This paper explores a logistic regression procedure for estimating item parameters in the Rasch model and testing the hypothesis of item parameter invariance across several groups/populations. Rather than using item responses directly, the procedure relies on "pseudo-paired comparisons" (PC) statistics defined over all possible pairs of items. Methods of computing the PC statistics in non-independent and independent fashions are described. Two simulation studies were conducted. Both studies used a 2 x 2 factorial design in which the number of items (6 or 11) and the number of subjects (100 or 500) varied. There were 100 replications in each cell of the design, and for each replication, two samples of ability parameters were randomly drawn from a standard normal distribution. In the first study, the PCs were computed in a non-independent fashion. In the second study, the PCs were computed in an independent fashion; however, only the two cells involving 500 subjects had been analyzed to date. The results of these studies suggest that the procedure yields negligibly biased estimates of item difficulty parameters even with small numbers of items. The simulation data were used to compare the distribution of observed test statistics under the null hypothesis of invariant item parameters across groups to the theoretical Student's t-distribution and the theoretical chi-square distribution. An application to sixth-grade mathematics achievement data for 178 fall mathematics test takers and 153 spring mathematics test takers is presented. Five data tables and a 15-item list of references are included. (Author/RLC)