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Garson, G. D. (2016). Logistic Regression: Binomial and Multinomial, 2016 Edition. Asheboro, NC: Statistical Associates Publishers.

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Table of Contents
ISBN-10: 1-62638-042-2
ISBN-13: 978-1-62638-042-4
@c 2016 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.


An illustrated tutorial and introduction to binary and multinomial logistic regression using SPSS, SAS, or Stata for examples. Suitable for introductory graduate-level study.

The 2016 edition is a major update to the 2014 edition. Among the new features are these:

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Below is the unformatted table of contents.

Table of Contents
Overview	10
Data examples	12
Key Terms and Concepts	13
Binary, binomial, and multinomial logistic regression	13
The logistic model	14
The logistic equation	15
Logits and link functions	17
Saving predicted probabilities	19
The dependent variable	20
The dependent reference default in binary logistic regression	21
The dependent reference default in multinomial logistic regression	22
Factors: Declaring	27
Overview	27
SAS	29
Stata	30
Factors: Reference levels	31
Overview	31
SAS	33
Stata	35
Covariates	36
Overview	36
SAS	37
Stata	38
Interaction Terms	38
Overview	38
SAS	39
Stata	40
Estimation	41
Overview	41
Complex samples	41
Maximum likelihood estimation (ML)	41
Weighted least squares estimation (WLS)	43
Ordinary least squares estimation (OLS)	44
Residuals	44
Overview	44
Residuals vs. distance, influence, and leverage	45
Types of residuals and influence	46
Covariance pattern vs. individual observation residuals	50
Which type of residual to use?	50
Residuals and model misspecification	51
A basic binary logistic regression model in SPSS	51
Example	51
SPSS input	51
SPSS output	54
Parameter estimates and odds ratios	54
Omnibus tests of model coefficients	56
Model summary	56
Classification table	57
Classification plot	59
Probabilities of group membership	61
Hosmer-Lemeshow test of goodness of fit	61
Residual analysis	63
Checking for outliers	68
A basic binary logistic regression model in SAS	74
Example	74
SAS input	74
Reconciling SAS and SPSS output	75
SAS output	76
Parameter estimates	76
Odds ratio estimates	77
Global null hypothesis tests	78
Model fit statistics	79
The classification table	80
The association of predicted probabilities and observed responses table	83
Hosmer and Lemeshow test of goodness of fit	83
Residual analysis	84
A basic binary logistic regression model in STATA	92
Overview and example	92
Data setup	93
Stata input	94
Stata output	94
Parameter estimates	94
Odds ratios	95
Likelihood ratio test of the model	96
Model fit statistics	97
The classification table	98
Classification plot	99
Measures of association	100
Hosmer-Lemeshow test	101
Residual analysis	102
Probability (marginal) analysis for binary logistic regression	111
Overview	111
How probabilities are conditional on covariate values	113
Example	117
Stata	117
The margins and mchange commands	117
The binary logistic model and its odds ratios	118
Adjusted predictions at the means (APM)	120
Marginal effects at means (MEM)	124
Problems with APM and MEM measures	126
Adjusted predictions at representative values (APR)	127
Marginal effects at representative values (MER)	130
Average marginal effects (AME)	135
Average adjusted predictions (AAP)	138
Command summary	140
Interactions in probability analysis	141
Comparison of odds-ratio and probabilistic interpretations	143
Common options for marginal analysis in Stata	144
SAS	149
SAS input	149
SAS output	151
SPSS	151
A basic multinomial logistic regression model in SPSS	151
Example	151
Model	152
SPSS statistical output	153
Step summary	155
Model fitting information table	155
Goodness of fit tests	156
Likelihood ratio tests	156
Parameter estimates	157
Pseudo R-square	159
Classification table	160
Observed and expected frequencies	160
Asymptotic correlation matrix	160
Residual analysis in multinomial logistic regression	161
A basic multinomial logistic regression model in SAS	161
Example	161
SAS syntax	161
SAS statistical output	162
Overview	162
Model fit	162
Goodness of fit tests	163
Parameter estimates	164
Pseudo R-Square	166
Classification table	166
Observed and predicted functions and residuals	166
Correlation matrix of estimates	167
A basic multinomial logistic regression model in STATA	168
Example	168
Stata data setup	168
Stata syntax	169
Stata statistical output	170
Overview	170
Model fit	170
AIC and BIC	171
Pseudo R-square	172
Goodness of fit test	172
Likelihood ratio tests	173
Parameter estimates	173
Odds ratios/ relative risk ratios	174
Classification table	175
Observed and expected frequencies	176
Asymptotic correlation matrix	176
Probability (marginal) analysis for multinomial regression	176
Overview	176
Stata	177
Example	177
Average marginal effects (AME) model for multinomial regression	177
The mchange command	182
SAS	184
SPSS	184
ROC curve analysis	184
Overview	184
Comparing models	185
Example	185
