Akaike's information criterion in generalized estimating equations

Variable Selection for Marginal Longitudinal Generalized Linear Models

Variable selection is an essential part of any statistical analysis and yet has been somewhat neglected in the context of longitudinal data analysis. In this article, we propose a generalized version of Mallows's C(p) (GC(p)) suitable for use with both parametric and nonparametric models. GC(p) provides an estimate of a measure of model's adequacy for prediction. We examine its performance with popular marginal longitudinal models (fitted using GEE) and contrast results with what is typically done in practice: variable selection based on Wald-type or score-type tests. An application to real data further demonstrates the merits of our approach while at the same time emphasizing some important robust features inherent to GC(p).

Effects of Variance-Function Misspecification in Analysis of Longitudinal Data

The approach of generalized estimating equations (GEE) is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within-subject correlations. The variance is often assumed to be a known function of the mean. This article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses. Our numerical studies indicate that (1) correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified; (2) misspecification of the variance function impacts much more on estimators for within-cluster covariates than for cluster-level covariates; and (3) if the variance function is misspecified, correct choice of the correlation structure may not necessarily improve estimation efficiency. We illustrate impacts of different variance functions using a real data set from cow growth.

Spontaneous revegetation of mined peatlands in eastern Canada

Many North American peatlands previously mined for horticultural peat have been abandoned recently, allowing natural recolonization to occur. The two dominant methods for peat extraction, hand block-cutting and vacuum-mining, have created distinctly different abandoned surfaces, leading to different recolonization patterns. Both types of exploitation can be found throughout eastern Canada where we conducted a vast survey of 26 abandoned mined peatlands in the provinces of Québec and New Brunswick. The aim of this study is to describe the revegetation patterns and to assess the impact of local and regional variables as well as the time since abandonment on Sphagnum re-colonization. We inventoried the vegetation structure in all trenches (2571) and baulks (2595) of abandoned block-cut areas as well as in all vacuum fields (395) of the mechanically mined areas. We also conducted detailed species relevés in 242 of these peat fields. In comparison to vacuum-mined peatlands, block-cut peatlands regenerated remarkably well. Approximately 80% of all baulks and trenches in block-cut peatlands had 50% or higher cover of ericaceous shrubs compared with only 16% found on vacuum fields. Herb cover in the three types of abandoned fields was similar to that in natural peatlands. However, Sphagnum percent cover was below 2% in baulks and vacuum fields and was 30% on average in the trenches, which is clearly below cover estimates in natural peatlands. Sphagnum cover and richness were both higher in trenches with thin residual peat deposit, and Sphagnum richness increased with latitude. Our surveys revealed that abandoned mined peatlands have a high diversity of peatland vascular plants species and a low diversity of non-peatland species.Key words: cutover peatlands, regeneration, milled peatlands, block-cut peatlands, vacuum-mined peatlands, colonization patterns.

Around-the-clock: parent work schedules and children's well-being in a 24-h economy

Family life in developed economies has undergone a fundamental change--shifting from single-breadwinner households (typical of the post war decades) to families where both parents are employed. Equally dramatic has been the emergence of around-the-clock economies, altering the way work is organised, especially working time. Many more children now live in households where one or both parents work non-standard hours (evenings, nights or on weekends). Are there any implications for children's well-being when parents work non-standard schedules? There has been virtually no investigation of how children are faring in these around-the-clock households, despite evidence that non-standard work times affect family functioning and are stressful for parents. Using data from a representative sample of 4433 dual-earner Canadian families and their 2--11-year-old children (N children=6361), we compared families where both parents worked standard hours, with families where one or both worked non-standard times (evenings, nights or weekends). In nearly three-quarters of the families one or both parents regularly worked non-standard times. We found associations between children's well-being and parent work schedules, with higher odds ratios for child difficulties when parents worked non-standard times. These associations persisted after adjusting for several confounding factors including socio-economic status, parent part-time or full-time work, and childcare use, and were evident whether mothers, fathers or both parents worked non-standard times. The findings raise questions about the implications for children of the 24-h economy.

Comparison of methods for analyzing longitudinal binary outcomes: cognitive status as an example

Longitudinal data generate correlated observations. Ignoring correlation can lead to incorrect estimation of standard errors, resulting in incorrect inferences of parameters. In the example used here, standard logistic regression, a population-averaged (PA) model fit using generalized estimating equations (GEE), and random-intercept models are used to model binary outcomes at baseline, three and six years later. The outcomes indicate cognitive impairment versus no cognitive impairment in a sample of community dwelling elders. The models include both time-invariant (age, gender) and time-varying (time, interactions with time) covariates. The absolute estimates from random-intercept models are larger than those of both standard logistic and GEE models. Compared to the model fit using GEE that accounts for time dependency, standard logistic regression models overestimate standard errors of time-varying covariates (such as time, and time by problems with activities of daily living), and underestimate the standard errors of time-invariant covariates (such as age and gender). The standard errors from the random-intercept model are larger than those from logistic regression and GEE models. The choice of models, GEE or random-intercept, depends on the research question and the nature of the covariates. Population-averaged methods are appropriate when between-subjects effects are of interest, and random-effects are useful when subject-specific effects are important.

Mapping quantitative trait Loci using generalized estimating equations

A number of statistical methods are now available to map quantitative trait loci (QTL) relative to markers. However, no existing methodology can simultaneously map QTL for multiple nonnormal traits. In this article we rectify this deficiency by developing a QTL-mapping approach based on generalized estimating equations (GEE). Simulation experiments are used to illustrate the application of the GEE-based approach.

Model selection in estimating equations

Model selection is a necessary step in many practical regression analyses. But for methods based on estimating equations, such as the quasi-likelihood and generalized estimating equation (GEE) approaches, there seem to be few well-studied model selection techniques. In this article, we propose a new model selection criterion that minimizes the expected predictive bias (EPB) of estimating equations. A bootstrap smoothed cross-validation (BCV) estimate of EPB is presented and its performance is assessed via simulation for overdispersed generalized linear models. For illustration, the method is applied to a real data set taken from a study of the development of ewe embryos.