Shrinkage empirical likelihood estimator in longitudinal analysis with time-dependent covariates-application to modeling the health of Filipino children

The method of generalized estimating equations (GEE) is a popular tool for analysing longitudinal (panel) data. Often, the covariates collected are time-dependent in nature, for example, age, relapse status, monthly income. When using GEE to analyse longitudinal data with time-dependent covariates, crucial assumptions about the covariates are necessary for valid inferences to be drawn. When those assumptions do not hold or cannot be verified, Pepe and Anderson (1994, Communications in Statistics, Simulations and Computation 23, 939–951) advocated using an independence working correlation assumption in the GEE model as a robust approach. However, using GEE with the independence correlation assumption may lead to significant efficiency loss (Fitzmaurice, 1995, Biometrics 51, 309–317). In this article, we propose a method that extracts additional information from the estimating equations that are excluded by the independence assumption. The method always includes the estimating equations under the independence assumption and the contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We apply the method to a longitudinal study of the health of a group of Filipino children.

Project-based organization as adaptation to risk and opportunity in small firms

Recent years have seen a rapid increase in SMEs working collaboratively in inter-organizational projects. But what drives the emergence of such projects, and what types of industries breed them the most? To address these questions, this paper extends the long running literature on the firm and industry antecedents of new venturing and alliance formation to the domain of project-based organization by SMEs. Based on survey data collected among 1,725 small and medium sized organizations and longitudinal industry data, we find an overall pattern that indicates that IOPV participation is primarily determined by a focal SME’s scope of innovative activities, and the munificence, dynamism and complexity of its environment. Unexpectedly, these variables have different effects on whether SMEs are likely to engage in IOPVs, compared to with how many there are in their portfolio at a time. Implications for theory development are discussed.

Alternative modes of entrepreneurial opportunity exploitation : the case on inter-organizational project

While entrepreneurship research has taken firm formation to be the predominant mode of opportunity exploitation, entrepreneurship can take place through many other types of organizational arrangements. In the present article, we consider one such alternative arrangement, namely the formation of inter-organizational projects (IOPs). We propose a multi-level contingency model that suggests that uncertainty both at the level of the firm and at the level of the environment makes the exploitation of opportunities through IOPs more likely. The model is tested by telephone survey data collected amongst a panel of 1725 SMEs and longitudinal industry data. Our findings provide strong support for the industry-level part of the model, but interestingly, only partial support for the firm level part of the model. This indicates that the effects of uncertainty need to be dissected into different levels of analysis to understand the conditions under which alternative modes of opportunity exploitation can be a prominent entrepreneurial alternative to new firm formation.

Alternative modes of entrepreneurial opportunity exploitation

While entrepreneurship research has taken firm formation to be the predominant mode of opportunity exploitation, entrepreneurship can take place through many other types of organizational arrangements. In the present article, we consider one such alternative arrangement, namely the formation of inter-organizational projects (IOPs). We propose a multi-level contingency model that suggests that uncertainty both at the level of the firm and at the level of the environment makes the exploitation of opportunities through IOPs more likely. The model is tested by telephone survey data collected amongst a panel of 1725 SMEs and longitudinal industry data. Our findings provide strong support for the industry-level part of the model, but interestingly, only partial support for the firm level part of the model. This indicates that the effects of uncertainty need to be dissected into different levels of analysis to understand the conditions under which alternative modes of opportunity exploitation can be a prominent entrepreneurial alternative to new firm formation.

Working covariance model selection for generalized estimating equations

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice.

Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

1. Ecological data sets often use clustered measurements or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance describes the degree of similarity among the repeated observations. 2. Three methods for choosing the covariance are: the Akaike information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We compared the methods using a simulation study and using a data set that explored effects of forest fragmentation on avian species richness over 15 years. 3. The overall success was 80.6% for the AIC, 29.4% for the QIC and 81.6% for the DIC. For the forest fragmentation study the AIC and DIC selected the unstructured covariance, whereas the QIC selected the simpler autoregressive covariance. Graphical diagnostics suggested that the unstructured covariance was probably correct. 4. We recommend using DIC for selecting the correct covariance structure.

Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

The validity of personal disturbance scale (DSSI/sAD) in people with diabetes mellitus, using longitudinal data

Despite being used since 1976, Delusions-Symptoms-States-Inventory/states of Anxiety and Depression (DSSI/sAD) has not yet been validated for use among people with diabetes. The aim of this study was to examine the validity of the personal disturbance scale (DSSI/sAD) among women with diabetes using Mater-University of Queensland Study of Pregnancy (MUSP) cohort data. The DSSI subscales were compared against DSM-IV disorders, the Mental Component Score of the Short Form 36 (SF-36 MCS), and Center for Epidemiologic Studies Depression Scale (CES-D). Factor analyses, odds ratios, receiver operating characteristic (ROC) analyses and diagnostic efficiency tests were used to report findings. Exploratory factor analysis and fit indices confirmed the hypothesized two-factor model of DSSI/sAD. We found significant variations in the DSSI/sAD domain scores that could be explained by CES-D (DSSI-Anxiety: 55%, DSSI-Depression: 46%) and SF-36 MCS (DSSI-Anxiety: 66%, DSSI-Depression: 56%). The DSSI subscales predicted DSM-IV diagnosed depression and anxiety disorders. The ROC analyses show that although the DSSI symptoms and DSM-IV disorders were measured concurrently the estimates of concordance remained only moderate. The findings demonstrate that the DSSI/sAD items have similar relationships to one another in both the diabetes and non-diabetes data sets which therefore suggest that they have similar interpretations.

Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests

Selection criteria and misspecification tests for the intra-cluster correlation structure (ICS) in longitudinal data analysis are considered. In particular, the asymptotical distribution of the correlation information criterion (CIC) is derived and a new method for selecting a working ICS is proposed by standardizing the selection criterion as the p-value. The CIC test is found to be powerful in detecting misspecification of the working ICS structures, while with respect to the working ICS selection, the standardized CIC test is also shown to have satisfactory performance. Some simulation studies and applications to two real longitudinal datasets are made to illustrate how these criteria and tests might be useful.

Quantile regression for longitudinal data with a working correlation model

This paper proposes a linear quantile regression analysis method for longitudinal data that combines the between- and within-subject estimating functions, which incorporates the correlations between repeated measurements. Therefore, the proposed method results in more efficient parameter estimation relative to the estimating functions based on an independence working model. To reduce computational burdens, the induced smoothing method is introduced to obtain parameter estimates and their variances. Under some regularity conditions, the estimators derived by the induced smoothing method are consistent and have asymptotically normal distributions. A number of simulation studies are carried out to evaluate the performance of the proposed method. The results indicate that the efficiency gain for the proposed method is substantial especially when strong within correlations exist. Finally, a dataset from the audiology growth research is used to illustrate the proposed methodology.

Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback-Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used for illustration.