Crash data on Alabama Interstates were collected across a five-year time period from 2009 to 2013, and true wrong-way driving (WWD) crashes were identified using the hardcopy of crash reports and existing maps. The crash data contained 18 explanatory variables representing the driver, temporal, vehicle, and environmental information. A Firth's penalized-likelihood logistic regression model was developed to examine the influence of the explanatory variable on the dichotomous dependent variable (type of crash, i.e., WWD vs. non-WWD). This model is an appropriate tool to control the influence of all confounding variables on the probability of WWD crashes while considering the rareness of the event (i.e., WWD). A separate model using the standard binary logistic regression was also developed. Two information criteria (AIC and BIC) obtained from both developed models indicate that for our database, Firth's model outperforms the standard binary logistic model and provides more reliable results. Using Firth's model, explanatory variables including month of the year, time of the day, driver age, driver mental and physical condition, driver's residency distance, vehicle age, vehicle damage, towing condition, airbag deployment status, and roadway condition were found to characterize WWD crashes. Based on the obtained odds ratio (OR), this paper discusses the various effect of the identified variables and recommends several countermeasures for policy makers in order to reduce the WWD issue on Alabama Interstates.