Marginal Correlation from Logit- and Probit-Beta-Normal Models for Hierarchical Binary Data

In hierarchical data settings, be it of a longitudinal, spatial, multi-level, clustered, or otherwise repeated nature, often the association between repeated measurements attracts at least part of the scientific interest. Quantifying the association frequently takes the form of a correlation function, including but not limited to intraclass correlation. Vangeneugden et al. (2010 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C., Sotto, C. (2010). Marginal correlation in longitudinal binary data based on generalized linear mixed models. Communi. Stati. Theory &; Methods. 39:3542–3557. [Google Scholar]) derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models. Here, we consider the extended model family proposed by Molenberghs et al. (2010 Molenberghs, G., Verbeke, G., Demétrio, C., Vieira, A. (2010). A family of generalized linear models for repeated measures with normal and conjugate random effects. Stat. Sci. 25:325–347.[Crossref], [Web of Science ®] , [Google Scholar]). This family flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. The family allows for closed-form means, variance functions, and correlation function, for a variety of outcome types and link functions. Unfortunately, for binary data with logit link, closed forms cannot be obtained. This is in contrast with the probit link, for which such closed forms can be derived. It is therefore that we concentrate on the probit case. It is of interest, not only in its own right, but also as an instrument to approximate the logit case, thanks to the well-known probit-logit ‘conversion.’ Next to the general situation, some important special cases such as exchangeable clustered outcomes receive attention because they produce insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. (2010 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C., Sotto, C. (2010). Marginal correlation in longitudinal binary data based on generalized linear mixed models. Communi. Stati. Theory &; Methods. 39:3542–3557. [Google Scholar]) and with approximations derived for the so-called logistic-beta-normal combined model. A simulation study explores performance of the method proposed. Data from a schizophrenia trial are analyzed and correlation functions derived.     

Empirical Bayes estimates for correlated hierarchical data with overdispersion

An extension of the generalized linear mixed model was constructed to simultaneously accommodate overdispersion and hierarchies present in longitudinal or clustered data. This so‐called combined model includes conjugate random effects at observation level for overdispersion and normal random effects at subject level to handle correlation, respectively. A variety of data types can be handled in this way, using different members of the exponential family. Both maximum likelihood and Bayesian estimation for covariate effects and variance components were proposed. The focus of this paper is the development of an estimation procedure for the two sets of random effects. These are necessary when making predictions for future responses or their associated probabilities. Such (empirical) Bayes estimates will also be helpful in model diagnosis, both when checking the fit of the model as well as when investigating outlying observations. The proposed procedure is applied to three datasets of different outcome types. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatment‐control average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), Heckman, Ichimura, and Todd (1998), and Robins, Mark, and Newey (1992). We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score.     

One size fits all? The social construction of dis-employ-abled women

This article is based on an evaluation of a labour-market training programme for women with ‘mental health problems’ in a social workplace in Belgium. The research team explored the retrospective insider perspectives on the work aspirations of the women involved in the programme to identify critical dynamics in their high drop-out from the social workplace. The central findings provide evidence of a prevalent one-size-fits-all discourse in these practices wherein complex and interrelated processes of discrimination take place that are based on both disability and gender. The findings demonstrate that the social workplace functions as a male bastion, in which the oversized overalls that women are forced to wear are symbolically relevant. In conclusion, we discuss and challenge the dominance of the neo-liberal norm of economic productivity and employability.     

Clustering in dividends: Do managers rely on cognitive reference points?

Prior studies (see e.g. [Rosch, E. (1975). Cognitive reference points. Cognitive Psychology, 7, 532–547]) indicate that multiples of ten serve as cognitive reference points with a view to perceiving and evaluating numbers. In order to explore whether managers set dividends per share (henceforth DPS) at or just above a cognitive reference point, we perform a digital analysis on US firms’ DPS for the period 1995–2004. That is, based on the theory of cognitive reference points, DPS of $2.00 will be viewed as being abnormally larger than DPS of $1.99, whereas the actual difference only amounts to a marginal $0.01. Results presented in this paper indicate that managers fall back on cognitive reference points when they set DPS, which shows in significantly more (fewer) zeroes (large digits) in the second-from-the-left position of DPS than would normally be expected. Overall, results presented in this paper tally with prior findings on odd-ending prices and price clustering documented in related disciplines.     

Community perceptions of people with disabilities in the North West region of Cameroon: what is the impact on their access to services?

Community perceptions of people with disabilities are not uncommon and also have impact on access to services. This article discusses the results from interviews, participant observations as well as field notes with 62 participants (people with disabilities, families of people with disabilities, regular school teachers and principals, community-based rehabilitation personnel, non-governmental organization personnel, traditional leaders, religious leaders and social workers) regarding their perceptions of people with disabilities and the impact on access to services. The findings from the study revealed that community’s perceptions of people with disabilities are both negative and positive and have an impact on their access to schooling, health and rehabilitation services. The discussions/conclusions include difference in perspectives, beliefs and practices, impact of perceptions as non-linear, sensitization/flow of information and context difference.     

A comparative study on estimation methods to deal with the endogeneity in linear random-intercept models with an extension

In this paper, we investigate estimation methods to deal with situations where random intercepts are associated to time-varying covariates in the context of linear mixed models. First, a review of previous ways to deal with this so-called endogeneity issue is presented, then a new method based on shared random effects is proposed. Simulation studies and an empirical example are utilized to assess the performance of our proposed method. It is shown that our new approach is more efficient than most competitors and is robust to the misspecification of the random-effects distributions.     

A shared parameter model of longitudinal measurements and survival time with heterogeneous random-effects distribution

Typical joint modeling of longitudinal measurements and time to event data assumes that two models share a common set of random effects with a normal distribution assumption. But, sometimes the underlying population that the sample is extracted from is a heterogeneous population and detecting homogeneous subsamples of it is an important scientific question. In this paper, a finite mixture of normal distributions for the shared random effects is proposed for considering the heterogeneity in the population. For detecting whether the unobserved heterogeneity exits or not, we use a simple graphical exploratory diagnostic tool proposed by Verbeke and Molenberghs [34] to assess whether the traditional normality assumption for the random effects in the mixed model is adequate. In the joint modeling setting, in the case of evidence against normality (homogeneity), a finite mixture of normals is used for the shared random-effects distribution. A Bayesian MCMC procedure is developed for parameter estimation and inference. The methodology is illustrated using some simulation studies. Also, the proposed approach is used for analyzing a real HIV data set, using the heterogeneous joint model for this data set, the individuals are classified into two groups: a group with high risk and a group with moderate risk.