Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

Many psychometric measures yield data that are compatible with (a) an essentially unidimensional factor analysis solution and (b) a correlated-factor solution. Deciding which of these structures is the most appropriate and useful is of considerable importance, and various procedures have been proposed to help in this decision. The only fully…

Test score users often demand the reporting of subscores due to their potential diagnostic, remedial, and instructional benefits. Therefore, there is substantial pressure on testing programs to report subscores. However, professional standards require that subscores have to satisfy minimum quality standards before they can be reported. In this…

The purpose of this paper is to describe briefly the development and utility of the "Assessment of Reading Instructional Knowledge-Adults" ("ARIK-A"), the only nationally normed (n?=?468) measure of adult reading instructional knowledge, created to facilitate professional development of adult educators. Developmental data…

In this article, the authors describe procedures used in the development of a new scale of militant extremist mindset. A 2-step approach consisted of (a) linguistic analysis of the texts produced by known terrorist organizations and selection of statements from these texts that reflect the mindset of those belonging to these organizations and (b)…

Multiracial Americans represent a rapidly growing population (Shih & Sanchez, 2009); however, very little is known about the types of challenges and resilience experienced by these individuals. To date, few psychological measures have been created specifically to investigate the experiences of multiracial people. This article describes 2…

In this article, I describe studies conducted over 25 years with secondary and post-secondary L2 learners in the United States. The evidence from these studies shows that there are important connections between students' early L1 skills and their L2 aptitude and L2 proficiency and that individual differences in students' L1 skills in elementary…

Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual's placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and…

A large literature emphasizes the importance of testing for measurement equivalence in scales that may be used as observed variables in structural equation modeling applications. When the same construct is measured across more than one developmental period, as in a longitudinal study, it can be especially critical to establish measurement…

This paper describes the Confirmatory Factor Analysis (CFA) parameterization of the Profile Analysis via Multidimensional Scaling (PAMS) model to demonstrate validation of profile pattern hypotheses derived from multidimensional scaling (MDS). Profile Analysis via Multidimensional Scaling (PAMS) is an exploratory method for identifying major…

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

Treating Likert rating scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, and so forth, it seems nevertheless possible to recover true parameter values if the data stem from a…

This article considers a structured latent curve model for multiple repeated measures. In a structured latent curve model, a smooth nonlinear function characterizes the mean response. A first-order Taylor polynomial taken with regard to the mean function defines elements of a restricted factor matrix that may include parameters that enter…

This paper explains the meaning and use of three important factor analytic statistics: factor scores, factor structure coefficients, and communality coefficients. For the discussion, 301 observations of junior high school students 11 measured variables from a previous study are analyzed. While factors provide the researcher with general…