ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01059.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Spearman invented factor analysis but his almost exclusive concern with the notion of a general factor prevented him from realizing its full potential. The leadership passed to others, notably Thurstone and Thomson, but progress was hampered by inadequate computing facilities and a limited conceptual framework. It is argued that the fitful progress of factor analyais and its slow and incomplete assimilation into the mainstream of statistical theory can be traced to the lack of a clear idea, until relatively recently, of the role of a model in the development of statistical methods. The combination of an appropriate modelling framework with Spearman's original idea provides a base for further development.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01060.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

This paper examines the origins of test theory in Spearman's early work on the attenuation of correlations due to errors of measurement. His purposes, assumptions, algebraic style and his caveats are featured. Brief attention is given to his early critics. Subsequent developments associated with true score theory and the assessment of reliability are indicated. One or two additional features of Spearman's writings deserve re‐emphasis in a modern conte

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01061.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

In 1928, the American mathematician E.B. Wilson had the ammunition to kill off Charles Spearman's two‐factor theory of mental ability — at least according to certain recent commentators. In their view, the two‐factor theory, and indeed factor analysis as a general technique, was dealt thecoup de grâceby Wilson's demonstration of the indeterminacy of the factor solution and only survived by, in effect, denying the problem. However, a rather different story emerges of the ensuing interchange between Spearman and Wilson when we examine not just the public record but unpublished correspondence between the two principals and with other interested parties. We have, thus, been able to paint a richer and more historically complete picture of the Spearman‐Wilson episode than previous chronicles have achieved. In addition, we argue that the spirit in which their protracted interchange was conducted illustrates the socially negotiated nature of

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01062.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Spearman's Rank Correlation coefficientrhois the one nonparametric measure of association to feature in most modern courses, textbooks and computer packages in elementary statistics. This paper covers the tortuous route to the present position over the period 1904 to the early 1950s, casting considerable doubt on the way as to the easy identification of any one person (including Spearman) with the coefficient.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01063.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

We study the attenuation of a correlation coefficient when one of the underlying measurement variables is categorized. We show that the attenuation depends critically on the distribution of the underlying latent variable, and on the scores assigned to the categories. Practical implications of these results are discussed.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01064.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

A least squares optimization strategy is first reviewed and applied to the task of fitting a given collection of symmetric proximity values defined between the objects from one set by a collection of reconstructed proximity values, satisfying a fixed set of constraints, generated from some specified graph‐theoretic structure, such as an ultrametric or an additive tree, selected for representing the objects. Our method uses itcrative projection on to closed convex sets defined by the collection of given constraints characterizing the structural representation specified, and in contrast to least squares optimization methods that impose such constraints through the use of penalty functions, avoids the use of the latter, as well as the implementation of any gradient‐based optimization technique. Secondly, just as various penalty‐function/ gradient‐based optimization techniques have been turned into heuristic search strategies for such particular structures of interest as ultrametrics or additive trees, the use of iterative projection is suggested as a general heuristic search strategy for locating the best structural representations to impose in the first place, where the collection of constraints used may vary over the course of the optimization process. Our evaluation of the expected results uses several data sets previously analysed in the literature. Finally, several other applications of iterative projection as a heuristic optimization technique are discussed, including the consideration of data beyond that of a single symmetric proximity matrix (for example, extensions to two‐mode proximity matrices, i.e. between two distinct object sets, and to three‐way proximity matrices either symmetric or not), and to representations based on sums of matrices where each is constrained separately to conform to some desired representationa

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01065.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

One strategy which has been recommended for examining effects in repeated measures designs combines a degrees of freedom (d.f.)‐adjusted univariateFtest and a multivariate test. The results of a simulation study for a groups × trials repeated measures design are presented, and demonstrate that for balanced designs this combined strategy rarely provided superior Type I error control to that afforded by uniformly adopting either a univariate or multivariate test. For unbalanced repeated measures designs, all three strategies typically resulted in very conservative or very liberal Type I error rates when covariance matrices and group sizes were positively and negatively paired, respectively. For such designs, the approximate d.f. Welch‐James (James, 1951, 1954; Welch, 1947, 1951) multivariate statistic developed by Johansen (1980) is preferable to any of the other strategies investigated in this paper. Power comparisons also favour the use of the Welch‐Jame

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01066.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

This paper develops a computationally efficient procedure for analysis of structural equation models with continuous and polytomous variables. A partition maximum likelihood approach is used to obtain the first stage estimates of the thresholds and the polyserial and polychoric correlations in the underlying correlation matrix. Then, based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, a generalized least squares approach is employed to estimate the structural parameters in the correlation structure. Asymptotic properties of the estimators are derived. Some simulation studies are conducted to study the empirical behaviours and robustness of the procedure, and compare it with some existing methods.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01067.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Recent investigations have revealed that widely available software can be adapted to provide maximum likelihood (ML) estimates for a general class of multilevel covariance structure models if the data are balanced (e.g. equal numbers of students in each of many schools). When the data are unbalanced, finding ML estimates is more challenging. However, by viewing the ‘complete data’ as balanced, one can calculate ML estimates for unbalanced data by constructing a comparatively simple EM algorithm. Computation using standard single‐level structural equation software performs the ‘M step’, and an auxiliary program computes the E‐step. Simple computational formulas for this E‐step are provided in the case of two‐level data, and recent experience with its implementation discussed. Asymptotic standard errors are found by computing the observed‐data information matr

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1995.tb01068.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY