A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based…

The present simulation study indicates that a method where the regression effect of a predictor (X) on an outcome at follow-up (Y1) is calculated while adjusting for the outcome at baseline (Y0) can give spurious findings, especially when there is a strong correlation between X and Y0 and when the test-retest correlation between Y0 and Y1 is…

The estimation of racial test score gap trends plays an important role in monitoring educational equality. Documenting gap trends is complex, however, and estimates can differ depending on the metric, modeling strategy, and psychometric assumptions. The sensitivity of summer learning gap estimates to these factors has been under-examined. Using…

The purpose of this report is to review ETS psychometric contributions that focus on test scores. Two major sections review contributions based on assessing test scores' measurement characteristics and other contributions about using test scores as predictors in correlational and regression relationships. An additional section reviews additional…

Educational researchers commonly use the rule of thumb of "design effect smaller than 2" as the justification of not accounting for the multilevel or clustered structure in their data. The rule, however, has not yet been systematically studied in previous research. In the present study, we generated data from three different models…

The focus of this paper is assessing the impact of measurement errors on the prediction error of an observed-score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor…

Nearly all quantitative analyses in higher education draw from incomplete datasets-a common problem with no universal solution. In the first part of this paper, we explain why missing data matter and outline the advantages and disadvantages of six common methods for handling missing data. Next, we analyze real-world data from 5,905 students across…

This case study relates to distance learning students on open access courses. It demonstrates the use of predictive analytics to generate a model of the probabilities of success and retention at different points, or milestones, in a student journey. A core set of explanatory variables has been established and their varying relative importance at…

In educational research, a randomized controlled trial is the best design to eliminate potential selection bias in a sample to support valid causal inferences, but it is not always possible in educational research because of financial, ethical, and logistical constrains. One alternative solution is use of the propensity score (PS) methods.…

The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample…

A common finding in studies of differential prediction across groups is that although regression slopes are the same or similar across groups, group differences exist in regression intercepts. Building on earlier work by Birnbaum (1979), Millsap (1998) presented an invariant factor model that would explain such intercept differences as arising due…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

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…

The relationship between complexity and usefulness can be captured by a U-shaped curve. This comment explores that relationship. Complexity may be useful for one of the main aims of developmental psychology (causal inference) but not for another (description of developmental phenomena). Currently, developmentalists conduct complex analyses that…