Discriminant Analysis – Basic RelationshipsDiscriminant analysisDiscriminant scoresDiscriminant functionsNumber of functionsOverall test of relationshipInterpreting the relationship between independent and dependent variablesGroups, functions, and variablesFunctions at Group CentroidsStructure MatrixGroup StatisticsWhich independent variables to interpretDiscriminant analysis and classificationEvaluating usefulness for discriminant modelsComparing accuracy ratesComputing by chance accuracyComparing the cross-validated accuracy rateDiscriminant analysis – standard variable entryLevel of measurement - answerSample size requirements - questionRequest simultaneous discriminant analysisSelecting the dependent variableDefining the group valuesCompleting the range of group valuesSelecting the independent variablesSpecifying the method for including variablesRequesting statistics for the outputSpecifying statistical outputSpecifying details for classificationDetails for classification - 1Details for classification - 2Details for classification - 3Completing the discriminant analysis requestSample size – ratio of cases to variables evidence and answerSample size – minimum group size evidence and answerOverall relationship - questionOverall relationship – evidence and answerRelationship of functions to groups - questionRelationship of functions to groups – evidence and answerRelationship of first independent variable - questionRelationship of first independent variable – evidence and answer: loadings on functionsRelationship of first independent variable – evidence and answer: comparison of meansRelationship of second independent variable - questionRelationship of second independent variable – evidence and answer: loadings on functionsRelationship of third independent variable - questionRelationship of third independent variable – evidence and answer: loadings on functionsRelationship of third independent variable – evidence and answer: comparison of meansRelationship of fourth independent variable - questionRelationship of fourth independent variable – evidence and answer: loadings on functionsClassification accuracy - questionClassification accuracy – evidence and answer: by chance accuracy rateClassification accuracy – evidence and answer: classification accuracyAnalysis summary - questionAnalysis summary – evidence and answerSlide 55Discriminant analysis – stepwise variable entrySlide 57Sample size requirementsThe stepwise discriminant analysisSlide 60Slide 61Slide 62Slide 63Slide 64Slide 65Specifying details for the stepwise methodDetails for the stepwise methodSlide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Slide 77Slide 78Best subset of predictors - questionBest subset of predictors – evidence and answer which predictors to interpretBest subset of predictors – evidence and answer test of statistical significanceSlide 82Relationship of first independent variable – evidence and answer: order of entrySlide 84Slide 85Slide 86Relationship of second independent variable – evidence and answer: order of entrySlide 88Relationship of second independent variable – evidence and answer: comparison of meansSlide 90Relationship of third independent variable – evidence and answer: order of entrySlide 92Slide 93Slide 94Relationship of fourth independent variable – evidence and answer: order of entrySlide 96Slide 97Slide 98Slide 99Slide 100Slide 101Steps in discriminant analysis: 1Steps in discriminant analysis: 2aSteps in discriminant analysis: 2bSteps in discriminant analysis: 3Steps in discriminant analysis: 4Steps in discriminant analysis: 5aSteps in discriminant analysis: 6bSteps in discriminant analysis: 7Steps in discriminant analysis: 8aSteps in discriminant analysis: 8bDiscriminant Analysis Homework Problems Basic Relationships - 1Discriminant Analysis Homework Problems Basic Relationships - 2Discriminant Analysis Homework Problems Basic Relationships - 3Discriminant Analysis Homework Problems Basic Relationships - 4Discriminant Analysis Homework Problems Basic Relationships - 5Discriminant Analysis Homework Problems Basic Relationships - 6Discriminant Analysis Homework Problems Basic Relationships - 7Discriminant Analysis Homework Problems Basic Relationships - 8Discriminant Analysis Homework Problems Basic Relationships - 9Discriminant Analysis Homework Problems Basic Relationships - 10SW388R7Data Analysis & Computers IISlide 1Discriminant Analysis – Basic RelationshipsDiscriminant Functions and ScoresDescribing RelationshipsClassification AccuracySample ProblemsSteps in Solving ProblemsHomework ProblemsSW388R7Data Analysis & Computers IISlide 2Discriminant analysisDiscriminant analysis is used to analyze relationships between a non-metric dependent variable and metric or dichotomous independent variables.Discriminant analysis attempts to use the independent variables to distinguish among the groups or categories of the dependent variable.The usefulness of a discriminant model is based upon its accuracy rate, or ability to predict the known group memberships in the categories of the dependent variable.SW388R7Data Analysis & Computers IISlide 3Discriminant scoresDiscriminant analysis works by creating a new variable called the discriminant function score which is used to predict to which group a case belongs.Discriminant function scores are computed similarly to factor scores, i.e. using eigenvalues. The computations find the coefficients for the independent variables that maximize the measure of distance between the groups defined by the dependent variable.The discriminant function is similar to a regression equation in which the independent variables are multiplied by coefficients and summed to produce a score.SW388R7Data Analysis & Computers IISlide 4Discriminant functionsConceptually, we can think of the discriminant function or equation as defining the boundary between groups. Discriminant scores are standardized, so that if the score falls on one side of the boundary (standard score less than zero, the case is predicted to be a member of one group) and if the score falls on the other side of the boundary (positive standard score), it is predicted to be a member of the other group.SW388R7Data Analysis & Computers IISlide 5Number of functionsIf the dependent variable defines two groups, one statistically significant discriminant function is required to distinguish the groups; if the