I've run a simulation study in order to determine type I error rate of a statistic.My simulation design includes threes factors as sample size (4 levels), test length or number of items (3 levels) and estimator (3 levels). The statistic is developed to measure person fit with test data in educational testing situation.I've replicated the analysis in each cell (i.e. the design is fully-crossed) 100 times.
Now, I have the results and type I error rates range from 0.005 to 0.105 (i.e. across the whole analysis). I want to analyze how factors affect type I error rate using something similar to ANOVA. I tried Beta Regression in R using
betareg package but I received this error message:
invalid dependent variable, all observations must be in (0, 1)
Any idea on how to determine the effect of design factors on type I error rate?