Strategy for Complete discriminant AnalysisAssumptions of normality, linearity, and homogeneity of varianceAssumption of linearity in discriminant analysisAssumption of homogeneity of varianceDetecting outliers in discriminant analysis - 1Detecting outliers in discriminant analysis - 2MulticollinearityValidationOverall strategy for solving problemsProblem 1Dissecting problem 1 - 1Dissecting problem 1 - 2Dissecting problem 1 - 3Dissecting problem 1 - 4Dissecting problem 1 - 5LEVEL OF MEASUREMENT - 1LEVEL OF MEASUREMENT - 2PATTERNS OF MISSING DATA - 1PATTERNS OF MISSING DATA - 2PATTERNS OF MISSING DATA - 3PATTERNS OF MISSING DATA - 4The baseline discriminant analysisSelecting the dependent variableDefining the group valuesCompleting the range of group valuesSpecifying the method for including variablesRequesting statistics for the outputSpecifying statistical outputSpecifying details for the stepwise methodDetails for the stepwise methodSpecifying details for classificationDetails for classification - 1Details for classification - 2Details for classification - 3Completing the discriminant analysis requestClassification accuracy before transformations or removing outliersASSUMPTION OF NORMALITYNormality of independent variable: highest year of school completedSlide 39Normality of independent variable: number of hours worked in the past weekNormality of independent variable: incomeUsing the script to detect outliersOutliers in the data setOmitting outliersClassification accuracy using transformations and excluding outliersSAMPLE SIZE - 1SAMPLE SIZE - 2ASSUMPTION OF EQUAL DISPERSION FOR DEPENDENT VARIABLE GROUPSSlide 49Slide 50NUMBER OF DISCRIMINANT FUNCTIONS - 1NUMBER OF DISCRIMINANT FUNCTIONS - 2MULTICOLLINEARITYIndependent variables and group membership: relationship of functions to groupsIndependent variables and group membership: which predictors to interpretIndependent variables and group membership: predictor loadings on functionsIndependent variables and group membership: predictors associated with first function - 1Independent variables and group membership: predictors associated with first function - 2Independent variables and group membership: predictors associated with second functionCLASSIFICATION USING THE DISCRIMINANT MODEL: by chance accuracy rateCLASSIFICATION USING THE DISCRIMINANT MODEL: criteria for classification accuracyCLASSIFICATION USING THE DISCRIMINANT MODEL: VALIDATION OF THE DISCRIMINANT ANALYSISAnswering the problem question - 1Answering the problem question - 2Answering the problem question - 3Answering the problem question - 4Complete discriminant analysis: level of measurementComplete discriminant analysis: analyzing missing dataComplete discriminant analysis: assumption of normalityComplete discriminant analysis: detecting outliersComplete discriminant analysis: picking discriminant model for interpretationComplete discriminant analysis: sample sizeComplete discriminant analysis: assumption of equal dispersionComplete discriminant analysis: usable discriminant modelComplete discriminant analysis: relationships between IV's and DVComplete discriminant analysis: classification accuracyComplete discriminant analysis: adding cautions to solutionSW388R7Data Analysis & Computers IISlide 1Strategy for Complete discriminant AnalysisAssumption of normality, linearity, and homogeneityOutliersMulticollinearityValidationSample problemSteps in solving problemsSW388R7Data Analysis & Computers IISlide 2Assumptions of normality, linearity, and homogeneity of varianceThe ability of discriminant analysis to extract discriminant functions that are capable of producing accurate classifications is enhanced when the assumptions of normality, linearity, and homogeneity of variance are satisfied.We will use the script for testing for normality and test substituting the log, square root, or inverse transformation when they induce normality in a variable that fails to satisfy the criteria for normality.We can compare the accuracy rates in a model using transformed variables to one that does not to evaluate whether or not the improvement gained by transformed variables is sufficient to justify the interpretational burden of explaining transformations.SW388R7Data Analysis & Computers IISlide 3Assumption of linearity in discriminant analysisSince the dependent variable is non-metric in discriminant analysis, there is not a linear relationship between the dependent variable and an independent variable. In discriminant analysis, the assumption of linearity applies to the relationships between pairs of independent variable. To identify violations of linearity, each metric independent variable would have to be tested against all others.Since non-linearity only reduces the power to detect relationships, the general advice is to attend to it only when we know that a variable in our analysis consistently demonstrated non-linear relationships with other independent variables. We will not test for linearity in our problems.SW388R7Data Analysis & Computers IISlide 4Assumption of homogeneity of varianceThe assumption of homogeneity of variance is particular important in the classification stage of discriminant analysis. If one of the groups defined by the dependent variable has greater dispersion than others, cases will tend to be over classified in it.Homogeneity of variance is tested with Box's M test, which tests the null hypotheses that the group variance-covariance matrices are equal. If we fail to reject this null hypothesis and conclude that the variances are equal, we use the SPSS default of using a pooled covariance matrix in classification.If we reject the null hypothesis and conclude that the variances are heterogeneous, we substitute separate covariance matrices in the classification, and evaluate whether or not our classification accuracy is improved.SW388R7Data Analysis & Computers IISlide 5Detecting outliers in discriminant analysis - 1For multiple regression, we used z scores, studentized residuals, and Mahalanobis distance as criteria for omitting a case from the analysis as an outlier.Since the independent variables in a discriminant analysis are either metric or dichotomous, Mahalanobis distance can be used to detect a case that is an outlier for the combination of independent variables.Tabachnick suggests eliminating cases that are multivariate outliers using Mahalanobis distance. In the output for discriminant analysis,