A Monte Carlo simulation study of sample size requirements for the Graded Response Model

by Tatsuya Ikeda Background The graded response model (GRM) is commonly used in psychometrics to analyze ordinal response data. Despite its growing application in scale development and validation, sample size recommendations—such as those provided by the COSMIN guidelines (e.g., n ≥ 1000)—are often based on expert consensus rather than empirical validation.

Furthermore, the extent to which the number of items ( J ) and the number of response categories ( K ) contribute to parameter estimation accuracy remains insufficiently explored. Methods We conducted a Monte Carlo simulation to examine how three design conditions—sample size ( n = 500–1500), number of items ( J = 5–50), and a number of response categories ( K = 4–7)—influence the estimation accuracy of the latent trait parameter (θ) and the item discrimination parameter ( a ) under the GRM.

For each condition, we generated a large population dataset based on predefined distributions for θ, a , and b , and then randomly drew samples ( n ) for estimation. The GRM was fitted using the EM algorithm.