An illustrated tutorial and introduction to binary and multinomial logistic regression using SPSS or SAS for examples. Suitable for introductory graduate-level study.
The 2013 edition is a minor update to the 2012 edition. The planned 2014 edition will be a major revision and expansion.
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Below is the unformatted table of contents.
LOGISTIC REGRESSION Table of Contents Overview 10 Key Terms and Concepts 11 Binary, binomial, and multinomial logistic regression 11 The logistic model 12 The logistic equation 13 The dependent variable 14 Factors 19 Covariates and Interaction Terms 22 Estimation 23 A basic binary logistic regression model in SPSS 24 Example 24 SPSS user interface 24 Omnibus tests of model coefficients 26 Model summary 27 Classification table 27 Variables in the equation table 29 Optional output 31 Classification plot 31 Hosmer and Lemeshow test of goodness of fit 32 Casewise listing of residuals for outliers > 2 standard deviations 34 A basic binary logistic regression model in SAS 35 SAS syntax 35 Reconciling SAS and SPSS output 37 Statistical Output in SAS 38 Global null hypothesis tests 38 Model fit statistics 39 The classification table 39 The association of predicted probabilities and observed responses table 40 Analysis of parameter estimates 42 Odds ratio estimates 43 Hosmer and Lemeshow test of goodness of fit 44 Regression diagnostics table 45 A basic multinomial logistic regression model in SPSS 46 Example 46 Model 47 Default statistical output 48 Pseudo R-square 50 Step summary 50 Model fitting information table 50 Goodness of fit tests 51 Likelihood ratio tests 51 Parameter estimates 52 Optional statistical output for multinomial regression in SPSS 53 Classification table 54 Observed and expected frequencies 54 Asymptotic correlation matrix 54 A basic multinomial logistic regression model in SAS 54 Example 54 SAS syntax 55 Statistical output for multinomial regression in SAS 55 Maximum likelihood anova table 55 Maximum likelihood estimates table 56 Parameter Estimates and Odds Ratios 58 Parameter estimates and odds ratios in binary logistic regression 58 Example 58 A second binary example 62 Parameter estimates and odds ratios in multinomial logistic regression 64 Example 64 A second example 67 Logistic coefficients and correlation 69 Reporting odds ratios 69 Odds ratios: summary 70 Effect size 71 Confidence interval on the odds ratio 71 Warning: very high or low odds ratios 72 Comparing the change in odds for different values of X 72 Comparing the change in odds when interaction terms are in the model 72 Probabilities, logits, and odds ratios 73 Probabilities 73 Relative risk ratios (RRR) 77 Logistic coefficients and logits 77 Parameter estimate for the intercept 77 Logits 78 Significance Tests 79 Significance tests for binary logistic regression 79 Omnibus tests of model coefficients 79 Hosmer and Lemeshow test of goodness of fit 80 Fit tests in stepwise or block-entry logistic regression 80 Wald tests for variables in the model 81 Significance tests for multinomial logistic regression 82 Likelihood ratio test of the model 82 Wald tests of parameters 82 Goodness of fit tests 82 Likelihood ratio tests 83 Testing individual model parameters 85 Goodness of Fit Index (obsolete) 87 Effect Size Measures 88 Effect size for the model 88 Pseudo R-squared 88 Classification tables 89 Terms associated with classification tables: 94 The c statistic 96 Information theory measures of model fit 97 Effect size for parameters 99 Odds ratios 99 Standardized vs. unstandardized logistic coefficients in model comparisons 99 Stepwise logistic regression 100 Overview 100 Forward selection vs. backward elimination 101 Cross-validation 102 Rao's efficient score as a variable entry criterion for forward selection 103 Score statistic 103 Which step is the best model? 104 Contrast Analysis 105 Repeated contrasts 105 Indicator contrasts 105 Contrasts and ordinality 106 Analysis of residuals 107 Overview 107 Residual analysis in binary logistic regression 107 Outliers 107 The DfBeta statistic 107 The leverage statistic 108 Cook's distance 108 Residual analysis in multinomial logistic regression 108 Conditional logistic regression for matched pairs data 108 Overview 108 Data setup 109 SPSS dialogs 109 Output 110 Assumptions 111 Data level 111 Meaningful coding 112 Proper specification of the model 112 Independence of irrelevant alternatives 112 Error terms are assumed to be independent (independent sampling) 113 Low error in the explanatory variables 113 Linearity 113 Additivity 115 Absence of perfect separation 115 Absence of perfect multicollinearity 115 Absence of high multicollinearity 115 Centered variables 116 No outliers 116 Sample size 116 Sampling adequacy 117 Expected dispersion 117 Frequently Asked Questions 117 How should logistic regression results be reported? 118 Why not just use regression with dichotomous dependents? 118 When is OLS regression preferred over logistic regression? 119 When is discriminant analysis preferred over logistic regression? 119 What is the SPSS syntax for logistic regression? 119 Can I create interaction terms in my logistic model, as with OLS regression? 122 Will SPSS's logistic regression procedure handle my categorical variables automatically? 122 Can I handle missing cases the same in logistic regression as in OLS regression? 122 Explain the error message I am getting about unexpected singularities in the Hessian matrix. 122 Explain the error message I am getting in SPSS about cells with zero frequencies. 123 Is it true for logistic regression, as it is for OLS regression, that the beta weight (standardized logit coefficient) for a given independent reflects its explanatory power controlling for other variables in the equation, and that the betas will change if variables are added or dropped from the equation? 123 What is the coefficient in logistic regression which corresponds to R-Square in multiple regression? 124 Is there a logistic regression analogy to adjusted R-square in OLS regression? 124 Is multicollinearity a problem for logistic regression the way it is for multiple linear regression? 124 What is the logistic equivalent to the VIF test for multicollinearity in OLS regression? Can odds ratios be used? 124 How can one use estimated variance of residuals to test for model misspecification? 125 How are interaction effects handled in logistic regression? 125 Does stepwise logistic regression exist, as it does for OLS regression? 126 What are the stepwise options in multinomial logistic regression in SPSS? 126 What if I use the multinomial logistic option when my dependent is binary? 129 What is nonparametric logistic regression and how is it more nonlinear? 130 How many independent variables can I have? 130 How do I express the logistic regression equation if one or more of my independent variables is categorical? 131 How do I compare logit coefficients across groups formed by a categorical independent variable? 131 How do I compute the confidence interval for the unstandardized logit (effect) coefficients? 132 What is ROC curve analysis in relation to binary logistic regression? 132 What is the STATA approach to multinomial logistic regression? 134 Bibliography 135 Pagecount: 139