This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional three-parameter models for vertically equating test levels when the scaling method was applied to a multilevel achievement test battery. Two grades, fourth and eighth, and two subtests, reading and mathematics, were selected for analysis. For each content area, approximately 500 students per grade completed both the scaling test and the regular battery test. There appeared to be no evidence to recommend the three-parameter logistic model over the two-parameter modified logistic model when the scaling test approach was used to equate multilevel achievement batteries. Each method appeared to provide a different definition of score-to-equivalence. The moderate rank correlations between lower asymptote estimates for those few items for which estimates were possible in the three-parameter model suggested that the Norton methodology may provide a reasonable alternative for estimating lower asymptotes when sample sizes are small. (PN)