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 variable in problemsProblem 1Dissecting problem 1 - 1Dissecting problem 1 - 2Dissecting problem 1 - 3Dissecting problem 1 - 4Dissecting problem 1 - 5Request multinomial logistic regressionSelecting the dependent variableSelecting metric independent variablesSpecifying statistics to include in the outputRequesting the classification tableCompleting the multinomial logistic regression requestLEVEL OF MEASUREMENT - 1LEVEL OF MEASUREMENT - 2Sample size – ratio of cases to variablesOVERALL RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLESNUMERICAL PROBLEMSRELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 1RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 2RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 3RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 4RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 5CLASSIFICATION USING THE MULTINOMIAL LOGISTIC REGRESSION MODEL: BY CHANCE ACCURACY RATECLASSIFICATION USING THE MULTINOMIAL LOGISTIC REGRESSION MODEL: CLASSIFICATION ACCURACYAnswering the question in problem 1 - 1Answering the question in problem 1 - 2Problem 2Dissecting problem 2 - 1Dissecting problem 2 - 2Dissecting problem 2 - 3Dissecting problem 2 - 4Dissecting problem 2 - 5Slide 56Slide 57Slide 58Slide 59Selecting non-metric independent variablesSlide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Answering the question in problem 2Steps in multinomial logistic regression: level of measurement and initial sample sizeSteps in multinomial logistic regression: overall relationship and numerical problemsSteps in multinomial logistic regression: relationships between IV's and DVSteps in multinomial logistic regression: classification accuracy and adding cautionsSW388R7Data Analysis & Computers IISlide 1Multinomial Logistic RegressionBasic RelationshipsMultinomial Logistic RegressionDescribing RelationshipsClassification AccuracySample 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 or influential cases.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 by the dependent is based on the reduction in the likelihood values for a model which does not contain any independent variables and the model that contains