The Effect of Link Function on the Monitoring of Logistic Regression Profiles

Abstract— In some real case problems, a relationship between a response variable and one or more explanatory variables called as profile is desirable to be monitored over time instead of the response variable itself. There are many techniques in the literature for monitoring the profiles. A special case of the profiles is where the response variable follows a binomial distribution known as Logistic regression profile. In the logistic regression profile, a link function relates the mean of response variable to explanatory variables. There are many kinds of link function in the literature of logistic regression methods such as Logit, Probit, Log-Log, and so on. This paper investigates the effect of applying various link functions on the performance of T2 control chart in monitoring the parameters of a logistic profile.