The logistic and confined exponential curves are frequently used in studies of growth and learning. These models, which are nonlinear in their parameters, can be estimated using structural equation modeling software. This paper proposes a single combined model, a weighted combination of both models. Mplus, Proc Calis, and lavaan code for the model…

The accuracy of certain internal consistency estimators have been questioned in recent years. The present study tests the accuracy of six reliability estimators (Cronbach's alpha, omega, omega hierarchical, Revelle's omega, and greatest lower bound) in 140 simulated conditions of unidimensional continuous data with uncorrelated errors with varying…

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture's ability to produce "stable" results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that…

Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the…

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

Coefficient omega and alpha are both measures of the composite reliability for a set of items. Unlike coefficient alpha, coefficient omega remains unbiased with congeneric items with uncorrelated errors. Despite this ability, coefficient omega is not as widely used and cited in the literature as coefficient alpha. Reasons for coefficient omega's…

In this study, we apply jackknifing to anchor items to evaluate the impact of anchor selection on equating stability. In an ideal world, the choice of anchor items should have little impact on equating results. When this ideal does not correspond to reality, selection of anchor items can strongly influence equating results. This influence does not…

A common question asked by researchers using regression models is, What sample size is needed for my study? While there are formulae to estimate sample sizes, their assumptions are often not met in the collected data. A more realistic approach to sample size determination requires more information such as the model of interest, strength of the…

Component Universe Score Profile analysis (CUSP) is introduced in this paper as a psychometric alternative to multivariate profile analysis. The theoretical foundations of CUSP analysis are reviewed, which include multivariate generalizability theory and constrained principal components analysis. Because CUSP is a combination of generalizability…

The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…

Though much research and attention has been directed at assessing the correlation coefficient under range restriction, the assessment of reliability under range restriction has been largely ignored. This article uses item response theory to simulate dichotomous item-level data to assess the robustness of KR-20 ([alpha]), [omega], and test-retest…

Issues with correlation attenuation due to measurement error are well documented. More than a century ago, Spearman proposed a correction for attenuation. However, this correction has seen very little use since it can potentially inflate the true correlation beyond one. In addition, very little confidence interval (CI) research has been done for…

The purpose of this research is to examine eight of the different methods for computing confidence intervals around alpha that have been proposed to determine which of these, if any, is the most accurate and precise. Monte Carlo methods were used to simulate samples under known and controlled population conditions. In general, the differences in…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

Sample size recommendations in confirmatory factor analysis (CFA) have recently shifted away from observations per variable or per parameter toward consideration of model quality. Extending research by Marsh, Hau, Balla, and Grayson (1998), simulations were conducted to determine the extent to which CFA model convergence and parameter estimation…