This study discusses quantile regression methodology and its usefulness in education and social science research. First, quantile regression is defined and its advantages vis-à-vis vis ordinary least squares regression are illustrated. Second, specific comparisons are made between ordinary least squares and quantile regression methods. Third, the…

In linear regression models estimated by ordinary least squares, it is often desirable to use hypothesis tests and confidence intervals that remain valid in the presence of heteroskedastic errors. Wald tests based on heteroskedasticity-consistent covariance matrix estimators (HCCMEs, also known as sandwich estimators or simply "robust"…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time. When the response data are categorical, item response theory (IRT) model can be used as the measurement model of a second-order latent growth model (referred to as LGM-IRT) to measure…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…

Recently, studies have adopted fixed effects modeling to identify the returns to college. This method has the advantage over ordinary least squares estimates in that unobservable, individual-level characteristics that may bias the estimated returns are differenced out. But the method requires extensive longitudinal data and involves complex…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

Researchers and data analysts are sometimes faced with the problem of very small samples, where the number of variables approaches or exceeds the overall sample size; i.e. high dimensional data. In such cases, standard statistical models such as regression or analysis of variance cannot be used, either because the resulting parameter estimates…

A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically, these exams are prepared several days in advance, and generic question scores are used based on rough approximation of the question difficulty and length. For example, for a recent class taught by the author, there were…

Using a rich sample created from the Longitudinal Survey of Australian Children, we investigate the extent to which the relationship between body size at birth and early childhood cognitive skills is mediated by physical development indicators. Consistent with existing evidence from other countries, we find a significant relationship between body…

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

We explore the use of instrumental variables (IV) analysis with a multisite randomized trial to estimate the effect of a mediating variable on an outcome in cases where it can be assumed that the observed mediator is the only mechanism linking treatment assignment to outcomes, an assumption known in the IV literature as the exclusion restriction.…

The assessment of the achievement of students and the quality of schools has drawn increasing attention from educational researchers, policy makers, and practitioners. Various test-based accountability and feedback systems involving the use of value-added techniques have been developed for evaluating the effectiveness of individual teaching…

Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed…

The demand for distance education has been increasing at a rapid pace all around the world. This, in turn, places a special importance on the need for the development of more distance education systems. However, there is an alarming rise in the number of distance education students that drop out of the system without asking for any help. The…

We explore the use of instrumental variables (IV) analysis with a multi-site randomized trial to estimate the effect of a mediating variable on an outcome in cases where it can be assumed that the observed mediator is the only mechanism linking treatment assignment to outcomes, as assumption known in the instrumental variables literature as the…