A ‘subdivision regression’ model for data analysis

2011

Segmented mixed models with random changepoints: a maximum likelihood approach with application to treatment for depression study

Regression analysis is a widely used statistical technique to build a model from a set of data on two or more variables. Linear regression is based on linear correlation, and assumes that change in one variable is accompanied by a proportional change in another variable. Simple linear regression, or bivariate regression, is used for predicting the value of one variable from another variable (predictor); however, multiple linear regression, which enables us to analyse more than one predictor or variable, is more commonly used. This paper explains both simple and multiple linear regressions illustrated with an example of analysis and also discusses some common errors in presenting the results of regression, including inappropriate titles, causal language, inappropriate conclusions, and misinterpretation.

2010

Calculates type-II or type-III analysis-of-variance tables for model objects produced by lm, glm, multinom (in the nnet package), polr (in the MASS package), coxph (in the survival package), coxme (in the coxme pckage), svyglm (in the survey package), rlm (in the MASS package), lmer in the lme4 package, lme in the nlme package, and (by the default method) for most models with a linear predictor and asymptotically normal coefficients (see details below). For linear models, F-tests are calculated; for generalized linear models, likelihood-ratio chisquare, Wald chisquare, or F-tests are calculated; for multinomial logit and proportional-odds logit models, likelihood-ratio tests are calculated. Various test statistics are provided for multivariate linear models produced by lm or manova. Partial-likelihood-ratio tests or Wald tests are provided for Cox models. Wald chi-square tests are provided for fixed effects in linear and generalized linear mixed-effects models. Wald chi-square or F tests are provided in the default case.

except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Depends R (>= 3.1.0), MASS, Matrix (>= 1.0), stats, lme4 (>= 1.0) Description Functions to accompany A. Gelman and J. Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, Cambridge University Press, 2007.

Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces and demonstrates a wide variety of models, at the same time instructing the reader in how to fit these models using freely available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen in the authors' own applied research, with programming code provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.

2011

Calculates type-II or type-III analysis-of-variance tables for model objects produced by lm, glm, multinom (in the nnet package), polr (in the MASS package), coxph (in the survival package), coxme (in the coxme pckage), svyglm (in the survey package), rlm (in the MASS package), lmer in the lme4 package, lme in the nlme package, and (by the default method) for most models with a linear predictor and asymptotically normal coefficients (see details below). For linear models, F-tests are calculated; for generalized linear models, likelihood-ratio chisquare, Wald chisquare, or F-tests are calculated; for multinomial logit and proportional-odds logit models, likelihood-ratio tests are calculated. Various test statistics are provided for multivariate linear models produced by lm or manova. Partial-likelihood-ratio tests or Wald tests are provided for Cox models. Wald chi-square tests are provided for fixed effects in linear and generalized linear mixed-effects models. Wald chi-square or F tests are provided in the default case.

annual meeting of …, 2004