Structural equation models are increasingly used as a modeling tool for multivariate time series data in the social and behavioral sciences. Standard error estimators of SEM models, originally developed for independent data, require modifications to accommodate the fact that time series data are inherently dependent. In this article, we extend 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.…

This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations.…

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…

A scaled difference test statistic T[tilde][subscript d] that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (Psychometrika 66:507-514, 2001). The statistic T[tilde][subscript d] is asymptotically equivalent to the scaled difference test statistic T[bar][subscript…

This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by…

Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of…

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, "2005"; Psychometrika 71:713-732, "2006") introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are…

In behavioural sciences, local dependence and DIF are common, and purification procedures that eliminate items with these weaknesses often result in short scales with poor reliability. Graphical loglinear Rasch models (Kreiner & Christensen, in "Statistical Methods for Quality of Life Studies," ed. by M. Mesbah, F.C. Cole & M.T.…

The generalized logit-linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM…

Recently, there has been increasing interest in reporting subscores. This paper examines reporting of subscores using multidimensional item response theory (MIRT) models (e.g., Reckase in "Appl. Psychol. Meas." 21:25-36, 1997; C.R. Rao and S. Sinharay (Eds), "Handbook of Statistics, vol. 26," pp. 607-642, North-Holland, Amsterdam, 2007; Beguin &…

Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into…

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure…

The critical reactions of Bentler (2009, doi: 10.1007/s11336-008-9100-1), Green and Yang (2009a, doi: 10.1007/s11336-008-9098-4 ; 2009b, doi: 10.1007/s11336-008-9099-3), and Revelle and Zinbarg (2009, doi: 10.1007/s11336-008-9102-z) to Sijtsma's (2009, doi: 10.1007/s11336-008-9101-0) paper on Cronbach's alpha are addressed. The dissemination of…