Flexible Approaches to Computing Mediated Effects in Generalized Linear Models: Generalized Estimating Equations and Bootstrapping

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by which the regression coefficient of X on Y changes after adjusting for M. Advantages of this method are: (a) it applies to the class of generalized linear models, including linear, logistic, and Poisson regression as special cases; (b) it allows multiple independent variables and mediators in the same model; and (c) asymptotically valid standard errors and confidence intervals are obtained using standard software. This methodology is compared with the bootstrap, another general methodology that can be applied to the same broad class of models, and is evaluated using simulation in both linear and logistic regression scenarios. The methods are utilized to examine the degree to which the effect of low birthweight status on internalizing symptoms at age 20 is mediated through IQ at age 8.     

Fuzzy Clusterwise Growth Curve Models via Generalized Estimating Equations: An Application to the Antisocial Behavior of Children

The growth curve model has been a useful tool for the analysis of repeated measures data. However, it is designed for an aggregate-sample analysis based on the assumption that the entire sample of respondents are from a single homogenous population. Thus, this method may not be suitable when heterogeneous subgroups exist in the population with qualitatively distinct patterns of trajectories. In this paper, the growth curve model is generalized to a fuzzy clustering framework, which explicitly accounts for such group-level heterogeneity in trajectories of change over time. Moreover, the proposed method estimates parameters based on generalized estimating equations thereby relaxing the assumption of correct specification of the population covariance structure among repeated responses. The performance of the proposed method in recovering parameters and the number of clusters is investigated based on two Monte Carlo analyses involving synthetic data. In addition, the empirical usefulness of the proposed method is illustrated by an application concerning the antisocial behavior of a sample of children.     

Assessment of Multiple Membership Multilevel Models: An Application to Interviewer Effects on Nonresponse

Multilevel multiple membership models account for situations where lower level units are nested within multiple higher level units from the same classification. Not accounting correctly for such multiple membership structures leads to biased results. The use of a multiple membership model requires selection of weights reflecting the hypothesized contribution of each level two unit and their relationship to the level one outcome. The Deviance Information Criterion (DIC) has been proposed to identify such weights. For the case of logistic regression, this study assesses, through simulation, the model identification rates of the DIC to detect the correct multiple membership weights, and the properties of model variance estimators for different weight specifications across a range of scenarios. The study is motivated by analyzing interviewer effects across waves in a longitudinal study. Interviewers can substantially influence the behavior of sample survey respondents, including their decision to participate in the survey. In the case of a longitudinal survey several interviewers may contact sample members to participate across different waves. Multilevel multiple membership models are suitable to account for the inclusion of higher-level random effects for interviewers at various waves, and to assess, for example, the relative importance of previous and current wave interviewers on current wave nonresponse. To illustrate the application, multiple membership models are applied to the UK Family and Children Survey to identify interviewer effects in a longitudinal study. The paper takes a critical view on the substantive interpretation of the model weights and provides practical guidance to statistical modelers. The main recommendation is that it is best to specify the weights in a multiple membership model by exploring different weight specifications based on the DIC, rather than prespecifying the weights.     

Partial Likelihood Estimation of IRT Models with Censored Lifetime Data: An Application to Mental Disorders in the ESEMeD Surveys

Developmental studies of mental disorders based on epidemiological data are often based on cross-sectional retrospective surveys. Under such designs, observations are right-censored, causing underestimation of lifetime prevalences and correlations, and inducing bias in latent trait models on the observations. In this paper we propose a Partial Likelihood (PL) method to estimate unbiased IRT models of lifetime predisposition to develop a certain outcome. A two-step estimation procedure corrects the IRT likelihood of outcome appearance with a function depending on (a) projected outcome frequencies at the end of the risk period, and (b) outcome censoring status at the time of the observation. Simulation results showed that the PL method yielded good recovery of true frequencies and intercepts. Slopes were best estimated when events were sufficiently correlated. When PL is applied to lifetime mental health disorders (assessed in the ESEMeD project surveys), estimated univariate prevalences were, on average, 1.4 times above raw estimates, and 2.06 higher in the case of bivariate prevalences.