Multinomial Logistic Regression Basic RelationshipsMultinomial logistic regressionWhat multinomial logistic regression predictsLevel of measurement requirementsAssumptions and outliersSample size requirementsMethods for including variablesOverall test of relationship - 1Overall test of relationship - 2Strength of multinomial logistic regression relationshipEvaluating usefulness for logistic modelsComputing by chance accuracyComparing accuracy ratesNumerical problemsRelationship of individual independent variables and the dependent variableSlide 16Slide 17Slide 18Interpreting relationship of individual independent variables to the dependent variableSlide 20Slide 21Interpreting relationship of individual independent variables and the dependent variableInterpreting relationships for independent variables in problemsLevel of Measurement - questionLevel of Measurement – evidence and answerSample Size - questionRequest multinomial logistic regressionSelecting the dependent variableSelecting metric independent variablesSpecifying statistics to include in the outputRequesting the classification tableCompleting the multinomial logistic regression requestSample size – ratio of cases to variables evidence and answerMulticollinearity and Numerical Problems - questionMulticollinearity and Numerical Problems – evidence and answerOverall Relationship - questionOverall Relationship – evidence and answerIndividual Relationships – Age questionIndividual Relationships – Age evidence and answerIndividual Relationships – highest year of school questionIndividual Relationships – highest year of school evidence and answerIndividual Relationships – confidence in Congress questionIndividual Relationships – confidence in Congress evidence and answer - 1Individual Relationships – confidence in Congress evidence and answer - 2Individual Relationships – confidence in Congress evidence and answer - 3Individual Relationships – confidence in Congress evidence and answer - 4Individual Relationships – confidence in Congress evidence and answer - 5Individual Relationships – confidence in Congress evidence and answer - 6Classification Accuracy - questionClassification Accuracy – evidence and answer 1Classification Accuracy – evidence and answer 2Steps in solving multinomial logistic regression problems: level of measurementSteps in solving multinomial logistic regression problems: sample sizeSteps in solving multinomial logistic regression problems: multicollinearity/numerical problemsSteps in solving multinomial logistic regression problems: overall relationshipSteps in solving multinomial logistic regression problems: relationships between IV's and DVSteps in solving multinomial logistic regression problems: classification accuracySW388R7Data Analysis & Computers IISlide 1Multinomial Logistic RegressionBasic RelationshipsMultinomial Logistic RegressionDescribing RelationshipsClassification AccuracySample ProblemSteps in Solving ProblemsSW388R7Data Analysis & Computers IISlide 2Multinomial logistic regressionMultinomial logistic regression is used to analyze relationships between a non-metric dependent variable and metric or dichotomous independent variables. Multinomial logistic regression compares multiple groups through a combination of binary logistic regressions. The group comparisons are equivalent to the comparisons for a dummy-coded dependent variable, with the group with the highest numeric score used as the reference group.For example, if we wanted to study differences in BSW, MSW, and PhD students using multinomial logistic regression, the analysis would compare BSW students to PhD students and MSW students to PhD students. For each independent variable, there would be two comparisons.SW388R7Data Analysis & Computers IISlide 3What multinomial logistic regression predictsMultinomial logistic regression provides a set of coefficients for each of the two comparisons. The coefficients for the reference group are all zeros, similar to the coefficients for the reference group for a dummy-coded variable.Thus, there are three equations, one for each of the groups defined by the dependent variable.The three equations can be used to compute the probability that a subject is a member of each of the three groups. A case is predicted to belong to the group associated with the highest probability.Predicted group membership can be compared to actual group membership to obtain a measure of classification accuracy.SW388R7Data Analysis & Computers IISlide 4Level of measurement requirementsMultinomial logistic regression analysis requires that the dependent variable be non-metric. Dichotomous, nominal, and ordinal variables satisfy the level of measurement requirement.Multinomial logistic regression analysis requires that the independent variables be metric or dichotomous. Since SPSS will automatically dummy-code nominal level variables, they can be included since they will be dichotomized in the analysis.In SPSS, non-metric independent variables are included as “factors.” SPSS will dummy-code non-metric IVs.In SPSS, metric independent variables are included as “covariates.” If an independent variable is ordinal, we will attach the usual caution.SW388R7Data Analysis & Computers IISlide 5Assumptions and outliersMultinomial logistic regression does not make any assumptions of normality, linearity, and homogeneity of variance for the independent variables.Because it does not impose these requirements, it is preferred to discriminant analysis when the data does not satisfy these assumptions.SPSS does not compute any diagnostic statistics for outliers. To evaluate outliers, the advice is to run multiple binary logistic regressions and use those results to test the exclusion of outliers.SW388R7Data Analysis & Computers IISlide 6Sample size requirementsThe minimum number of cases per independent variable is 10, using a guideline provided by Hosmer and Lemeshow, authors of Applied Logistic Regression, one of the main resources for Logistic Regression.For preferred case-to-variable ratios, we will use 20 to 1.SW388R7Data Analysis & Computers IISlide 7Methods for including variablesThe only method for selecting independent variables in SPSS is simultaneous or direct entry.SW388R7Data Analysis & Computers IISlide 8Overall test of relationship - 1The overall test of relationship among the independent variables and groups defined