Poisson regression

About: Poisson regression is a research topic. Over the lifetime, 3395 publications have been published within this topic receiving 114136 citations. The topic is also known as: Poisson model.

A Modified Poisson Regression Approach to Prospective Studies with Binary Data

Abstract: Relative risk is usually the parameter of interest in epidemiologic and medical studies. In this paper, the author proposes a modified Poisson regression approach (i.e., Poisson regression with a robust error variance) to estimate this effect measure directly. A simple 2-by-2 table is used to justify the validity of this approach. Results from a limited simulation study indicate that this approach is very reliable even with total sample sizes as small as 100. The method is illustrated with two data sets.

Applied Linear Regression Models

Abstract: Part1 Simple Linear Regression 1Linear Regression with One Predictor Variable 2Inferences in Regression and Correlation Analysis 3Diagnostics and Remedial Measures 4 Simultaneous Inferences and Other Topics in Regression Analysis 5Matrix Approach to Simple Linear Regression Analysis Part 2Multiple Linear Regression 6Multiple Regression I 7 Multiple Regression II 8Building the Regression Model I: Models for Quantitative and Qualitative Predictors 9 Building the Regression Model II: Model Selection and Validation 10Building the Regression Model III: Diagnostics 11Remedial Measures and Alternative Regression Techniques 12Autocorrelation in Time Series Data Part 3Nonlinear Regression 13Introduction to Nonlinear Regression and Neural Networks 14Logistic Regression, Poisson Regression, and Generalized Linear Models

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

Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio

Abstract: Cross-sectional studies with binary outcomes analyzed by logistic regression are frequent in the epidemiological literature. However, the odds ratio can importantly overestimate the prevalence ratio, the measure of choice in these studies. Also, controlling for confounding is not equivalent for the two measures. In this paper we explore alternatives for modeling data of such studies with techniques that directly estimate the prevalence ratio. We compared Cox regression with constant time at risk, Poisson regression and log-binomial regression against the standard Mantel-Haenszel estimators. Models with robust variance estimators in Cox and Poisson regressions and variance corrected by the scale parameter in Poisson regression were also evaluated. Three outcomes, from a cross-sectional study carried out in Pelotas, Brazil, with different levels of prevalence were explored: weight-for-age deficit (4%), asthma (31%) and mother in a paid job (52%). Unadjusted Cox/Poisson regression and Poisson regression with scale parameter adjusted by deviance performed worst in terms of interval estimates. Poisson regression with scale parameter adjusted by χ2 showed variable performance depending on the outcome prevalence. Cox/Poisson regression with robust variance, and log-binomial regression performed equally well when the model was correctly specified. Cox or Poisson regression with robust variance and log-binomial regression provide correct estimates and are a better alternative for the analysis of cross-sectional studies with binary outcomes than logistic regression, since the prevalence ratio is more interpretable and easier to communicate to non-specialists than the odds ratio. However, precautions are needed to avoid estimation problems in specific situations.

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...