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Preface | |
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Introduction | |
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Notational conventions and acronyms | |
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A short review of generalized linear models | |
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A brief history of GLMs | |
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GLMs as likelihood-based models | |
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GLMs and correlated data | |
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GLMs and overdispersed data | |
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Scaling standard errors | |
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The modified sandwich variance estimator | |
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The basics of GLMs | |
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Link and variance functions | |
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Algorithms | |
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Software | |
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R | |
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SAS | |
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Stata | |
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SUDAAN | |
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Exercises | |
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Model Construction and Estimating Equations | |
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Independent data | |
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Optimization | |
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The FLML estimating equation for linear regression | |
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The FLML estimating equation for Poisson regression | |
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The FLML estimating equation for Bernoulli regression | |
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The LLML estimating equation for GLMs | |
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The LLMQL estimating equation for GLMs | |
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Estimating the variance of the estimates | |
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Model-based variance | |
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Empirical variance | |
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Pooled variance | |
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Panel data | |
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Pooled estimators | |
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Fixed-effects and random-effects models | |
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Unconditional fixed-effects models | |
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Conditional fixed-effects models | |
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Random-effects models | |
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Population-averaged and subject-specific models | |
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Estimation | |
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Summary | |
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Exercises | |
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R code for selected output | |
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Generalized Estimating Equations | |
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Population-averaged (PA) and subject-specific (SS) models | |
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The PA-GEE for GLMs | |
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Parameterizing the working correlation matrix | |
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Exchangeable correlation | |
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Autoregressive correlation | |
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Stationary correlation | |
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Nonstationary correlation | |
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Unstructured correlation | |
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Fixed correlation | |
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Free specification | |
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Estimating the scale variance (dispersion parameter) | |
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Independence models | |
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Exchangeable models | |
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Estimating the PA-GEE model | |
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The robust variance estimate | |
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A historical footnote | |
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Convergence of the estimation routine | |
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ALR: Estimating correlations for binomial models | |
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Quasi-least squares | |
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Summary | |
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The SS-GEE for GLMs | |
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Single random-effects | |
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Multiple random-effects | |
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Applications of the SS-GEE | |
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Estimating the SS-GEE model | |
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Summary | |
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The GEE2 for GLMs | |
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GEEs for extensions of GLMs | |
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Multinomial logistic GEE regression | |
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Proportional odds GEE regression | |
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Penalized GEE models | |
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Cox proportional hazards GEE models | |
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Further developments and applications | |
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The PA-GEE for GLMs with measurement error | |
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The PA-EGEE for GLMs | |
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The PA-REGEE for GLMs | |
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Quadratic inference function for marginal GLMs | |
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Missing data | |
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Choosing an appropriate model | |
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Marginal effects | |
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Marginal effects at the means | |
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Average marginal effects | |
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Summary | |
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Exercises | |
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R code for selected output | |
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Residuals, Diagnostics, and. Testing | |
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Criterion measures | |
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Choosing the best correlation structure | |
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Alternatives to the original QIC | |
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Choosing the best subset of covariates | |
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Analysis of residuals | |
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A nonparametric test of the randomness of residuals | |
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Graphical assessment | |
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Quasivariance functions for PA-GEE models | |
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Deletion diagnostics | |
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Influence measures | |
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Leverage measures | |
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Goodness of fit (population-averaged models) | |
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Proportional reduction in variation | |
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Concordance correlation | |
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A X<sup>2</sup> goodness of fit test for PA-GEE binomial models | |
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Testing coefficients in the PA-GEE model | |
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Likelihood ratio tests | |
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Wald tests | |
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Score tests | |
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Assessing the MCAR assumption of PA-GEE models | |
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Summary | |
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Exercises | |
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Programs and Datasets | |
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Programs | |
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Fitting PA-GEE models in Stata | |
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Fitting PA-GEE models in SAS | |
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Fitting PA-GEE models in R | |
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Fitting ALR models in SAS | |
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Fitting PA-GEE models in SUDAAN | |
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Calculating QIC(P) in Stata | |
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Calculating QIC(HH) in Stata | |
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Calculating QICu in Stata | |
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Graphing the residual runs test in R | |
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Using the fixed correlation structure in Stata | |
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Fitting quasi/variance PA-GEE models in R | |
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Fitting GLMs in R | |
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Fitting FE models in R using the GAMLSS package | |
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Fitting RE models in R using the LME4 package | |
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Datasets | |
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Wheeze data | |
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Ship accident data | |
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Progabide data | |
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Simulated logistic data | |
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Simulated user-specified correlated data | |
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Simulated measurement error data for the PA-GEE | |
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References | |
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Author index | |
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Subject index | |