The article tried to compare three reliability traditionally used in the literature, one is maximal reliability ρ, unweighted sum score-based ω, and an IRT-based reliability coefficient π. Under the single-factor model, theρ>=ω. The factor loading λ can be connected to the α parameter of the GRM via mathematical equation. Under the MLE, the reliability can be expressed as 1/(1+1/information). The simulation studies were conducted to investigate the relationship among the three indexes. As expected, the ρ>=ω. However, forπ, the amount ofπ depends on the information that the categories chosen. As more categories were used, the higher theπ.
Comments:
1. Although this study is trivial, but to be a practical evidence and a reference.
2. The formula of reliability coefficient used in Conquest can be compared to the one derived from GRM.