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Reference:
Garson, G. D. (2014). Logistic Regression: Binomial and Multinomial. Asheboro, NC: Statistical Associates Publishers.
 

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ISBN: 978-1-62638-024-0
ASIN: B007YAO4XI .
 
@c 2014 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.
 


LOGISTIC REGRESSION: BINARY & MULTINOMIAL

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 2014 edition is a major update to the 2012 edition. Among the new features are these:

The full content is now available from Statistical Associates Publishers. Click here.

Below is the unformatted table of contents.

LOGISTIC REGRESSION
Table of Contents
Overview	12
Data examples	14
Key Terms and Concepts	15
Binary, binomial, and multinomial logistic regression	15
The logistic model	16
The logistic equation	17
Logits and link functions	19
Saving predicted probabilities	21
The dependent variable	22
The dependent reference default in binary logistic regression	23
The dependent reference default in multinomial logistic regression	24
Factors: Declaring	29
Overview	29
SPSS	29
SAS	31
Stata	32
Factors: Reference levels	33
Overview	33
SPSS	34
SAS	35
Stata	37
Covariates	38
Overview	38
SPSS	38
SAS	39
Stata	40
Interaction Terms	40
Overview	40
SPSS	40
SAS	41
Stata	42
Estimation	43
Overview	43
Maximum likelihood estimation (ML)	43
Weighted least squares estimation (WLS)	44
Ordinary least squares estimation (OLS)	45
A basic binary logistic regression model in SPSS	45
Example	45
SPSS input	45
SPSS output	48
Parameter estimates and odds ratios	48
Omnibus tests of model coefficients	50
Model summary	50
Classification table	51
Classification plot	53
Hosmer-Lemeshow test of goodness of fit	55
Casewise listing of residuals for outliers > 2 standard deviations	56
A basic binary logistic regression model in SAS	57
Example	57
SAS input	58
Reconciling SAS and SPSS output	58
SAS output	59
Parameter estimates	59
Odds ratio estimates	60
Global null hypothesis tests	61
Model fit statistics	62
The classification table	63
The association of predicted probabilities and observed responses table	66
Hosmer and Lemeshow test of goodness of fit	66
Regression diagnostics table	67
A basic binary logistic regression model in STATA	68
Overview and example	68
Data setup	69
Stata input	70
Stata output	70
Parameter estimates	70
Odds ratios	71
Likelihood ratio test of the model	72
Model fit statistics	73
The classification table	74
Classification plot	75
Measures of association	76
Hosmer-Lemeshow test	77
Residuals and regression diagnostics	78
A basic multinomial logistic regression model in SPSS	81
Example	81
Model	83
SPSS statistical output	84
Step summary	86
Model fitting information table	86
Goodness of fit tests	87
Likelihood ratio tests	87
Parameter estimates	88
Pseudo R-square	90
Classification table	91
Observed and expected frequencies	91
Asymptotic correlation matrix	91
A basic multinomial logistic regression model in SAS	92
Example	92
SAS syntax	92
SAS statistical output	93
Overview	93
Model fit	93
Goodness of fit tests	94
Parameter estimates	95
Pseudo R-Square	96
Classification table	97
Observed and predicted functions and residuals	97
Correlation matrix of estimates	98
A basic multinomial logistic regression model in STATA	99
Example	99
Stata data setup	99
Stata syntax	100
Stata statistical output	101
Overview	101
Model fit	101
AIC and BIC	102
Pseudo R-square	103
Goodness of fit test	103
Likelihood ratio tests	104
Parameter estimates	104
Odds ratios/ relative risk ratios	105
Classification table	106
Observed and expected frequencies	107
Asymptotic correlation matrix	107
ROC curve analysis	107
Overview	107
Comparing models	108
Optimal classification cutting points	108
Example	109
SPSS	109
Comparing models	109
Optimal classification cutting points	114
SAS	118
Overview	118
Comparing Models	120
Optimal classification cutting points	122
Stata	124
Overview	124
Comparing Models	126
Optimal classification cutting points	130
Conditional logistic regression for matched pairs	131
Overview	131
Example	131
Data setup	131
Conditional logistic regression in SPSS	132
Overview	132
SPSS input	133
SPSS output	136
Conditional logistic regression in SAS	138
Overview	138
SAS input	139
SAS output	139
Conditional logistic regression in Stata	141
Overview	141
Stata input	141
Stata output	141
