Extending latent class solutions to other variables

A procedure is derived for estimating the latent parameters of items not initially included in a latent class solution, on the assumption that the relations between those additional items and the original ones are accounted for by the same latent structure. A chi-square test is proposed for evaluating the relatedness of the additional items to the latent structure. The extension is generalized to associate continuous outside variables with the original solution, and this is accompanied by the suggestion that a simple analysis of variance be used to assess the results. Finally, this latent structure extension is compared with the Dwyer extension of factor analysis.I am grateful to J. J. Mellinger for clarifying discussions of the statistical portions of this paper.Opinions expressed herein are the author's, not the Army's.     

A latent structure for the simplex

A perfect Guttman scale generates a perfect Guttman simplex. This is capitalized on to get a transformation useful in a kind of non-linear factor analysis applicable to empirical correlations resembling but not necessarily conforming to a perfect simplex.A Gramian factorization—square, symmetric, possibly of low rank but with no negative characteristic roots—of empirical correlations is transformed into latent information about nonlinear regressions of tests on a single underlying dimension. Class intervals on that continuum are defined in terms of their standard score profiles on the tests. Each class interval exhibits local independence, so that individual members may vary but may not covary in their profiles.The method is flexible as to choice of diagonals, fitted rank, and exact shape of resulting non-linear regressions, so long as those regressions are essentially monotonic and have a proper progression of curvatures. Construction of the needed transformation for data of any size is outlined, and the problem of metric for the latent continuum is given several solutions.An empirical example is provided with full and low rank solutions involving different diagonal choices.This research was conducted under Grant Nonr(G)-00033-63 of the Office of Naval Research. Reproduction of this paper, in whole or in part, is permitted for any purpose of the United States government.     

Properties and applications of gramian factoring

The Gramian factorizationG of a GramianR is square and symmetric and has no negative characteristic roots. It is shown to be that square factorization that is, in the least-squares sense, most isomorphic toR, most like a scalarK, and most highly traced, and to be the necessary and sufficient relation between the oblique vectors of an oblique transformation and the orthogonal vectors of the least-squares orthogonal counterpart. A slightly modified Gramian factorization is shown to be the factorization that is most isomorphic to a specified diagonalD, and to be the main part of an iterative procedure for obtaining simplimax, a square factor matrix with simple structure maximized in the sense of having the largest sum of squared diagonal loadings. Several published applications of Gramian factoring are cited.     

The High School Dropout Goes to College

662 former secondary school leavers of academic potential were identified for a program designed to give selected dropouts a chance to enter the University of Toledo. Following responses to questionnaires, 94 students were selected for further screening, which resulted in the final selection of 50 candidates. 34 members of the experimental group attended pre-school workshops in reading, writing, and study habit skills. 31 enrolled as regularly admitted students in academic programs of the university for the academic year. 11 completed their freshman year, although only 4 were making satisfactory academic progress.     

A developmental study of visual search behavior

Children in second, fourth and sixth grades and college sophomores were compared on a visual search and scanning task under three experimental conditions. In Condition I, a single target letter was sought in a list of letters of low visual confusability. In Condition II, two target letters were sought but only one appeared in a given list. In Condition III, a single target letter was sought in a list of letters of high confusability. Search time decreased with age in all three tasks. Searching for two targets was no harder than searching for one. A highly confusable visual context increased search time at all age levels.     

Remarks on tucker's inter-battery method of factor analysis

Tucker's inter-battery method of factor analysis is shown to assume implicitly that, within the factor space of overlap between the vector configurations of the two test batteries involved, the locations of the two sets of principal axes and the sizes of the associated characteristic roots are identical. A suggested modification of the inter-battery method to avoid these restrictions is considered.The opinions expressed are those of the author and are not to be construed as reflecting official Department of Army policy.