Generalized linear mixed model for monitoring autocorrelated logistic regression profiles

Profile monitoring is used to monitor the regression relationship between a response variable and one or more explanatory variables over time. Many researches have been done in this area, but in most of them, the distribution of the response variable is assumed to be normal. However, this assumption is violated in many real case problems. In these instances, classic methods cannot be used for monitoring the profiles. For example, when the response variable is binary, logistic regression methods should be used rather than ordinary least square or other classic regression methods. There are some methods for monitoring logistic profiles in the literature, but the basic assumption of these methods is the independency of the consecutive observations, while this assumption is violated in some instances for example when the successive samples are taken in short intervals. This paper considers the effect of autocorrelation presence between the observations in different levels of the independent variable in a logistic regression profile on the monitoring procedure (T2 control chart) and proposes two remedies to account for the autocorrelation within logistic profiles. In one of the remedies, upper control limit of the traditional T2 control chart is modified. In the second one, we use a generalized linear mixed model (GLMM) to estimate the regression parameters and then use the T2 control chart for monitoring autocorrelated logistic regression profiles. Simulation studies show the better performance of T2 control chart when the regression parameters are estimated by the GLMM method under both step shifts and drifts.