The Andersen LRT uses sample characteristics as split criteria to evaluate Rasch model fit, or theory driven hypothesis testing for a test. The power and Type I error of a random split criterion was evaluated with a simulation study. Results consistently show a random split criterion lacks power.
Krammer, G. (2018). The Andersen likelihood ratio test with a random split criterion lacks power. Journal of Modern Applied Statistical Methods, 17(2), eP2685. doi: 10.22237/jmasm/1555594442