A Simulation Study of Some Ridge Regression Estimators under Different Distributional Assumptions

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 new robust ridge parameter estimator based on search method for linear regression model

A large and wide variety of ridge parameter estimators proposed for linear regression models exist in the literature. Actually proposing new ridge parameter estimator lately proving its efficiency on few cases seems endless. However, so far there is no ridge parameter estimator that can serve best for any sample size or any degree of collinearity among regressors. In this study we propose a new robust ridge parameter estimator that serves best for any case assuring that is free of sample size, number of regressors and degree of collinearity. This is in fact realized by choosing three best from enormous number of ridge parameter estimators performing well in different cases in developing the new ridge parameter estimator in a way of search method providing the smallest mean square error values of regression parameters. After that a simulation study is conducted to show that the proposed parameter is robust. In conclusion, it is found that this ridge parameter estimator is promising in any case. Moreover, a recent data set is used as an example for illustration to show that the proposed ridge parameter estimator is performing better.

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program.