Linear Model For Longitudinal Data Research Articles

Summarizing the goodness of fit of generalized linear models for longitudinal data

Summarizing the goodness of fit of generalized linear models for longitudinal data

Residuals analysis of the generalized linear models for longitudinal data

Residuals analysis of the generalized linear models for longitudinal data

Summarizing the goodness of fit of generalized linear models for longitudinal data

This paper extends four goodness-of-fit measures of a generalized linear model (GLM) to random effects and marginal models for longitudinal data. The four measures are the proportional reduction in entropy measure, the proportional reduction in deviance measure, the concordance correlation coefficient and the concordance index. The extended measures satisfy the basic requirements for measures of association. Two examples illustrate their use in model selection.

General multivariate linear models for longitudional studies

Longitudinal studies occcur frequently in many different disciplines. To fully utilize the potential value of the information contained in a longitudinal data, various multivariate linear models have been proposed. The methodology and analysis are somewhat unique in their own ways and their relationships are not well understood and presented. This article describes a general multivaritate linear model for longitudinal data and attempts to provide a constructive formulation of the components in the mean response profile. The objective is to point out the extension and connections of some well-known models that have been obscured by different areas of application. More imporiantly, the model is expressed in a unified regression form from the subject matter considerations. Such an approach is simpler and more intuitive than other ways to modeling and parameter estimation. As a cmsequeace the analyses of the general class cf models for longitudional data can be casily implemented with standard software.

Longitudinal data analysis: non-stationary error structures and antedependent models

Non-stationary covariance structures had not been analyzed in detail for longitudinal data mainly because the existing applications did not require their use. Data from the Iowa Cochlear Implant Project showed this type of structure and the problem needed to be addressed. We propose a linear model for longitudinal data in which the correlation structure includes the Box-Cox transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects, with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation (REML) are discussed and the method is applied to speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown. Possible extensions for the model are suggested. © 1998 John Wiley & Sons, Ltd.

Decadal-scale dynamics at the Gus Pearson Natural Areas: evidence for inverse (a)symmetric competition?

The Gus Pearson Natural Area is one of the longest maintained individual-based forest-monitoring sites in the world. It is an 800 × 400 m plot established in 1908 within pristine ponderosa pine (Pinusponderosa Dougl. ex Laws, van scopulorum) forest near Flagstaff, Arizona. I quantified decadal-scale growth trends of individual trees and of the entire stand from timber inventories repeated at 10-year intervals between 1920 and 1990. A mixed linear model for longitudinal data was used to test significance of temporal trends. Stand density increased throughout the 20th century because of successful regeneration pulses, active fire control, and no tree cutting. Aboveground growth rates of the stand as a whole did not change significantly from 1920 to 1990, but individual growth rates declined. Mixed linear model results indicated that decadal basal area increment of large pines declined more than that of small pines. In 1920–1930 large pines were growing faster than small pines, but by 1980–1990 large pines were growing slower than small pines. Since the number of small pines multiplied and the number of large pines changed slightly, I inferred that competition for resources was more detrimental for large pines than for small pines.

On Joint Estimation of Regression and Overdispersion Parameters in Generalized Linear Models for Longitudinal Data

Liang and Zeger introduced a class of estimating equations that gives consistent estimates of regression parameters and of their variances in the class of generalized linear models for longitudinal data. When the response variable in such models is subject to overdispersion, the oerdispersion parameter does not only influence the marginal variance, it may also influence the mean of the response variable. In such cases, the overdispersion parameter plays a significant role in the estimation of the regression parameters. This raises the necessity for a joint estimation of the regression, as well as overdispersion parameters, in order to describe the marginal expectation of the outcome variable as a function of the covariates. To correct for the effect of overdispersion, we, therefore, exploit a general class of joint estimating equations for the regression and overdispersion parameters. This is done, first, under the working assumption that the observations for a subject are independent and then under the general condition that the observations are correlated. In the former case, both score and quasi-score estimating equations are developed. The score equations are obtained from the marginal likelihood of the data, and the quasi-score equations are derived by exploiting the first two moments of the marginal distribution. This quasi-score equations approach requires a weight matrix, usually referred to as the pseudo-covariance weight matrix, which we construct under the assumption that the observations for a subject (or in a cluster) are independent. In the later case when observations are correlated, quasi-score estimating equations are developed in the manner similar to that of the independence case but the pseudo-covariance weight matrix is constructed from a suitable working covariance matrix of the longitudinal observations, the joint distribution of the observations being unknown. Asymptotic theory is provided for the general class of joint estimators for the regression and overdispersion parameters. The asymptotic distributional results are also applied to develop suitable chi-square test for testing for the regression of the overdispersed data.

Variable selection in strong hierarchical semiparametric models for longitudinal data.

In this paper, we consider the variable selection problem in semiparametric additive partially linear models for longitudinal data. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Meanwhile, we enforce the strong hierarchical restriction on the model, that is, an interaction can be included in the model only if both the associated main effects are included. Based on B-splines basis approximation for the nonparametric components, we propose an iterative estimation procedure for the model by penalizing the likelihood with a partial group minimax concave penalty (MCP), and use BIC to select the tuning parameter. To further improve the estimation efficiency, we specify the working covariance matrix by maximum likelihood estimation. Simulation studies indicate that the proposed method tends to consistently select the true model and works efficiently in estimation and prediction with finite samples, especially when the true model obeys the strong hierarchy. Finally, the China Stock Market data are fitted with the proposed model to illustrate its effectiveness.