多层统计分析模型:SAS与应用

《多层统计分析模型:SAS与应用》讲述了：Multilevel Models: Appfications Using SAS is written in nontechnical terms, focuses on the methods and applications of various multilevel models, including liner multilevel models,multilevel logistic regression models, multilevel Poisson regression models, multilevel negative binomial models, as well as some cutting-edge applications, such as multilevel zero-inflated Poisson (ZIP) model, random effect zero-inflated negative binomial model (RE-ZINB), mixed-effect mixed-distribution models, bootstrapping multilevel models, and group-based trajectory models. Readers will learn to build and apply multilevel models for hierarchically structured cross-sectional data and longitudinal data using the internationally distributed software package Statistics Analysis System (SAS). Detailed SAS syntax and output are provided for model applications, providing students, research scientists and data analysts with ready templates for their applications.

Dr. Jichuan Wang is a professor in the Center for Clinical and Community Research, the Children's National Medical Center, the George Washington Universty School of Medicine.
Dr. Haiyi Xie is an associate professor of Community and Family Medicine, Dartmouth Medical School, Dartmouth College.
Dr. James Henry Fisher is a senior planner for the HancockCounty Planning Commission in EIIsworth, Maine.

Chapter 1 Introduction
1.1 Conceptual framework of multilevel modeling
1.2 Hierarchically structured data
1.3 Variables in multilevel data
1.4 Analytical problems with multilevel data
1.5 Advantages and limitations of multilevel modeling
1.6 Computer software for multilevel modeling

Chapter 2 Basics of Linear Multilevel Models
2.1 Intraclass correlation coefficient (ICC)
2.2 Formulation of two-level multilevel models
2.3 Model assumptions
2.4 Fixed and random regression coefficients
2.5 Cross-level interactions
2.6 Measurement centering
2.7 Model estimation
2.8 Model fit, hypothesis testing, and model comparisons
2.8.1 Model fit
2.8.2 Hypothesis testing
2.8.3 Model comparisons
2.9 Explained level-1 and level-2 variances
2.10 Steps for building multilevel models
2.11 Higher-level multilevel models

Chapter 3 Application of Two-level Linear Multilevel Models
3.1 Data
3.2 Empty model
3.3 Predicting between-group variation
3.4 Predicting within-group variation
3.5 Testing random level-1 slopes
3.6 Across-level interactions
3.7 Other issues in model development

Chapter 4 Application of Multilevel Modeling to Longitudinal Data
4.1 Features of longitudinal data
4.2 Limitations of traditional approaches for modeling longitudinal data
4.3 Advantages of multilevel modeling for longitudinal data
4.4 Formulation of growth models
4.5 Data description and manipulation
4.6 Linear growth models
4.6.1 The shape of average outcome change over time
4.6.2 Random intercept growth models
4.6.3 Random intercept and slope growth models
4.6.4 Intercept and slope as outcomes
4.6.5 Controlling for individual background variables in models
4.6.6 Coding time score
4.6.7 Residual variance/covariance structures
4.6.8 Time-varying covariates
4.7 Curvilinear growth models
4.7.1 Polynomial growth model
4.7.2 Dealing with collinearity in higher order polynomial growth model
4.7.3 Piecewise (linear spline) growth model

Chapter 5 Multilevel Models for Discrete Outcome Measures
5.1 Introduction to generalized linear mixed models
5.1.1 Generalized linear models
5.1.2 Generalized linear mixed models
5.2 SAS Procedures for multilevel modeling with discrete outcomes
5.3 Multilevel models for binary outcomes
5.3.1 Logistic regression models
5.3.2 Probit models
5.3.3 Unobserved latent variables and observed binary outcome measures
5.3.4 Multilevel logistic regression models
5.3.5 Application of multilevel logistic regression models
5.3.6 Application of multilevel logit models to longitudinal data
5.4 Multilevel models for ordinal outcomes
5.4.1 Cumulative logit models
5.4.2 Multilevel cumulative logit models
5.5 Multilevel models for nominal outcomes
5.5.1 Multinomial logit models
5.5.2 Multilevel multinomial logit models
5.5.3 Application of multilevel multinomial logit models
5.6 Multilevel models for count outcomes
5.6.1 Poisson regression models
5.6.2 Poisson regression with over-dispersion and a negative binomial model
5.6.3 Multilevel Poisson and negative binomial models
5.6.4 Application of multilevel Poisson and negative binomial models

