Overcoming the problems caused by collinearity in mixed-effects logistic model: determining the contribution of various types of violence on depression in pregnant women

Background Collinearity is a common and problematic phenomenon in studies on public health. It leads to inflation in variance of estimator and reduces test power. This phenomenon can occur in any model. In this study, a new ridge mixed-effects logistic model (RMELM) is proposed to overcome consequences of collinearity in correlated binary responses. Methods Parameters were estimated through penalized log-likelihood with combining expectation maximization (EM) algorithm, gradient ascent, and Fisher-scoring methods. A simulation study was performed to compare new model with mixed-effects logistic model(MELM). Mean square error, relative bias, empirical power, and variance of random effects were used to evaluate RMELM. Also, contribution of various types of violence, and intervention on depression among pregnant women experiencing intimate partner violence(IPV) were analyzed by new and previous models. Results Simulation study showed that mean square errors of fixed effects were decreased for RMELM than MELM and empirical power were increased. Inflation in variance of estimators due to collinearity was clearly shown in the MELM in data on IPV and RMELM adjusted the variances. Conclusions According to simulation results and analyzing IPV data, this new estimator is appropriate to deal with collinearity problems in the modelling of correlated binary responses.

A generalized linear model for multivariate correlated binary response data on mobility index

Dependence in multivariate binary outcomes in longitudinal data is a challenging and an important issue to address. Numerous studies have been performed to test the dependence in binary responses either using conditional or marginal probability models. Since the con- ditional and marginal approach provide inadequate or misleading results, the joint models based on both are implemented for bivariate correlated binary responses. In the current paper, we consider a joint modeling approach and a generalized linear model (GLM) for tri-variate correlated binary responses. The link function of the GLM is used to test the dependence of response variables. The mobility index with two categories, no difficulty and difficulty, over the duration of three waves of Health and Retirement Survey (HRS) is chosen as the binary response variable. Initial analysis with Marshall-Olkin correlation coefficients and logistic regression coefficients provide moderate correlation in mobility indices implying dependence in the response variables. We also found statistically significant dependence among the response variables using the joint modeling approach. The mobility at current wave not only depends on the previous mobility status, but also depends on covariates such as age, gender, and race.

Some New Random Effect Models for Correlated Binary Responses

Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity of the inference to the specification of the copula family is also investigated through simulations. Numerical examples are presented.