An introduction to logistic regression with an application to the analysis of language recovery following a stroke

The aim of a statistical model is to present a simplified representation of the underlying structure in a data set by separating systematic features from random variation. Sometimes the purpose of a statistical model is to provide a simple descriptive summary of the data and sometimes it is to use the data for comparative or inferential purposes. In practice, the specification of a statistical model requires a thorough understanding of the substantive area of application, an assessment of the validity of the assumptions of the model, and an evaluation of the fit of the model to the data. In this paper, as an illustration of these aspects of the statistical modeling of data, we consider the specification, application, and interpretation of a logistic regression model for the investigation of relationships between binary response data and a collection of explanatory variables. We illustrate applications of the methodology using data from a prospective study of spontaneous language recovery following a stroke (Holland, Greenhouse, Fromm, & Swindell, 1989).