among relationships Watch for multicollinearity among independent variables during stepwise regressions.

    18. Estimation and Assessing Fit Computational Method Simultaneous versus stepwise Statistical Significance of Functions Wilks lamda, Hotellings trace, Pilliais criterion. Mahalanobis D2 and Raos V for stepwise. Assessing Overall Fit Calculate Discriminant Z-scores Evaluate Group Differences Classification Matrices Cutting Scores Specifying probabilities of classification Measures of predictive accuracy Statistically-based measures of classification accuracy relative to chance.

    23. Interpretation of Results Discriminant Weights Discriminant Loadings Partial F Values Interpretation of Two or More Functions Rotation of Discriminant Functions Potency index Graphical Display of Group Centroids Grapical Display of Discriminant Loadings

    24. Potency Index A relative measure among all variables that is indicative of each variables discriminating power.

    26. Validation of Results Split sample or Cross-Validation Procedures Profiling Group Differences Variables used within the analysis New variables

    29. SPSS Classify: Discriminant Analysis Grouping Variate Independents enter together or use step wise Statistics mean, ANOVAs Box M, Matrices, function coefficients (select unstandardized) Classify All groups equal / compute from groups Display casewise results, summary table, leave one-out classification

    37. Assignment 2 Group (Specification Buying/Total Value Analysis) by delivery speed, price level, price flexibility, manufacturer image, overall service, salesforce image, product quality. 3 Group (Buying situation X14) by same DVs. Factor scores of Consumer Sentiment predicting Males vs. Females.

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