Logistic regression is one of the most fundamental tools in predictive analytics. Graduate business analytics students are often familiarized with implementation of logistic regression using Python, R, SPSS, or other software packages. However, an understanding of the underlying maximum likelihood model and the mechanics of estimation are often…

Large amounts of missing data could distort item parameter estimation and lead to biased ability estimates in educational assessments. Therefore, missing responses should be handled properly before estimating any parameters. In this study, two Monte Carlo simulation studies were conducted to compare the performance of four methods in handling…

Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the…

Misclassification means the observed category is different from the underlying one and it is a form of measurement error in categorical data. The measurement error in continuous, especially normally distributed, data is well known and studied in the literature. But the misclassification in a binary outcome variable has not yet drawn much attention…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix [sigma] of group-level varying coefficients are often degenerate. One can do better, even…

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is…

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…

Latent class regression models relate covariates and latent constructs such as psychiatric disorders. Though full maximum likelihood estimation is available, estimation is often in three steps: (i) a latent class model is fitted without covariates; (ii) latent class scores are predicted; and (iii) the scores are regressed on covariates. We propose…

The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration…

Regression discontinuity design is an alternative to randomized experiments to make causal inference when random assignment is not possible. This article first presents the formal identification and estimation of regression discontinuity treatment effects in the framework of Rubin's causal model, followed by a thorough literature review of…

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…

Factor score estimation is a controversial topic in psychometrics, and the estimation of factor scores from exploratory factor models has historically received a great deal of attention. However, both confirmatory factor models and the existence of missing data have generally been ignored in this debate. This article presents a simulation study…