Chapter 6 Other Applications of Multilevel Modeling and Related Issues
6.1 Multilevel zero-inflated models for count data with extra zeros
6.1.1 Fixed-effect ZIP model
6.1.2 Random effect zero-inflated Poisson (RE-ZIP) models
6.1.3 Random effect zero-inflated negative binomial (RE-ZINB) models
6.1.4 Application of RE-ZIP and RE-ZINB models
6.2 Mixed-effect mixed-distribution models for semi-continuous outcomes
6.2.1 Mixed-effects mixed distribution model
6.2.2 Application of the Mixed-Effect mixed distribution model
6.3 Bootstrap multilevel modeling
6.3.1 Nonparametric residual bootstrap multilevel modeling
6.3.2 Parametric residual bootstrap multilevel modeling
6.3.3 Application of nonparametric residual bootstrap multilevel modeling
6.4 Group-based models for longitudinal data analysis
6.4.1 Introduction to group-based model
6.4.2 Group-based logit model
6.4.3 Group-based zero-inflated Poisson (ZIP) model
6.4.4 Group-based censored normal models
6.5 Missing values issue
6.5.1 Missing data mechanisms and their implications
6.5.2 Handling missing data in longitudinal data analyses
6.6 Statistical power and sample size for multilevel modeling
6.6.1 Sample size estimation for two-level designs
6.6.2 Sample size estimation for longitudinal data analysis
Reference
Index

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In the linear model case, this integral can be solved in closed form, and the resulting likelihood or restricted likelihood can be maximized directly. For nonlinear multilevel models, however, the integral is usually unknown and must be approximated. Many methods have been proposed for such maximization approximation. Two basic methods are: 1） linearizati'on, which approximates the integrated likelihood function using techniques such as Taylor series expansion, 2） integral approximation with numerical methods. These approaches are implemented in two SAS procedures, PROC GLIMMIX and PROC NLMIXED and two macros, ％GLIMMIX and ％NLMIXED, respectively.
Prior to the current version of SAS （SAS 9.2） （SAS Institute Inc., 2008）, PROC GLIMMIX is solely based on linearization methods. In version 9.2 of PROC GLIMMIX, linearization is the default estimation method, and two numerical integration methods——Laplace approximation method and adaptive Gauss-Hermite quadrature have been added as options. The linearization method is also called a pseudo-likelihood method, in which pseudo-data are generated from the original data, and likelihood function is approximated using Taylor series expansions （Schabenberger, 2005）. The essential idea of the linearization method is to approximate GLMM using normal linear mixed model estimates repeatedly. Among the various linearization methods available in the procedure, the default method is the restricted or residual pseudo-likelihood （REPL） （Wolfinger & O'Connell, 1993）. The maximization of the pseudo-likelihood can be carried out by various optimization techniques in PROC GLIMMIX. The default optimization technique is the Newton-Raphson algorithm.
The major advantages of linearization-based methods include: First, they can fit models for which the joint distribution is difficult or impossible to ascertain. Second, compared with numerical integration methods, they allow a larger number of random effects to be estimated in the model. Third, the variance/covariance structure of the level-1 residual matrix （i.e., R matrix） can be readily accommodated. Fourth, the model is iteratively estimated based on the linear mixed model, thus both ML and REML are available for model estimation （Schabenberger, 2005）. In addition, in our experience, linearization based models are much faster to run.
The disadvantages of linearization-based methods include: First, they are based on iterative model estimation using pseudo-data constructed from the original data; as such, they do not have a real likelihood, and therefore -2LL or deviance statistic cannot be used for model comparisons. Second, PROC GLIMMIX does not support a broad array of variance/covariance structures of the R matrix that you can draw on with the PROC MIXED procedure （Schabenberger, 2005）.