Advanced Log-Linear Models Using SAS

Overview

In Advanced Log-Linear Models Using SAS, Daniel Zelterman applies his extensive SAS knowledge and biostatistics experience to illustrate how to use the GENMOD procedure to analyze log-linear models for categorical data. His wide variety of examples illustrate the statistical applications PROC GENMOD can perform. He thoroughly describes the models, provides real data examples, supplies the necessary code, and explains the output from GENMOD. The topics covered include the Pearson goodness-of-fit statistic; tables ...
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Overview

In Advanced Log-Linear Models Using SAS, Daniel Zelterman applies his extensive SAS knowledge and biostatistics experience to illustrate how to use the GENMOD procedure to analyze log-linear models for categorical data. His wide variety of examples illustrate the statistical applications PROC GENMOD can perform. He thoroughly describes the models, provides real data examples, supplies the necessary code, and explains the output from GENMOD. The topics covered include the Pearson goodness-of-fit statistic; tables of categorical data; a review of log-linear model methods for rectangular tables of categorical data; extrapolation methods to estimate population size; new models and distributions for statistical analysis of data; and issues in power analysis and estimating sample size in experiments. The models take advantage of the wide class of generalized linear models and use real data from pharmaceutical studies and epidemiology, wildlife, and government statistics. Statisticians who have a basic understanding both of SAS and of the analysis of categorical data will greatly benefit from this book. The discussion of each model and method emphasizes statistical aspects, such as interpretation of results, rather than programming skills. The numerous examples are used to motivate the theory and methods as they are discussed.
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Product Details

  • ISBN-13: 9781590470800
  • Publisher: SAS Institute Inc.
  • Publication date: 10/28/2002
  • Pages: 202
  • Sales rank: 440,222
  • Product dimensions: 8.25 (w) x 11.00 (h) x 0.43 (d)

Table of Contents

Preface v
Acknowledgments ix
1 Discrete Distributions 1
1.1 Introduction 1
1.2 The Binomial Distribution 2
1.3 The Poisson Distribution 8
1.4 The Multinomial Distribution 11
1.5 Negative Binomial and Negative Multinomial Distributions 12
2 Basic Log-Linear Models and the GENMOD Procedure 19
2.1 Introduction 19
2.2 Log-Linear Models for a 2 x 2 Table 19
2.3 Log-Linear Models in Higher Dimensions 30
2.4 Residuals for Log-Linear Models 38
2.5 Tests of Statistical Significance 40
2.6 The Likelihood Function 45
3 Ordered Categorical Variables 53
3.1 Introduction 53
3.2 Log-Linear Models with One Ordered Category 53
3.3 Two Cross-Classified Ordered Categories 59
4 Non-Rectangular Tables 69
4.1 Introduction 69
4.2 Independence in a Triangular Table 69
4.3 Interactions in a Circular Table 72
4.4 Bradley-Terry Model for Pairwise Comparisons 79
5 Poisson Regression 85
5.1 Introduction 85
5.2 Poisson Regression for Mortality Data 87
5.3 Poisson Regression with Overdispersion 92
6 Finite Population Size Estimation 101
6.1 Introduction 101
6.2 A Small Example 101
6.3 A Larger Number of Lists 105
7 Truncated Poisson Regression 111
7.1 Introduction 111
7.2 Mathematical Background 112
7.3 Truncated Poisson Models with Covariates 117
7.4 An Example with Overdispersion 119
7.5 Diagnostics and Options 121
8 The Hypergeometric Distribution 129
8.1 Introduction 129
8.2 Derivation of the Distribution 131
8.3 Extended Hypergeometric Distribution 136
8.4 Hypergeometric Regression 139
8.5 Comparing Several 2 x 2 Tables 144
9 Sample Size Estimation and Power for Log-Linear Models 149
9.1 Introduction 149
9.2 Background Theory 149
9.3 Power for a 2 x 2 Table 154
9.4 Sample Size for an Interaction 161
9.5 Power for a Known Sample Size 167
A The Output Delivery System 173
B Programming Statements for Generalized Linear Models 177
C Additional Readings 181
References 183
Index 185
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