Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques…

Cluster randomized trials involving participants nested within intact treatment and control groups are commonly performed in various educational, psychological, and biomedical studies. However, recruiting and retaining intact groups present various practical, financial, and logistical challenges to evaluators and often, cluster randomized trials…

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Missing data is endemic in much educational research. However, practices such as step-wise regression common in the educational research literature have been shown to be dangerous when significant data are missing, and multiple imputation (MI) is generally recommended by statisticians. In this paper, we provide a review of these advances and their…

Large surveys often use probability sampling in order to obtain representative samples, and these data sets are valuable tools for researchers in all areas of science. Yet many researchers are not formally prepared to appropriately utilize these resources. Indeed, users of one popular dataset were generally found "not" to have modeled…

Instrumental variables (IV) methods allow for consistent estimation of causal effects, but suffer from poor finite-sample properties and data availability constraints. IV estimates also tend to have relatively large standard errors, often inhibiting the interpretability of differences between IV and non-IV point estimates. Lastly, instrumental…

This chapter summarizes ten selected issues and common problems that arise in most assessment research projects. These include: (1) the uses of grades in assessment; (2) institutional review boards; (3) research design as a compromise; (4) standardized testing; (5) self-reported measures; (6) missing data; (7) weighting data; (8) conditional…

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate…

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes…

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. Least squares estimation procedures are compared to maximum likelihood procedures. The conclusion, based on the data used in this study, is that two of the procedures seem to work well. (Author/JKS)