Maximum Likelihood and Firth Logistic Regression of the Pedestrian Route Choice

To investigate how a pedestrian chooses a particular route in an urban center, this study analyzes the effects of individual and built environment characteristics on the route choice using binary logistic regression of 524 survey responses. Conducted in a strategic area, the survey, as often is the case, collects data that are skewed and face the separation issuethe same outcome always occurs for a particular value of a predictoraccording to which estimates by the conventional maximum likelihood (ML) method are inflated. Thus, one mechanical and one statistical alternative are employed: (1) exclusion of a variable that causes separation and (2) estimation by Firth's penalized method. The two alternatives produce comparable results of the significance testing, that is, p values, but their coefficient estimates considerably differ inasmuch as the mechanical approach used for the ML logistic regression forcefully omits the important variable and subsequently biases the estimates of other predictors. Compared to these ML estimates, empirical findings from the Firth logistic regression are presented in a way that corrects for the ML bias.