The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA…

In this literature review, we examined 30 years of play-literacy inquiry through a quantitative lens in order to identify, assemble and summarize studies of sufficient methodological strength to form a corpus of research that encourages meta-analytic thinking. First, a multi-phase search of the literature was conducting yielding 192 studies that…

Using the elementary tools of matrix theory, we show that the product of two rotations in the three-dimensional Euclidean space is a rotation again. For this purpose, three types of rotation matrices are identified which are of simple structure. One of them is the identity matrix, and each of the other two types can be uniquely characterized by…

Numerous procedures have been suggested for determining the number of factors to retain in factor analysis. However, previous studies have focused on comparing methods using normal data sets. This study had two phases. The first phase explored the Kaiser method, Scree test, Bartlett's chi-square test, Minimum Average Partial (1976&2000),…

This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the…

If M[subscript ij] are minors of an n x n determinant D with elements a[subscript ij] (1 less than or equal to i,j less than or equal to n), then we prove the following relationship [vertical bar]M[subscript k][vertical bar] = [vertical bar]D[vertical bar][superscript k-1]delta[subscript k] where M[subscript k] is any square sub matrix of order k…

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a…

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…

In this article, the authors have 2 aims. First, hierarchical, nonhierarchical, and nonstandard log-linear models are defined. Second, application scenarios are presented for nonhierarchical and nonstandard models, with illustrations of where these scenarios can occur. Parameters can be interpreted in regard to their formal meaning and in regard…

This paper presents the row-column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were…

The article is aimed at a partial problem of science process skills development--the evaluation of educational outcomes. In comparison to evaluation of obtained knowledge, the skills development is not so easy to be objectively evaluated. The article provides a proposal of an evaluation tool and describes the first results of its research…

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

Figural matrix items are a popular task type for assessing general intelligence (Spearman's g). Items of this kind can be constructed rationally, allowing the implementation of computerized generation algorithms. In this study, the influence of different task parameters on the degree of difficulty in matrix items was investigated. A sample of N =…

The mathematics for finding and plotting the locations of stars and constellations are available in many books on astronomy, but the steps involve mystifying and fragmented equations, calculations, and terminology. This paper will introduce an entirely new unified and cohesive technique that is easy to understand by mathematicians, and simple…