Generalised linear mixed logit and probit models applied to US Army and Navy data

We apply the generalised linear mixed model (GLMM) with logit and probit links to data (Stevens and Anderson-Cook, 2017a, 2017b), which is univariate data with binary response of passing or failing for complex munitions generated to match age and usage rate found in US Department of Defense complex systems (Army and Navy). Instead of the generalised linear model (GLM) used in Stevens and Anderson-Cook (2017b), we propose to apply the adaptive Gaussian hermite quadrature approach (GLMM-AGHQ) (Ha et al., 2017) to predict binary response of passing or failing for the Army and Navy data. We suggest two methods to find the best models for the Army and Navy. The first method is based on statistical inference, the variance of random effect for intercept term for every GLMM given in this paper, and the log-likelihood. The second method focuses on the accuracy of prediction of each model. We compare the GLMMs with the GLMs in terms of inter quartile range (IQR) of the residuals. We find that the models capturing random effects lead to smaller IQR which in the end results in the high accuracy of the models. This accuracy is measured by area under receiver operating characteristic curve (AUC).