# A consistent estimator for logistic mixed effect models

## News

• Author: Yizheng Wei, Yanyuan Ma, Tanya P. Garcia and Samiran Sinha
• Date: 10 July 2019
• Copyright: Image copyright of Patrick Rhodes

In a paper published in The Canadian Journal of Statistics, the authors propose a consistent and locally efficient method of estimating the model parameters of a logistic mixed effect model with random slopes. Their approach relaxes two typical assumptions: the random effects being normally distributed, and the covariates and random effects being independent of each other. Adhering to these assumptions is particularly difficult in health studies where, in many cases, they have limited resources to design experiments and gather data in long‐term studies, while new findings from other fields might emerge, suggesting the violation of such assumptions. So it is crucial to have an estimator that is robust to such violations; then the authors could make better use of current data harvested using various valuable resources. Their method generalizes the framework presented in Garcia & Ma (2016) which also deals with a logistic mixed effect model but only considers a random intercept.

The paper is available via this link and the authors explain their findings in further detail below:

A consistent estimator for logistic mixed effect models

Yizheng Wei, Yanyuan Ma, Tanya P. Garcia and Samiran Sinha

The Canadian Journal of Statistics, Volume 47, Issue 2, June 2019, pages 140-156

Logistic mixed effect model has been widely used to analyze clustered binary data arising in longitudinal studies of behavioral, social, health, and biomedical science. When designing experiments, due to the constraint of current available methods, there are two typical assumptions researchers usually tent to impose in various degree, but in practice they are sometimes difficult to adhere. The first assumption is that the random effects being normally distributed, and the second assumption is that the covariates and random effects being independent of each other. In addition, in long term study, it is common that researchers have new data from other research projects $B$, $C$,$\cdots$, which might be useful for their original research project $A$. But those data may violate the normality assumption and independence assumption originally imposed in their experiment for research project $A$, researchers still like to take advantage of these new data. Or it is possible that new findings in other fields might reveal that their original assumptions are violated, for example, the random effects are indeed dependent with certain covariate. So it is desirable that they could have an estimator for logistic mixed effect model that is robust to the violation of those two assumptions.

In this paper, the authors propose a consistent and locally efficient estimator to estimate the model parameters for a logistic mixed effect model with random slopes. Their estimator doesn't require the normality assumption and independence assumption. A simulation study shows that their proposed estimator remains consistent even when the independence assumption and normality assumption are violated. While as a comparison, the traditional maximum likelihood estimator is likely to be inconsistent when there is a dependence between the covariates and the random effects. Application of this work to a Huntington disease study reveals that disease diagnosis can be further improved using assessments of cognitive performance.

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