“…We may consider a factor analysis model for the latent scores; for instance, the one-factor model is {Φ −1 (d k ); k = 1, • • • , K} = µ + Λη + , where Λ is a K × 1 loading vector, η is a subject specific factor following standard normal distribution and follows a multivariate Kdimensional normal distribution with zero mean and diagonal covariance E. Then this model corresponds to {Φ −1 (d k ); k = 1, • • • , K} ∼ N (µ, ΛΛ + E), which has fewer model parameters than the proposed model in Section 2 (when K ≥ 4). The above factor analysis modeling is similar to the higher-order factor models and higher-order CDMs proposed in de la Torre and Douglas ( 2004), Templin et al (2008), andCulpepper andChen (2019); this is also related to the multidimensional IRT model (Reckase, 2009). However, as discussed in Section 3.1, our method differs from these existing studies due to the different cognitive diagnosis modeling from the latent scores to responses.…”