LAUSR

Multistage estimation is frequently and extensively used in behavioral science research. However, the uncertainty carried over from a previous estimation stage to the next is often overlooked, which may lead to biased estimates of standard errors and other significant quantities of interest (e.g., test reliability, model goodness-offit statistics, and so forth). Multiple imputation (MI; Rubin, 1987) is one of the most powerful strategies for dealing with missing at random data. This technique involves first substituting missing values with imputed plausible values, then analyzing multiple imputed datasets and finally combining these estimates. Motivated by Yang, Hansen, and Cai (2012), this article proposes to use an MI-based approach that uses routinely printed output in flexMIRTVR (Cai, 2015) to improve standard error estimates of panelist effects on item parameters of the English Language Proficiency Assessment for the 21st century (ELPA 21), Blind/Lowvision form test. In stage-one estimation, point estimates and the asymptotic variance-covariance matrix of item parameters of Item i ði 1⁄4 1:::IÞ were obtained, denoted as hi and F 1 i , respectively. A nonlinear mixed effect model was applied in stage two to study the panelist effects on item parameters, which are denoted here as c. To improve estimates of c, we first drew multiple plausible values of item parameters to generate M ðM 1⁄4 25Þ datasets. Then, we fitted the nonlinear mixed effect model to the M datasets to get point estimates of c, ĉm, ðm 1⁄4 1:::MÞ, and the associated variance-covariance matrix, Vm. Finally, we combined ĉm and Vm to produce the corrected point estimates and corresponding standard errors. Compared with the analysis that invloves only stage-one point estimates (i.e., hi), the proposed method yields close point estimates of panelist effects but larger standard errors. For example, the point estimate and standard error of panelists’ multiplicative effect on item slope paramaters are 0.911 and 0.0012; while with the proposed method, the point estimate and corresponding standard error are 0.911 and 0.032, respecively.