Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to estimate these quantities. Unfortunately, standard estimators of mixture parameters, like the MLE, are known…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…

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…

A common methodological problem in the evaluation of the predictive validity of selection methods, e.g. in educational and employment selection, is that the correlation between predictor and criterion is biased. Thorndike's (1949) formulas are commonly used to correct for this biased correlation. An alternative approach is to view the selection…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…

The problem of factor score indeterminacy implies that the factor and the error scores cannot be completely disentangled in the factor model. It is therefore proposed to compute Harman's factor score predictor that contains an additive combination of factor and error variance. This additive combination is discussed in the framework of classical…

In education randomized control trials (RCTs), the misreporting of student outcome data could lead to biased estimates of average treatment effects (ATEs) and their standard errors. This article discusses a statistical model that adjusts for misreported binary outcomes for two-level, school-based RCTs, where it is assumed that misreporting could…

In randomized control trials (RCTs) of educational interventions, there is a growing literature on impact estimation methods to adjust for missing student outcome data using such methods as multiple imputation, the construction of nonresponse weights, casewise deletion, and maximum likelihood methods (see, for example, Allison, 2002; Graham, 2009;…

This paper examines the estimation of two-stage clustered RCT designs in education research using the Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the…

Misspecification of mean and covariance structures for metric endogenous variables is considered. Maximum likelihood estimation of model parameters and the asymptotic covariance matrix of the estimates are discussed. A Haussman test for misspecification is developed, which is sensitive to misspecification not detected by the test statistics…

The similarity of item and ability parameter estimations was investigated using two numerical analysis techniques via marginal maximum likelihood estimation (MMLE) with a large simulated data set (n=1,000 examinees) and changing the number of quadrature points. MMLE estimation uses a numerical analysis technique to integrate examinees' abilities…

Some extensions of the partial credit model are presented. A marginal maximum likelihood estimation procedure is developed to allow for incomplete data and linear restrictions on the item and population parameters. Two statistical tests for evaluating model fit are also presented. (SLD)

The linear logistic model with relaxed assumption is extended to designs with any number of time points or with different sets of items presented on different occasions, provided that one unidimensional subscale is available per latent trait. A sample application is presented. (SLD)

A modification index is presented to aid in reformulating hypothetical models rejected after analysis of empirical data. This index is an improvement over the one in the LISREL V computer program in that it takes into account changes in all parameters of the model when one parameter is freed. (SLD)