The topic of this article is the interpretation of structural equation modeling (SEM) solutions. Its purpose is to augment structural modeling's metatheoretic resources while enhancing awareness of how problematic is the causal significance of SEM-parameter solutions. Part I focuses on the nonuniqueness and consequent dubious interpretability of…

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…

Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

Several methodological issues in the multidimensional scaling of coarse dissimilarities were studied, examining whether it was better to scale dissimilarity data directly or to scale a new matrix derived from the original by row comparisons. Findings support an alternative row-comparison measure based on the Jacard coefficient. (SLD)

An iterative process is proposed for obtaining an orthogonal simple structure solution. At each iteration, a target matrix is constructed such that the relative contributions of the target majorize the original ones, factor by factor. The convergence of the procedure is proven, and the algorithm is illustrated. (SLD)

Assessed two models for confirmatory factor analysis of multitrait-multimethod data through Monte Carlo simulation. The correlated traits-correlated methods (CTCM) and the correlated traits-correlated uniqueness (CTCU) models were compared. Results suggest that CTCU is a good alternative to CTCM in the typical multitrait-multimethod matrix, but…

H. F. Kaiser, S. Hunka, and J. Bianchini have presented a method (1971) to compare two matrices of factor loadings based on the same variables, but different groups of individuals. The optimal rotation involved is examined from a mathematical point of view, and the method is shown to be invalid. (SLD)

The criteria for assessing convergent and discriminant validity proposed by D. T. Campbell and D. W. Fiske (1959) are shown to be inadequate for either the additive or multiplicative structures of data in a multitrait-multimethod matrix. Model-specific criteria are more promising for assessing convergent and discriminant validity. (Author/SLD)

An alternative to the PROMAX exploratory method is presented for constructing a target matrix in Procrustean rotation in factor analysis. A technique is proposed based on vector majorization. The approach is illustrated with several standard numerical examples. (SLD)

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

The common marketing research practice of standardizing the columns of a persons-by-variables data matrix prior to clustering the entities corresponding to the rows was evaluated with 10 large-scale data sets. Results indicate that the column standardization practice may be problematic for some kinds of data that marketing researchers used for…

The fundamental problems that ipsative measures impose for factor analysis are shown analytically. Normative and ipsative correlation matrices are used to show that the factor pattern induced by ipsativity will overwhelm any factor structure seen with normative factor analysis, making factor analysis not interpretable. (SLD)

An algorithm for obtaining initial values for the minimization process in covariance structure analysis is developed that is more generally applicable for computing parameters connected to latent variables than the currently existing ones. The algorithm is formulated in terms of the RAM model but can be extended. (SLD)

It is suggested that using an unbiased estimate of the weight matrix may eliminate the small or intermediate sample size bias of the asymptotically distribution-free (ADF) test statistic. Results of simulations show that test statistics based on the biased estimator or the unbiased estimate are highly similar. (SLD)

Two versions of a decision rule for determining the most appropriate number of clusters on the basis of a correlation matrix are presented, applied, and compared with three other decision rules. The new rule is efficient for determining the number of clusters on the surface level for multilevel data. (SLD)