The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

Simple noniterative estimators of the polyserial correlation coefficient are developed by exploiting a general relationship between the polyserial correlation and the point polyserial correlation to give extensions of the biserial estimators of K. Pearson (1909), H. E. Brogden (1949), and F. M. Lord (1963) to the multicategory setting. (SLD)

A method is proposed for partially analyzing additive ipsative data (PAID). Transforming the PAID according to a developed equation preserves the density of the transformed data, and maximum likelihood estimation can be carried out as usual. Simulation results show that the original structural parameters can be accurately estimated from PAID. (SLD)

Asymptotic distributions of H. Brogden's and F. Lord's modified sample biserial correlation coefficients (SBCCs) are derived. Asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the maximum likelihood estimator's asymptotic variance. These estimators are less variable than ordinary SBCCs when the…

A Monte Carlo study investigated the use of four cross-validation indices with confirmatory factor analysis models. Influences of sample size, loading size, and degree of model misspecification were studied. Larger sample sizes and better specified models result in better cross-validation results. (SLD)