The results of data analysis based on the multiplicative binomial model (MLTBIN) are compared with dichotomous data analyzed by using the simple logistic model (SLM). Specifically, the paper focuses on the issues of fit to these Rasch Models and estimates of item difficulty. The data indicate that the SLM and MLTBIN are not comparable in the estimates of item fit. Consequently, if Likert scale item analysis is conducted, it should be done using the MLTBIN since the logic and assumptions underlying the items and the model are congruent. Item difficulty estimates using items dichotomized at the midpoint are highly correlated with MLTBIN difficulty estimates. Item difficulties based on dichotomization at the median were found to be erroneous and should be avoided. (RC)