Kalkhoran and colleagues* investigated predictors of dual use of cigarettes and smokeless tobacco products. Although their original sample size was large (N = 1324), they were interested in running separate logistic regression analyses within subgroups. Most of the sample used only cigarettes. One of the smaller subgroups contained subjects who used both cigarettes and smokeless tobacco products

(N=61). For this problem we focus on this smaller subgroup of dual cigarette and smokeless tobacco users (the data are in Table D-41, Appendix D). The dependent variable, Q, is whether the subject made an attempt to quit using tobacco products (0 = no attempt to quit; 1 =

attempted to quit). There is one multi-category independent variable, intention to quit, I, with four levels: never intend to quit, may intend to quit but not in the next 6 months, intend to quit in the next 6 months, intend to quit in the next 30 days. Fit a logistic regression of Q on I using ordinary logistic regression estimated by maximum likelihood and then repeat the analysis using Firth’s method. Be sure to treat the independent variable I as categorical rather than as continuous in these analyses (hint: you will need to create dummy variables for each level of I or let the logistic regression software program create the dummy variables for you if it has that capability). What do you observe from the results from these two analyses?