Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite-scores is preferred for prediction and diagnosis of individuals. While path analysis with composite-scores has been criticized for yielding biased parameter estimates, recent literature pointed…

Cronbach's coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald's omega has been used as a popular alternative to alpha in the literature. Traditional estimation…

Cronbach's coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald's omega has been used as a popular alternative to alpha in the literature. Traditional estimation…

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package "rsem" to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables…

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…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

In this paper we propose an upward correction to the standard error (SE) estimation of theta[subscript ML], the maximum likelihood (ML) estimate of the latent trait in item response theory (IRT). More specifically, the upward correction is provided for the SE of theta[subscript ML] when item parameter estimates obtained from an independent pretest…

Studied whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. An example illustrates that neither the factor loading estimates nor the standard error estimates possess scale…

In mean and covariance structure analysis, the chi-square difference test is often applied to evaluate the number of factors, cross-group constraints, and other nested model comparisons. Let model M[a] be the base model within which model M[b] is nested. In practice, this test is commonly used to justify M[b] even when M[a] is misspecified. The…

Retrospective or post hoc power analysis is recommended by reviewers and editors of many journals. Little literature has been found that gave a serious study of the post hoc power. When the sample size is large, the observed effect size is a good estimator of the true power. This article studies whether such a power estimator provides valuable…