摘要:

Two mathematical models of cognitive development are investigated. One model assumes that cognitive growth proceeds by stages, and the other assumes that cognitive growth is continuous. Both models make predictions concerning the percentages of the population at different cognitive levels. In the stage model, the cognitive level is identified with the stage, and in the continuous learning model, the cognitive level is defined by attainment above a given threshold and below the next highest threshold. The models are applied to three large‐scale experimental studies which categorize adolescents according to their Piagetian stage, namely a study by Lawson&Renner (1974) in the USA, a study by Shayer&Wylam (1978) in England, and a study by Shemesh, Eckstein&Lazarowitz (1992) in Israel. In all cases, the fit of the stage model to the experimental data was better than the fit of the continuous learning mode

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00974.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

This paper expands on a recent study by Muthen&Kaplan (1985) by examining the impact of non‐normal Likert variables on testing and estimation in factor analysis for models of various size. Normal theory GLS and the recently developed ADF estimator are compared for six cases of non‐normality, two sample sizes, and four models of increasing size in a Monte Carlo framework with a large number of replications. Results show that GLS and ADF chi‐square tests are increasingly sensitive to non‐normality when the size of the model increases. No parameter estimate bias was observed for GLS and only slight parameter bias was found for ADF. A downward bias in estimated standard errors was found for GLS which remains constant across model size. For ADF, a downward bias in estimated standard errors was also found which became increasingly worse with the size of th

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00975.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Thurstonian models have proven useful in a wide range of applications because they can describe the multidimensional nature of choice objects and the effects of similarity and comparability in choice situations. This paper presents a unified framework for applying the Thurstonian approach to partial ranking data that includes paired comparison data and first choices. As a result, several new Thurstonian ranking models are introduced by imposing different constraints on the covariance matrix of the random utilities and their mean scale values. Furthermore, the estimation of probabilities for a multivariate normal distribution by numerical integration procedures and the Clark algorithm are discussed. To illustrate the approach, data from two partial ranking experiments are analysed.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00976.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The paper examines the use of the ordered Dirichlet prior for binary logistic item response models. This prior is based on the investigator's prior information about the probabilities of correct response to items from examinees at several ability levels. The effect of the prior is examined in terms of the posterior mode of the item parameters computed via the EM algorithm. An illustration is used to explore the application of a 1981 ACT math test to form a prior that is then used on a similar 1987 test. A novel feature of the paper is the emphasis placed on the entire item response curves, rather than the item parametersper se. Detailed computational expressions for the three‐parameter logistic model are summarized in an Appendi

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00977.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

In a series of papers, the case has been argued for viewing the process of aggregating marks in an examination from a decision theoretic (or measurement theoretic) standpoint. The purpose of aggregating marks is to form an overall ranking of the candidates that corresponds with the ranking that the examiners would generate by holistic judgement, if they had the time and the powers of consistency required. Models of aggregation that parallel multi‐attribute value functions have been proposed. These models have not, until recently, been trialed with practising examiners, however. The problem has been that the interactive procedure, which the assessment of the models requires, needed to be implemented within a general examination processing package so that the context in which the models are used could be as realistic as possible. This has now been achieved for the restricted case of aggregating two components, and preliminary trials with examiners have begun.The implementation adopted was not thelock‐stepprocedure originally suggested, but rather a least‐squares fitting procedure of finite‐difference approximations to the aggregation functions. Although a least squares procedure is used, the assessment is iterative and allows the users to revise their judgements in the light of possible inconsistencies. The authors believe this approach has not been used before, either in the examination context or in the assessment of multi‐attribute utility

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00978.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Structural equation models are analysed in the presence of stochastic constraints. Based on a Bayesian perspective, a prior distribution on nuisance parameters in the unknown covariance matrix of error measurements with stochastic constraints is considered. An iterative procedure is implemented to produce the various Bayesian estimates with stochastic constraints. A simulation study is conducted to illustrate the accuracy and behaviour of this Bayesian approach. A real‐life example is provided to illustrate the theor

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00979.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The main purpose of this paper is to develop basic statistical theory for two‐level analysis of covariance structures. Major asymptotic results for statistical inference, such as the asymptotic distributions of the estimator and the goodness‐of‐fit test statistic are derived, based on an unbalanced design with only small numbers of level‐one units. Computationally, it is shown that the solution can be obtained via standard programs, such as LISREL, EQS and COSAN. The behaviour of the estimates is illustrated by an artificial example and a real‐life example. Some possibilities of extending the results to a more general two‐level model, and to situations with arbitrary distributions and elliptical distributions are also i

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00980.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Confirmatory factor analysis is widely used in the analysis of multitrait‐multimethod (MTMM) matrices. Sufficient conditions for rotational uniqueness in the additive MTMM model have not been fully discussed in the literature. A theorem giving sufficient conditions for uniqueness in the additive MTMM model is presented. This theorem reformulates the conditions given by Anderson&Rubin (1956), Howe (1955), and Jöreskog (1979) for the general confirmatory factor analysis model. Several corollaries of the theorem describe special cases of the additive MTMM model that will always be rotationally unique. One of these cases is illustrated with an example using real data. Some implications of these results are discuss

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00981.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The main purpose of this article is to develop statistical theory for analysing continuous and polytomous variables in several populations. A general multivariate model is defined with a set of identification conditions. Interpretations of these identification conditions are studied. To achieve the desirable asymptotic properties for statistical inferences, the maximum likelihood approach will be employed to estimate the unknown parameters in the model. Computationally, a program based on the Fletcher‐Powell algorithm is constructed to get the maximum likelihood estimates, and the information matrix is implemented to produce the standard error estimates. Statistical inference for various null hypotheses on comparisons of the means, variances, polychoric and polyserial correlations among the variables across or within different populations is discussed. A computationally more efficient partition maximum likelihood approach is also proposed. Finally, applications of the theory to some examples and a simulation study on the comparison of the maximum likelihood approach and partition maximum likelihood approach are presente

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00982.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Investigations of the characteristics of real data indicate that psychometric measures can have highly skewed distributions with heavy tails and outliers. In terms of power, the pairedttest is known to be unsatisfactory when distributions have heavy tails, and there is the issue of whether some measure of location, other than the mean, might be more appropriate when distributions are skewed. This paper proposes a method for comparing the medians of two dependent groups. Simulations indicate that the proposed procedure controls the probability of a Type I error to a reasonable degree. In terms of power, the new procedure is much less affected by contamination than the pairedttest or the Wilcoxon signed rank test. Brief consideration is also given to an extension of the proposed procedure to more than two groups.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00983.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY