摘要:

A least‐squares strategy is developed for representing a symmetric proximity matrix containing similarity or dissimilarity values between each pair of objects from some given set, as an approximate sum of a small number of symmetric matrices having the same size as the original but which satisfy certain simple order constraints on their entries. The primary class of constraints considered are of the Robinson (or anti‐Robinson) type, where the entries in such a matrix, subject to a suitable row/column ordering, never increase (or decrease) when moving away from a main diagonal entry within any row or column. Matrices satisfying either the Robinson or anti‐Robinson condition can be viewed as defining certain restricted collections of possibly overlapping subsets along with an associated measure of ‘compactness’ or ‘salience’ for each; these subsets and their compactness or salience indices form the basis for helping explain the patterning of entries in the initial proximity matrix as now reflected by the matrix sum. A number of empirical examples based on well‐known published data sets are used as illustrations of how such reconstructions might be carried out and interpreted. Finally, several other types of matrix order constraints are mentioned briefly, along with a few corresponding numerical examples, to show how alternative structures also can be considered using the same type of computational strategy as in the (anti

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01023.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

This paper gives two scaling procedures for measurement of asymmetry observed in comparative judgement in terms of three ordered categories. With a revised law of comparative judgement, a least squares solution and a maximum likelihood solution are suggested for the parameter estimation with some statistical tests. Numerical examples are illustrated, and features and applicability of the present work are discussed in comparison with related work.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01024.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

The asymptotically distribution‐free (ADF) test statistic for covariance structure analysis (CSA) has been reported to perform very poorly in simulation studies, i.e. it leads to inaccurate decisions regarding the adequacy of models of psychological processes. It is shown in the present study that the poor performance of the ADF test statistic is due to inadequate estimation of the weight matrix (W=−l), which is a critical quantity in the ADF theory. Bootstrap procedures based on Hall's bias reduction perspective are proposed to correct the ADF test statistic. It is shown that the bootstrap correction of additive bias on the ADF test statistic yields the desired tail behaviour as the sample size reaches 500 for a 15‐variable‐3‐factor confirmatory factor‐analytic model, even if the distribution of the observed variables is not multivariate normal and the latent factors are dependent. These results help to revive the ADF th

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01025.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

This paper presents a comparison of results from two methods for estimating and testing a model for the factor analysis of dichotomous variables. Forkmanifest dichotomous variables, the data can be cross‐classified to form a vector of 2kfrequencies, and nonlinear methods that use thefull informationin these 2kfrequencies are available for factor analysis. In addition, another method that uses only thelimited informationin the first‐, and second‐order marginal frequencies is available for the same model. Askbecomes larger, substantial differences between the full‐information and limited‐information methods become apparent in results from the test of fit. For largek. Type I and Type II error rates may be higher in the full‐information approach, because as the vector of 2kfrequencies becomes sparse, the chi‐square approximation for the distribution of the goodness‐of‐fit test statistic becomes poorer. In this paper, Monte Carlo experiments are used under a variety of conditions to compare the methods for rate of Type I errors when the model matches the simulated data and for the rate of Type II errors when the model does not match t

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01026.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

The present paper discusses several methods for (simultaneous) component analysis of scores of two or more groups of individuals on the same variables. Some existing methods are discussed, and a new method (SCA‐S) is developed for simultaneous component analysis in such a way that for each set essentially the same component structure is found (SCA‐S). This method is compared to alternative methods for analysing such data which employ the same component weights matrix (SCA‐W) or the same pattern matrix (SCA‐P) across data sets. Among these methods, SCA‐W always explains the highest amount of variance, SCA‐S the lowest, and SCA‐P takes the position in between. These explained variances can be compared to the amount of variance explained by separate PCAs. Implications of such fit differences are discussed. In addition, it is shown how, for cases where SCA‐S does not fit well, one can use SCA‐W (and SCA‐P) to find out if and how correlational structures differ. Finally, some attention is paid to facilitating the interpretation of an SCA‐S solution. Like the other SCA methods, SCA‐S has rotational freedom. This rotational freedom is exploited in a specially designed simple structure rotation technique for SCA‐S. This technique is illustrated

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01027.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

An alternative to multiple regression that is appropriate when the dependent variable is ordinal is suggested. The goal of the system is to predict correctly as many as possible of the binary ordinal relations on the dependent variable. This can be done by treating the problem as one in discriminant analysis by discriminating thepairsof subjects whose ordinal relations are in one direction from those with relations in the other. The bases of prediction can be raw score differences on predictors, their rank differences, or their directions of difference. For each, it is possible to find a system of weights that approximately maximizes discrimination. These turn out to depend on the variables' co‐variances, on their rank correlations, and on their tau correlations, respectively. It is also possible to estimate the odds that any given relation is in a particular direction. A solution for the weights that exactly maximizes probability of correct ordinal prediction is available in the case of predicting from directions of difference. An example is give

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01028.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

For split plot designs exact univariateFtests of the within‐subjects main effect and the between × within interaction are based on the assumption of multi‐sample sphericity. Type I error rates are reported for three tests designed for use when multisample sphericity is violated: the general approximation test, the improved general approximation test and a revised improved general approximation test. The results indicate that when sample sizes are unequal and dispersion matrices are unequal, using the improved general approximation or revised improved general approximation test of the interaction allows better control of the Type I error rate than does the ‐adjuste

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01029.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

A well‐known result is that slight departures from normality can have a large effect on the usual correlation coefficient rendering the magnitude of the correlation difficult to interpret and potentially misleading. In the context of a random effects model, which is the focus of attention in this paper, this means that effect size, as measured by the intraclass correlation, might be small due to outliers or heavy‐tailed distributions rather than a lack of differences among the groups being compared. Similarly, a large intraclass correlation might be due to trivial shifts away from normality which would become small if an adjustment for non‐normality were made. Moreover, this problem has to do with the effects of non‐normality on population parameters, not just statistics, so problems can arise even with large sample sizes. This follows almost immediately from results in Tukey (1960), and it is briefly illustrated here. One approach to this problem is to use a Winsorized analogue of the intraclass correlation. This paper suggests three ways the Winsorized intraclass correlation might be estimated and compares them via simulations. A bivariate generalization of the random effects model is also considered, and two methods of estimating the group‐level correlation are described and compared. Alternatives to Winsorization are also

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01030.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01031.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Book reviewed in this article:The Handbook of Psychological Testing.ByPaul Kline.Nonparametric Statistics: An Introduction.ByJean Dickinson Gibbons.Teaching Statistical Concepts.ByA. Hawkins, F. Jolliffe,&L. Glickman.Computer Simulation Applications: An Introduction.ByM. L. Whicker&L. Sigelman.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1994.tb01032.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY