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An introductory, graduate-level illustrated tutorial on generalized linear models and generalized estimating equations usuing SPSS. SAS, and Stata. Covers linear regression, gamma regression, binary logistic regression, binary probit regression, Poisson regression, log-linear analysis, negative binomial regression, ordinal logistic regression, ordinal probit regression, complementary log-log regression, and other GZLM models. Also covers repeated measures linear regression, repeated measures binary logistic regression, and other GEE models.

Why we think it's important: In addition to thorough coverage of an underused methodology which helps researchers pick the optimal type of regression, this volume explains why default output in SPSS, SAS, and Stata may well differ and lead researchers to different conclusions; and explains how to reconcile results.

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

```GENERALIZED LINEAR MODELS & GENERALIZED ESTIMATING EQUATIONS
Overview	11
Key Concepts and Terms	12
Types of data distribution, link function, and model	12
Types of data distributions	13
Overview	13
The normal distribution	13
The inverse Gaussian distribution	14
The gamma distribution	14
The multinomial distribution	15
The binomial distribution	16
The Poisson distribution	16
The negative binomial distribution	17
The Tweedie distribution	18
Overview	19
The negative binomial link function	22
The cumulative logit link function	23
The cumulative probit link function	23
The complementary log-log link (cloglog) function	24
The negative log-log link function	24
The cumulative logit link function	25
The cumulative probit link function	25
The cumulative Cauchit link function	25
The cumulative complementary log-log link function	25
The cumulative negative log-log link function	25
Types of estimation methods	26
Parameter Estimation	26
Scale Parameter	26
Statistical measures	26
Overview	26
Goodness of fit statistics	27
Likelihood ratio tests	32
Deviance ratios (scaled deviance)	33
Tests of model effects	33
Parameter estimates	34
Odds ratios	36
Pseudo R-square and other effect size measures	38
Contrast coeffiicents	39
Lagrange multiplier test	42
User interfaces for GZLM	42
SPSS interface	42
SAS interface	58
Stata interface	58
GZLM Models	61
Linear regression	62
Overview and data example	62
SPSS	63
SPSS linear regression input in GZLM	63
SPSS linear regression output in GZLM	63
SAS	70
SAS linear regression input for GZLM	70
SAS linear regression output for GZLM	71
Stata	82
Stata linear regression input for GZLM	82
Stata linear regression output for GZLM	83
Binary logistic regression	91
Overview and data example	91
SPSS	92
SPSS binary logistic regression input	92
SPSS binary logistic regression output	93
SAS	100
SAS binary logistic regression input	100
SAS binary logistic regression output	101
Stata	104
Stata binary logistic regression input	104
Stata binary logistic regression output	105
Binary probit regression	109
Overview and data example	109
Odds ratios in binary probit regression	109
The intercept in binary probit regression	109
SPSS	110
SPSS binary probit regression input	110
SPSS binary probit regression output	111
SAS	114
SAS binary probit regression input	114
SAS binary probit output	115
Stata	116
Stata binary probit regression input	116
Stata binary probit regression output	117
Complementary log-log (cloglog) models	118
Overview and data example	118
Exponentiated cloglog coefficients	118
Discrete time duration data	119
Example data	120
SPSS	121
SPSS cloglog regression input	121
SPSS cloglog regression output	122
SAS	124
SAS cloglog regression input	124
SAS cloglog output	125
Stata	126
Stata cloglog regression input	126
Stata cloglog output	127
Ordinal logistic regression	130
Overview	130
Example data	130
SPSS	131
SPSS ordinal logistic regression input	131
SPSS ordinal logistic regression output	132
SAS	135
SAS ordinal logistic regression input	135
SAS ordinal regression output	136
Stata	139
Stata ordinal logistic regression input	139
Stata ordinal logistic regression output	140
Ordinal probit regression	142
Overview	142
Example Data	143
SPSS	143
SPSS ordinal probit regression input	143
SPSS ordinal probit regression output	144
SAS	146
SAS ordinal probit regression input	146
SAS ordinal probit output	147
Stata	148
Stata ordinal probit regression input	148
Stata ordinal probit regression output	148
Gamma regression	149
Overview	149
Gamma regression with a log link	150
Gamma regression with an inverse power (reciprocal) link	151
Gamma regression with an identity link	151
The scale parameter	151
Estimation methods	152
Example data	153
SPSS	155
SPSS gamma regression input	155
SPSS output: gamma regression with log link	155
SPSS output: gamma regression with reciprocal link	160
SAS	163
SAS gamma regression input	163
SAS output: gamma regression with log link	164
SAS output: gamma regression with reciprocal link	166
Stata	167
Stata gamma regression input	167
Stata output: gamma regression with log link	167
Stata output: gamma regression with reciprocal link	168
Poisson regression	170
Overview	170
Poisson count models, rate models, and loglinear models	170
Count models	170
Rate  models	170
Loglinear models	171
Checking overdispersion	171
Fitting an overdispersed Poisson regression model	172
A negative binomial model as an alternative	172
Example Data	172
For count and rate models	172
For the loglinear model	174
Creating an aggregated file	175
SPSS	176
Poisson rate  models in SPSS	176
Poisson count models in SPSS	180
Poisson loglinear models in SPSS	180
SAS	184
Poisson rate  models in SAS	184
Poisson count models in SAS	186
Poisson loglinear models in SAS	186
Stata	189
Poisson rate  models in Stata	189
Poisson count models in Stata	190
Poisson loglinear models in Stata	190
Negative binomial regression	193
Overview	193
Value/df and the dispersion parameter	193
The ancillary parameter	194
The Lagrange multiplier test	194
Example data	194
Negative binomial models in SPSS	194
Negative binomial models in SAS	197
Negative binomial models in Stata	199
Mixture (Tweedie) models	200
GENERALIZED ESTIMATING EQUATIONS (GEE)	201
Overview	201
What is GEE?	201
Assumptions of GEE	203
Statistical packages and GEE	205
Types of GEE model	205
Subject and within-subject variables	206
Unbalanced designs	207
The assumed (working) correlation matrix	207
Goodness of fit measures in GEE	211
Data structure for GEE	211
Data Examples	212
Repeated measures linear regression using GEE	212
Repeated measures binary logistic regression	214
SPSS	215
The "Repeated" tab of the SPSS GEE procedure	216
SPSS repeated measures linear regression using GEE	220
Case processing summary	238
SPSS repeated measures binary logistic regression using GEE	244
SAS	249
SAS Repeated measures linear regression using GEE	249
SAS repeated measures binary logistic regression	253
Stata	258
Stata Repeated measures linear regression using GEE	258
Stata repeated measures binary logistic regression	260
Residual analysis	263
Overview	263
Variables available in GEE	263
Variables available in GZLM but not GEE	264
Assumptions	265
Not assumed	265
Linearity in the link function	265
Absence of high multicollinearity	265
Centered data	266
Data distribution	266
Independent vs. correlated data	266
Data levels	266
Missing data	267
Should I use GRZ or GZLM as the abbreviation for generalized linear models?	267
How do I convert among SPSS, SAS, and Stata data files?	267
SPSS to/from SAS or Stata	267
SAS to/from SPSS or Stata	268
Stata to/from SPSS or SAS	270
Will I get the same results as for OLS regression if I use GZLM with a normal distribution and identity link function? Could I use another link function implemented manually but using the OLS regression module?	271
Can the dependent/response variable in GZLM or GEE be distributed in any manner? Are these distribution-free models?	271
How do "Full" and "Kernel" likelihood functions differ?	272
What are influence statistics, distance coefficients, and types of residuals?	272
DfBeta	273
Standardized DfBeta	273
DfFit	273
Standardized DfFit	273
Covariance ratio	274
Leverage	274
Mahalabobis distance	274
Cook's distance	274
Residuals	275
What are types of sums of squares, like Type III?	277
Will the SPSS GZLM module handle random effects as does the SPSS linear mixed models module?	277
Can I have lag or lead variables in GEE analysis of time series?	278
What is a "canonical link"?	279
Can AIC, BIC, and other information theory measures be negative?	280
What is the SPSS syntax for generalized linear modeling?	280
What is the SAS syntax for PROC GENMOD?	283
What is the Stata syntax for the xtgee command?	283
Bibliography	286
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