Overdispersion

About: Overdispersion is a research topic. Over the lifetime, 1834 publications have been published within this topic receiving 79674 citations.

Approximate inference in generalized linear mixed models

Abstract: Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Im...

Multilevel and Longitudinal Modeling Using Stata

Abstract: Preface LINEAR VARIANCE-COMPONENTS MODELS Introduction How reliable are expiratory flow measurements? The variance-components model Modeling the Mini Wright measurements Estimation methods Assigning values to the random intercepts Summary and further reading Exercises LINEAR RANDOM-INTERCEPT MODELS Introduction Are tax preparers useful? The longitudinal data structure Panel data and correlated residuals The random-intercept model Different kinds of effects in panel models Endogeneity and between-taxpayer effects Residual diagnostics Summary and further reading Exercises LINEAR RANDOM-COEFFICIENT AND GROWTH-CURVE MODELS Introduction How effective are different schools? Separate linear regressions for each school The random-coefficient model How do children grow? Growth-curve modeling Two-stage model formulation Prediction of trajectories for individual children Complex level-1 variation or heteroskedasticity Summary and further reading Exercises DICHOTOMOUS OR BINARY RESPONSES Models for dichotomous responses Which treatment is best for toenail infection? The longitudinal data structure Population-averaged or marginal probabilities Random-intercept logistic regression Subject-specific vs. population-averaged relationships Maximum likelihood estimation using adaptive quadrature Empirical Bayes (EB) predictions Other approaches to clustered dichotomous data Summary and further reading Exercises ORDINAL RESPONSES Introduction Cumulative models for ordinal responses Are antipsychotic drugs effective for patients with schizophrenia? Longitudinal data structure and graphs A proportional-odds model A random-intercept proportional-odds model A random-coefficient proportional-odds model Marginal and patient-specific probabilities Do experts differ in their grading of student essays? A random-intercept model with grader bias Including grader-specific measurement error variances Including grader-specific thresholds Summary and further reading Exercises COUNTS Introduction Types of counts Poisson model for counts Did the German health-care reform reduce the number of doctor visits? Longitudinal data structure Poisson regression ignoring overdispersion and clustering Poisson regression with overdispersion but ignoring clustering Random-intercept Poisson regression Random-coefficient Poisson regression Other approaches to clustered counts Which Scottish countries have a high risk of lip cancer? Standardized mortality ratios Random-intercept Poisson regression Nonparametric maximum likelihood estimation Summary and further reading Exercises HIGHER LEVEL MODELS AND NESTED RANDOM EFFECTS Introduction Which method is best for measuring expiratory flow? Two-level variance-components models Three-level variance-components models Did the Guatemalan immunization campaign work? A three-level logistic random-intercept model Summary and further reading Exercises CROSSED RANDOM EFFECTS Introduction How does investment depend on expected profit and capital stock? A two-way error-components model How much do primary and secondary schools affect attainment at age 16? An additive crossed random-effects model Including a random interaction A trick requiring fewer random effects Summary and further reading Exercises APPENDIX A: Syntax for gllamm, eq, and gllapred APPENDIX B: Syntax for gllamm APPENDIX C: Syntax for gllapred APPENDIX D: Syntax for gllasim References Author Index Subject Index

Zero-inflated Poisson regression, with an application to defects in manufacturing

Abstract: Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ T ) for an unknown constant T . In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio test...

Negative Binomial Regression

Abstract: Preface 1. Introduction 2. The concept of risk 3. Overview of count response models 4. Methods of estimation and assessment 5. Assessment of count models 6. Poisson regression 7. Overdispersion 8. Negative binomial regression 9. Negative binomial regression: modeling 10. Alternative variance parameterizations 11. Problems with zero counts 12. Censored and truncated count models 13. Handling endogeneity and latent class models 14. Count panel models 15. Bayesian negative binomial models Appendix A. Constructing and interpreting interactions Appendix B. Data sets and Stata files References Index.

Logistic Regression Models

Abstract: Preface Introduction The Normal Model Foundation of the Binomial Model Historical and Software Considerations Chapter Profiles Concepts Related to the Logistic Model 2 x 2 Table Logistic Model 2 x k Table Logistic Model Modeling a Quantitative Predictor Logistic Modeling Designs Estimation Methods Derivation of the IRLS Algorithm IRLS Estimation Maximum Likelihood Estimation Derivation of the Binary Logistic Algorithm Terms of the Algorithm Logistic GLM and ML Algorithms Other Bernoulli Models Model Development Building a Logistic Model Assessing Model Fit: Link Specification Standardized Coefficients Standard Errors Odds Ratios as Approximations of Risk Ratios Scaling of Standard Errors Robust Variance Estimators Bootstrapped and Jackknifed Standard Errors Stepwise Methods Handling Missing Values Modeling an Uncertain Response Constraining Coefficients Interactions Introduction Binary X Binary Interactions Binary X Categorical Interactions Binary X Continuous Interactions Categorical X Continuous Interaction Thoughts about Interactions Analysis of Model Fit Traditional Fit Tests for Logistic Regression Hosmer-Lemeshow GOF Test Information Criteria Tests Residual Analysis Validation Models Binomial Logistic Regression Overdispersion Introduction The Nature and Scope of Overdispersion Binomial Overdispersion Binary Overdispersion Real Overdispersion Concluding Remarks Ordered Logistic Regression Introduction The Proportional Odds Model Generalized Ordinal Logistic Regression Partial Proportional Odds Multinomial Logistic Regression Unordered Logistic Regression Independence of Irrelevant Alternatives Comparison to Multinomial Probit Alternative Categorical Response Models Introduction Continuation Ratio Models Stereotype Logistic Model Heterogeneous Choice Logistic Model Adjacent Category Logistic Model Proportional Slopes Models Panel Models Introduction Generalized Estimating Equations Unconditional Fixed Effects Logistic Model Conditional Logistic Models Random Effects and Mixed Models Logistic Regression Other Types of Logistic-Based Models Survey Logistic Models Scobit-Skewed Logistic Regression Discriminant Analysis Exact Logistic Regression Exact Methods Alternative Modeling Methods Conclusion Appendix A: Brief Guide to Using Stata Commands Appendix B: Stata and R Logistic Models Appendix C: Greek Letters and Major Functions Appendix D: Stata Binary Logistic Command Appendix E: Derivation of the Beta-Binomial Appendix F: Likelihood Function of the Adaptive Gauss-Hermite Quadrature Method of Estimation Appendix G: Data Sets Appendix H: Marginal Effects and Discrete Change References Author Index Subject Index Exercises and R Code appear at the end of most chapters.