Dirk L. Knol

Empirical comparison between factor analysis and multidimensional item response models

Many factor analysis and multidimensional item response models for dichotomous variables have been proposed in literature. The models and various methods for estimating the item parameters are reviewed briefly. In a simulation study these methods are compared with respect to their estimates of the item parameters both in terms of an item response theory formulation and in terms of a factor analysis formulation. It is concluded that for multidimensional data a common factor analysis on the matrix of tetrachoric correlations performs at least as well as the theoretically appropriate multidimensional item response models.

Orthogonal rotations to maximal agreement for two or more matrices of different column orders

Methods for orthogonal Procrustes rotation and orthogonal rotation to a maximal sum of inner products are examined for the case when the matrices involved have different numbers of columns. An inner product solution offered by Cliff is generalized to the case of more than two matrices. A nonrandom start for a Procrustes solution suggested by Green and Gower is shown to give better results than a random start. The Green-Gower Procrustes solution (with nonrandom start) is generalized to the case of more than two matrices. Simulation studies indicate that both the generalized inner product solution and the generalized Procrustes solution tend to attain their global optima within acceptable computation times. A simple procedure is offered for approximating simple structure for the rotated matrices without affecting either the Procrustes or the inner product criterion.

Scale Construction on the Basis of Components Analysis: A Comparison of Three Strategies.

Cattell suggested constructing scales on the basis of components analysis by assigning weights 1 to variables with high positive loadings on the components and -1 to variables with high negative loadings on the components. This strategy is compared with other strategies of scale construction, which assign weights 1 or -1 to variables with high weights for the components. The latter strategies appear to yield scales which have higher correlations with the corresponding component scores and lower correlations among them, but also are less homogeneous then scales constructed by the former strategy. It is concluded that the former strategy, which is very popular among practitioners, can continue to be used if homogeneity of scales is preferred to orthogonality of scales.

Testing Predictive Developmental Hypotheses

Predictive developmental hypotheses play a crucial role in developmental theories. These hypotheses link early developmental behaviors or processes to later developmental outcomes. Empirical tests of predictive developmental hypotheses are generally based on standard regression models. It is argued that hierarchical linear models or longitudinal multilevel models offer a better alternative. A multivariate longitudinal model linking developmental data to a criterion is described and an application is given. The application, derived from attachment theory, pertains to the prediction of infant behavior in the Strange Situation. It is concluded that the proposed approach offers a valuable tool to the developmentalist, both from a theoretical and methodological point of view.