Mixed-type Data Monitoring Using Generalized Linear Model-Adjusted Scheme

As mixed-type data appear more and more often in the field of finance, manufactory, service and etc, we pay more and more attention in how to monitor this kind of data effectively. Because of the special complexity of mixed-type data, all the monitor schemes designed for multiple continuous or multiple discrete variables are not appropriate in this case. Enlightened by Hawkins' 1991 paper -Multivariate Quality control based on Regression adjusted Variables, we provides a method based on generalized linear models (mentioned as GLM here after). Generalized linear models are designed to build regression models for non-normal distributed data. Thus in GLM-adjusted methods, we use all the output variables to build generalized linear model and calculated residuals which approximately follow normal distributions. Then monitor these residuals using common used schemes for multivariate normal data. The examples cited in this paper show that this method is easy to be understood and practice. This GLM-adjusted method is also sensitive and robust to various kinds of shift. Specially, when all the variables are from normal distribution, GLM is simple regression model. In other words, we extend Hawkins' regression adjusted control scheme to monitor mixed-type variables.