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.