SPSS	186
Comparing models	186
Optimal classification cutting points	191
SAS	195
Overview	195
Comparing Models	197
Optimal classification cutting points	199
Stata	201
Overview	201
Comparing Models	203
Optimal classification cutting points	207
Conditional logistic regression for matched pairs	208
Overview	208
Example	208
Data setup	208
Conditional logistic regression in SPSS	209
Overview	209
SPSS input	210
SPSS output	213
Conditional logistic regression in SAS	215
Overview	215
SAS input	216
SAS output	216
Conditional logistic regression in Stata	218
Overview	218
Stata input	218
Stata output	218
More about parameter estimates and odds ratios	220
For binary logistic regression	220
Example 1	220
Example 2	223
For multinomial logistic regression	226
Example 1	226
Example 2	229
Coefficient significance and correlation significance may differ	231
Reporting odds ratios	231
Comparing the change in odds for different values of X	233
Odds ratios: Summary	233
Effect size	233
Confidence interval on the odds ratio	233
Warning: very high or very low odds ratios	234
Comparing the change in odds when interaction terms are in the model	234
Probabilities, logits, and odds ratios	235
Probabilities	235
Relative risk ratios (RRR)	239
More about significance tests	239
Overview	239
Significance of the model	239
SPSS	239
SAS	243
Stata	243
Significance of parameter effects	243
SPSS	243
SAS	247
Stata	247
Bootstrapped significance	248
What is bootstrapped significance?	248
Bootstrapping vs. jackknifing	249
SPSS	249
SAS	250
Stata	251
More about effect size measures	253
Overview	253
Effect size for the model	253
Pseudo R-squared	253
Classification tables	255
Terms associated with classification tables:	260
The c statistic	262
Information theory measures of model fit	263
Effect size for parameters	265
Odds ratios	265
Unstandardized logistic coefficients	265
Standardized logistic coefficients	265
Stepwise logistic regression	266
Overview	266
Forward selection vs. backward elimination	268
Cross-validation	269
Rao's efficient score as a variable entry criterion for forward selection	269
Score statistic	270
Which step is the best model?	271
Contrast Analysis	272
Repeated contrasts	272
Indicator contrasts	272
Contrasts and ordinality	273
Assumptions	274
Data level	274
Meaningful coding	275
Proper specification of the model	275
Independence of irrelevant alternatives	276
Error terms are assumed to be independent (independent sampling)	276
Low error in the explanatory variables	276
Linearity	276
Additivity	278
Absence of perfect separation	278
Absence of perfect multicollinearity	278
Absence of high multicollinearity	279
Centered variables	279
No outliers	279
Sample size	279
Sampling adequacy	280
Expected dispersion	280
Frequently Asked Questions	281
How should logistic regression results be reported?	281
Example	281
Why not just use regression with dichotomous dependents?	282
How does OLS regression compare to logistic regression?	283
What does "controlling for other variables" mean in logistic regression?	284
Why is there no R2 or percent of variance explained in logistic regression?	285
Do regression weights change if variables are added or dropped from the logistic equation?	288
When is discriminant analysis preferred over logistic regression?	288
What is the SPSS syntax for logistic regression?	288
What is the Stata syntax for the logistic command?	291
What is the Stata syntax for the margins command used for probability analysis?	291
What is the Stata syntax for the mchange command used for probability analysis?	293
Apart from indicator coding, what are the other types of contrasts?	295
Will SPSS's binary logistic regression procedure handle my categorical variables automatically?	298
Can I handle missing cases the same in logistic regression as in OLS regression?	299
Explain the error message I am getting about unexpected singularities in the Hessian matrix.	299
Explain the error message I am getting in SPSS about cells with zero frequencies.	300
Is multicollinearity a problem for logistic regression the way it is for multiple linear regression?	300
What is the logistic equivalent to the VIF test for multicollinearity in OLS regression? Can odds ratios be used?	300
How are interaction effects handled in logistic regression?	301
Does Bayesian logistic regression exist?	302
Does stepwise logistic regression exist, as it does for OLS regression?	302
What are the stepwise options in multinomial logistic regression in SPSS?	302
May I use the multinomial logistic option when my dependent variable is binary?	305
What is nonparametric logistic regression and how is it more nonlinear?	306
How many independent variables can I have?	306
What is the logistic regression equation if an independent variable is categorical?	307
How are logit coefficients compared across groups formed by a categorical variable?	307
How do I compute confidence intervals for unstandardized logit (effect) coefficients?	308
Acknowledgments	308
Bibliography	309 
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