More about parameter estimates and odds ratios	143
For binary logistic regression	143
Example 1	143
Example 2	146
For multinomial logistic regression	149
Example 1	149
Example 2	152
Coefficient significance and correlation significance may differ	154
Reporting odds ratios	154
Odds ratios: Summary	156
Effect size	156
Confidence interval on the odds ratio	156
Warning: very high or very low odds ratios	157
Comparing the change in odds for different values of X	157
Comparing the change in odds when interaction terms are in the model	157
Probabilities, logits, and odds ratios	158
Probabilities	158
Relative risk ratios (RRR)	162
More about significance tests	162
Overview	162
Significance of the model	162
SPSS	162
SAS	166
Stata	166
Significance of parameter effects	166
SPSS	166
SAS	170
Stata	170
More about effect size measures	171
Overview	171
Effect size for the model	171
Pseudo R-squared	171
Classification tables	173
Terms associated with classification tables:	177
The c statistic	179
Information theory measures of model fit	180
Effect size for parameters	182
Odds ratios	182
Standardized vs. unstandardized logistic coefficients in model comparisons	182
Stepwise logistic regression	183
Overview	183
Forward selection vs. backward elimination	184
Cross-validation	185
Rao's efficient score as a variable entry criterion for forward selection	186
Score statistic	186
Which step is the best model?	187
Contrast Analysis	188
Repeated contrasts	188
Indicator contrasts	188
Contrasts and ordinality	189
Analysis of residuals	190
Overview	190
Residual analysis in binary logistic regression	190
Outliers	190
The DfBeta statistic	190
The leverage statistic	191
Cook's distance	191
Residual analysis in multinomial logistic regression	191
Assumptions	192
Data level	192
Meaningful coding	193
Proper specification of the model	193
Independence of irrelevant alternatives	193
Error terms are assumed to be independent (independent sampling)	194
Low error in the explanatory variables	194
Linearity	194
Additivity	196
Absence of perfect separation	196
Absence of perfect multicollinearity	196
Absence of high multicollinearity	196
Centered variables	197
No outliers	197
Sample size	197
Sampling adequacy	198
Expected dispersion	198
Frequently Asked Questions	199
How should logistic regression results be reported?	199
Example	199
Why not just use regression with dichotomous dependents?	200
How does OLS regression compare to logistic regression?	201
When is discriminant analysis preferred over logistic regression?	201
What is the SPSS syntax for logistic regression?	202
Apart from indicator coding, what are the other types of contrasts?	204
Can I create interaction terms in my logistic model, as with OLS regression?	207
Will SPSS's binary logistic regression procedure handle my categorical variables automatically?	207
Can I handle missing cases the same in logistic regression as in OLS regression?	208
Explain the error message I am getting about unexpected singularities in the Hessian matrix.	208
Explain the error message I am getting in SPSS about cells with zero frequencies.	209
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?	209
What is the coefficient in logistic regression which corresponds to R-Square in multiple regression?	209
Is multicollinearity a problem for logistic regression the way it is for multiple linear regression?	210
What is the logistic equivalent to the VIF test for multicollinearity in OLS regression? Can odds ratios be used?	210
How can one use estimated variance of residuals to test for model misspecification?	211
How are interaction effects handled in logistic regression?	211
Does stepwise logistic regression exist, as it does for OLS regression?	212
What are the stepwise options in multinomial logistic regression in SPSS?	212
May I use the multinomial logistic option when my dependent variable is binary?	215
What is nonparametric logistic regression and how is it more nonlinear?	215
How many independent variables can I have?	216
How do I express the logistic regression equation if one or more of my independent variables is categorical?	217
How do I compare logit coefficients across groups formed by a categorical independent variable?	217
How do I compute the confidence interval for the unstandardized logit (effect) coefficients?	218
Acknowledgments	218
Bibliography	218
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