The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

Multidimensional scaling (MDS) a highly reliable measurement technique, often requires an overwhelming task of the subject in the data collection procedure. This investigation was designed to determine the loss of precision in solution associated with five degrees of systematic reduction in the data collection task. Data were simulated via Monte…

A study was made of the problem of representing the expectations of mean squares associated with analysis of variance sources of variation for experimental designs. These designs have a factorial structure over repeated measures or, for some other reason, have variates within a factorial design not all of which are mutually independent. A simple…

A rigorous definition for a factor analysis model and a complete solution of the factor score indeterminacy problem are presented in this technical paper. The meaning and application of these results are discussed. (Author/JKS)

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)

A group of factor analytic rotation procedures are developed which yield both hyperplane fittings and oblique Procrustean analyses as special cases. It is generally supposed that these techniques are rather different in approach. Illustrations are presented and discussed. (Author/JKS)

Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.…

An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. It is useful as an alternative to fitting property variables into a multidimensional scaling space. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations.…

This study formulates a property of a quantification method, the principle of equivalent partitioning. When used with Guttman's principle of internal consistency, the combination allows the analysis of correlational data in terms of the variate(s) chosen by the investigator. Applications to multiple-choice, rank-order, and paired comparison data…

The extension of regression estimation and poststratification to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISTREL framework. (Author/LMO)

Structural models that yield circumplex inequality patterns are reviewed, focusing on a model developed by T. W. Anderson (1960). A modification is proposed to this model to allow for negative correlations. This model may be reparameterized as a factor analysis model with nonlinear constraints on the factor loadings. (SLD)

An equal-level approach is proposed for investigating multitrait-multimethod (MTMM) matrices with respect to other organizational units that contain additional information concerning a MTMM matrix's validity. The approach requires equality in "data level" before coefficients are submitted for evaluation. Disaggregation is central to…

An algorithm based on the majorization theory of J. de Leeuw and W. J. Heiser is presented for fitting the slide-vector model. It views the model as a constrained version of the unfolding model. A three-way variant is proposed, and two examples from market structure analysis are presented. (SLD)

Applications of the confirmatory factor analysis block-diagonal model to published data on 18 multitrait-multimethod matrices were reviewed to show widespread estimation problems. Possible causes of estimation difficulties were explored using computer simulations. These problems make the block-diagonal approach less useful than has generally been…

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…