Journal ArticleDOI
Random-effects models for longitudinal data
Nan M. Laird,James H. Ware +1 more
Reads0
Chats0
TLDR
In this article, a unified approach to fitting two-stage random-effects models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed.Abstract:
Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a distribution specified at the second stage. A general family of models is discussed, which includes both growth models and repeated-measures models as special cases. A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed. Two examples are taken from a current epidemiological study of the health effects of air pollution.read more
Citations
More filters
Journal ArticleDOI
Fitting Linear Mixed-Effects Models Using lme4
TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.
Journal ArticleDOI
Longitudinal data analysis using generalized linear models
Kung Yee Liang,Scott L. Zeger +1 more
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Journal ArticleDOI
Bayesian measures of model complexity and fit
TL;DR: In this paper, the authors consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined and derive a measure pD for the effective number in a model as the difference between the posterior mean of the deviances and the deviance at the posterior means of the parameters of interest, which is related to other information criteria and has an approximate decision theoretic justification.
Journal ArticleDOI
Missing data: Our view of the state of the art.
Joseph L. Schafer,John W. Graham +1 more
TL;DR: 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI) are presented and may eventually extend the ML and MI methods that currently represent the state of the art.
Book
Experimental Design and Data Analysis for Biologists
Gerry P. Quinn,Michael J. Keough +1 more
TL;DR: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data is as discussed by the authors, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced.
References
More filters
Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Journal ArticleDOI
Recovery of inter-block information when block sizes are unequal
H. D. Patterson,Robin Thompson +1 more
TL;DR: In this article, a modified maximum likelihood procedure is proposed for estimating intra-block and inter-block weights in the analysis of incomplete block designs with block sizes not necessarily equal, and the method consists of maximizing the likelihood, not of all the data, but of selected error contrasts.
Journal ArticleDOI
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
TL;DR: In this paper, the authors proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects, and developed a satisfactory asymptotic theory for estimators of variance components.
Journal ArticleDOI
The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves
TL;DR: In the present paper, a class of problems where the dispersion matrix has a known structure is considered and the appropriate statistical methods are discussed.