In this study, we compared 12 statistical strategies proposed for selecting loglinear models for smoothing univariate test score distributions and for enhancing the stability of equipercentile equating functions. The major focus was on evaluating the effects of the selection strategies on equating function accuracy. Selection strategies' influence on the estimation of cumulative test score distributions was also assessed. The results of this simulation study differentiate the selection strategies and define the situations where their use has the most important implications for equating function accuracy. The recommended strategy for estimating test score distributions and for equating is AIC minimization.