A Monte Carlo study of the parameters of the logit model under small sample sizes and varying adjustment techniques
In psychological research, the use of log-linear and logit analyses may be problematic due to the occurrence of small sample sizes. This is unfortunate as these analyses produce estimates that are essential to interpreting the data and drawing relevant conclusions. There are methods for adjusting for the resulting small cell sizes that involve adding small constants to the cells so as to produce more interpretable parameter estimates. Through Monte Carlo simulation techniques using 100 replications, for sample sizes of 20, 30, 40, and 60, the effects on parameter estimates of no adjustment on frequency table cells, adding.5 to cells, and adding a proportional marginal distribution constant to cells, were examined. The dimensions of the frequency table were 2 x 3 x 2, and the saturated logit model was used to analyze the 1200 tables to obtain the standardized parameter estimates of interest. The distributions and Type I errors of the estimates were then examined to see if the proportional marginal method of adjusting was superior to the.5 method, or if both adjustments were equally preferable to no adjustment. Kolmogorov-Smirnov goodness-of-fit tests of the normality of the distributions showed significant violation of normality for all estimates at sample sizes 20 and 30, no adjustment, and for six of the eight estimates at $N$ = 40, no adjustment. Both the.5 and proportional methods of adjusting served equally to produce more normally distributed standardized estimates in those cases. The sample size of 60 had equally normally distributed estimates across all three adjustments. Similarly, analyses of Type I errors and error rates indicated equal improvement with both adjustment methods over no adjustment, especially for sample sizes 20 and 30, and somewhat for sample size 40. Due to these results, it was concluded that in the case of a logit analysis on a 2 x 3 x 2 frequency table using the saturated model, some type of adjustment, either the.5 or proportional marginal method, should be made in small sample sizes.
DeVictoria, Carol Lynn, "A Monte Carlo study of the parameters of the logit model under small sample sizes and varying adjustment techniques" (1991). ETD Collection for Fordham University. AAI9127030.