Abstract
This note underscores important considerations that should be taken into account when teaching students to check for inadequacies of a given linear, nonlinear or logistic regression models. Key illustrations are provided which underscore the shortcomings of currently used procedures. A brief overview of nonlinear regression models is given in order to lay the foundation for testing for lack of fit in nonlinear models. This paper also introduces a new ’scaled’ binary logistic regression model to highlight po tential problems with the usual logistic model, and implications for choosing a robust optimal experimental design are also underscored and discussed. Key words: Lack of fit, logistic regression, nonlinear regression, optimal de
Highlights
Box (1979) reminds us that no statistical model is ideal, some models are useful and beneficial for accurately representing diverse phenomena and mechanisms
We point out that once such a model is fit to a given set of data, it is incumbent upon the researcher or statistician to check the assumed model for inadequacies - that is, the so-called ’lack of fit’ of the model
It turns out that what is masked here is that the quadratic effect is significant, and this is not detected in the above Lack of Fit (LOF) test since the LOF test lacks power to detect intermediate departures from the assumed line
Summary
Box (1979) reminds us that no statistical model is ideal, some models are useful and beneficial for accurately representing diverse phenomena and mechanisms. In our statistics courses we underscore that scientific researchers often find that linear, generalized linear, nonlinear, and survival regression models are helpful for modelling various biological, chemical and medical processes. Regression models, and proposes important steps to take to guard against incorrect conclusions. Background and suggestions to detect lack of fit in nonlinear models are given in Sections 4 and 5.
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