SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.

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Longitudinal data analysis using generalized linear models

PAML, currently in version 4, is a package of programs for phylogenetic analyses of DNA and protein sequences using maximum likelihood (ML). The programs may be used to compare and test phylogenetic trees, but their main strengths lie in the rich repertoire of evolutionary models implemented, which can be used to estimate parameters in models of sequence evolution and to test interesting biological hypotheses. Uses of the programs include estimation of synonymous and nonsynonymous rates (d(N) and d(S)) between two protein-coding DNA sequences, inference of positive Darwinian selection through phylogenetic comparison of protein-coding genes, reconstruction of ancestral genes and proteins for molecular restoration studies of extinct life forms, combined analysis of heterogeneous data sets from multiple gene loci, and estimation of species divergence times incorporating uncertainties in fossil calibrations. This note discusses some of the major applications of the package, which includes example data sets to demonstrate their use. The package is written in ANSI C, and runs under Windows, Mac OSX, and UNIX systems. It is available at -- (http://abacus.gene.ucl.ac.uk/software/paml.html).

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PAML 4: Phylogenetic Analysis by Maximum Likelihood

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, 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 Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

In both corporate finance and asset pricing empirical work, researchers are often confronted with panel data. In these data sets, the residuals may be correlated across firms and across time, and OLS standard errors can be biased. Historically, the two literatures have used different solutions to this problem. Corporate finance has relied on clustered standard errors, while asset pricing has used the Fama-MacBeth procedure to estimate standard errors. This paper examines the different methods used in the literature and explains when the different methods yield the same (and correct) standard errors and when they diverge. The intent is to provide intuition as to why the different approaches sometimes give different answers and give researchers guidance for their use.

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Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches

"With its emphasis on practical and conceptual aspects, rather than mathematics or formulas, this accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA). Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities and differences between CFA and exploratory factor analysis (EFA); and report results from a CFA study. It is filled with useful advice and tables that outline the procedures. The companion website offers data and program syntax files for most of the research examples, as well as links to CFA-related resources. New to This Edition *Updated throughout to incorporate important developments in latent variable modeling. *Chapter on Bayesian CFA and multilevel measurement models. *Addresses new topics (with examples): exploratory structural equation modeling, bifactor analysis, measurement invariance evaluation with categorical indicators, and a new method for scaling latent variables. *Utilizes the latest versions of major latent variable software packages"--

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Confirmatory Factor Analysis for Applied Research

SUMMARY In recent years substantial research has been devoted to developing failure-time methodology which accounts for possible dependency between observations. An example is the univariate frailty model (Vaupel, Manton & Stallard, 1979), which incorporates an exchangeable dependence structure by the inclusion of cluster-specific random effects. In some studies it may be reasonable to expect more than one level of within-cluster association: for instance, association between a parent and child versus that between two siblings in studies of familial disease aggregation, or association between two village residents who live in different households versus that between residents of the same household in intervention studies. We propose a family of distributional models for failure-time data that accounts for multiple levels of clustering and reduces in the case of a single clustering level to a univariate frailty model. The resulting survival functions are constructed by a recursive nesting of univariate frailty-type distributions through which archimedean copula forms are determined for all bivariate margins. Properties of the proposed model are developed, illustrated and briefly contrasted with multivariate frailty model properties. In conclusion, we outline the application of our model to marginal risk regression problems.

Modelling failure-time associations in data with multiple levels of clustering

Summary

A robust approach for analysis of variance components models is presented which does not rely on the assumption of multivariate normality for its validity. This approach uses the multivariate normal distribution as a ‘working model’ but obtains standard errors for the final estimators which do not depend on this underlying distribution. By using the observed variance in the first derivatives of the multivariate normal ‘working model’ to modify the conventional score test, hypotheses regarding specific components can also be tested without relying directly on the assumption of multivariate normality. A special case is presented where both the modified score test and the likelihood ratio test are equally robust, and simulated data are used to illustrate this situation. Measurements of triglyceride levels in 391 individuals in 60 families randomly selected from the membership of a health maintenance organization are used to illustrate this robust approach to variance components.

Use of robust variance components models to analyse triglyceride data in families

Cognitive functioning in compulsive hoarding

This paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, θ = (γ, η), H(0) : γ = γ(0), based on the pseudolikelihood L(θ, ϕ), where ϕ is a consistent estimator of ϕ, the nuisance parameter. We show that the asymptotic distribution of T under H(0) is a weighted sum of independent chi-squared variables. Some sufficient conditions are provided for the limiting distribution to be a chi-squared variable. When the true value of the parameter of interest, θ(0), or the true value of the nuisance parameter, ϕ(0), lies on the boundary of parameter space, the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix, or from a mixture of multivariate normal distributions. A variety of examples are provided for which the limiting distributions of T may be mixtures of chi-squared variables. We conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments.

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On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems.

A regression model for estimating covariate effects on odds ratios to test for familial aggregation of common disease in first-degree relatives of cases and controls is presented and illustrated by using family data from a study of chronic obstructive pulmonary disease. These estimators are in essence an extension of the Mantel-Haenszel estimator of odds ratio but do not require the assumption of independence among relatives. A robust test statistic for possible effects of covariates such as the matching variables for cases and controls on odds ratio is also presented. In data on 156 adult first-degree relatives of 28 cases with demonstrated airway obstruction and 28 controls matched for age, sex, race, and hospital status, there appeared to be a difference in the odds ratio among families of black and white case-control pairs. However, the small sample size available prevents conclusive interpretation of this observation.

Kung Yee Liang

Papers

Modelling failure-time associations in data with multiple levels of clustering

Use of robust variance components models to analyse triglyceride data in families

Cognitive functioning in compulsive hoarding

On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems.

Application of odds ratio regression models for assessing familial aggregation from case-control studies