摘要:

The details of response distributions in the method of limits are known to violate both simple assumptions of monotone increasing stimulus–response functions, and the derived idea that change points on such functions, those points where sensory phenomenology changes abruptly, are strictly ordered correspondingly. The predictions of nonlinear psychophysics include mappings from responses back onto stimuli which are not single‐valued. Such predictions imply that outliers to change point distributions expressed in physical units will exist under some conditions. The detection of outliers is tractable from a Bayesian approach. An experiment using fractionation of perceived brightness by continuous response adjustment is used as an illustrative example both for theory and for statistical analy

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00987.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Traditional analysis of covariance (ANCOVA) assumptions beyond those required for analysis of variance (ANOVA) are described as unnecessary. The problem posed by the most common violation of traditional ANCOVA: heterogeneity of dependent variable on covariate regression coefficients across treatments is considered, as is the relationship between linear modelling and ANCOVA. The amelioration of problems due to covariate‐treatment covariation by heterogeneous regression ANCOVA is described and illustrated in terms of a hypothetical experiment. Subsequently, various parametric alternatives to the traditional ANCOVA are presented in terms of the types of analyses they provide. Finally, the theoretical issue of the relationship between the psychological model and the mathematical model is considered briefl

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00988.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 investigate various approaches in analysing the multivariate polychoric and polyserial correlation model in the presence of incomplete data. For the general case with missing entries in both continuous and polytomous variables, a pseudo maximum likelihood method, and a partition pseudo maximum likelihood are developed. Iterative procedures based on the Fletcher–Powell algorithm and the Newton–Raphson algorithm are implemented to obtain various solutions. For the special case with missing entries only in the polytomous variables, a full maximum likelihood estimate is obtained with the help of an appropriate one–one onto transformation that significantly simplifies the computational burden. The analogous approaches as in the general case are also investigated. Finally, a simulation study is conducted to compare the performances of the various appro

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00989.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

This paper describes a general class of reliability measures that contains the classical‐test‐theory measure as a special case. A particular member of this class is suggested for applied work, and some of its properties are studied. A lower bound for this new measure of reliability is derived which is a robust analogue of Cronbach's alpha. Here the term ‘robust’ is being used to describe a measure of reliability that is relatively insensitive to small fluctuations in the tails of the distributions under study. The idea is that the value of aparameter, intended to reflect reliability, should be determined by the bulk of the distribution associated with whatever is being measured. If, for example, a test is considered unreliable when test scores have a normal distribution, it should not be possible to make the test appear to be reliable with a trivial change in the tails of the distributions. It is illustrated that Cronbach's alpha does not have this characteristic. In statistical jargon, Cronbach's alpha is not a resistant measure of reliability, while the reverse is true for the new measure of reliability introduced here. Included in this paper is a method for computing a confidence interval for the new lowe

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00990.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Actual Type I error rates (τ) for James's second‐order test and Wilcox'sHmtest on means were estimated for various conditions in which variances were either homoscedastic or heteroscedastic and distributions were either normal or non‐normal. Actual Type I error rates for both James's second‐order and Wilcox'sHmtests were affected by non‐normality. However, the two tests tended to have τ near the nominal Type I error rate (α) when applied to data sampled from symmetric non‐normal distributions. When applied to data sampled from asymmetric distributions, larger values of τ‐α occurred and τ‐α tended to increase as the degree of

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00991.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The use of automated subset search algorithms is reviewed and issues concerning model selection and selection criteria are discussed. In addition, a Monte Carlo study is reported which presents data regarding the frequency with which authentic and noise variables are selected by automated subset algorithms. In particular, the effects of the correlation between predictor variables, the number of candidate predictor variables, the size of the sample, and the level of significance for entry and deletion of variables were studied for three automated subset algorithms: BACKWARD ELIMINATION, FORWARD SELECTION, and STEPWISE. Results indicated that: (1) the degree of correlation between the predictor variables affected the frequency with which authentic predictor variables found their way into the final model; (2) the number of candidate predictor variables affected the number of noise variables that gained entry to the model; (3) the size of the sample was of little practical importance in determining the number of authentic variables contained in the final model; and (4) the population multiple coefficient of determination could be faithfully estimated by adopting a statistic that is adjusted by the total number of candidate predictor variables rather than the number of variables in the final model.

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00992.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

A recent survey of simulation studies concluded that an overwhelming majority of papers do not report a rationale for the decision regarding the number of Monte Carlo iterations. A surprisingly large number of reports do not contain a justifiable definition of robustness and many studies are conducted with an insufficient number of iterations to achieve satisfactory statistical conclusion validity. The implication is that we do not follow our own advice regarding the management of Type I and Type II errors when conducting Monte Carlo experiments. This paper reports a straightforward application of a well‐known procedure for the purpose of objectively determining the exact number of iterations necessary to confidently detect departures from robustness in Monte Carlo results. A table of the number of iterations necessary to detect departures from a series of nominal Type I error rates is include

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00993.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Inadmissible estimates, like negative variance estimates, frequently occur when a theoretical covariance matrix is fitted to a sample covariance matrix. When this happens, it is common practice to re‐estimate subject to non‐negativity constraints and to count the ensuing zeros as true zeros. We derive conditions under which this approach has a valid frequentist interpretat

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00994.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Bartholomew (1980, 1984a) has laid down a foundation for factor analysis based on latent variable models. Shea (1984, 1985) has provided computer programs for estimating one‐factor latent variable models when responses are binary or polytomous variables. However, the programs have limitations on number of variables and the sample size, which limits their applicability, especially when variables are polytomous. However, the more important limitation is that it is not possible to use two‐factor models when one‐factor models are not adequate.Here, we have gone further and successfully obtained maximum likelihood estimates for both the one‐factor and two‐factor latent variable models for binary and polytomous variables. The new algorithm is much faster because of careful and efficient programming. More importantly, generalization to high latent domensions is straightforward. Formal hypothesis testing is very difficult when variables are very large in number. However, we have shown in our examples that some interesting graphical interpretations ca

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00995.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Copas&Loeber's (1990) measure of association for 2times2 tables, relative improvement over chance (RIOC), is shown to be identical to Levin's measure of attributable risk. It is demonstrated that both measures are equal to the difference between the true positive rate and the false negative rate, standardized for the ratio of base rate and selection ratio. Also, it is shown that Copas&Loeber's formula for the variance of RIOC in large samples is identical to the formula for the variance of attributable risk in cross‐sectional research as developed by Walter (1976). Relationships between RIOC and some existing measures of association are mentioned. By using Copas&Loeber's numerical example, it is concluded that they rightly make a distinction between large and small sample

ISSN:0007-1102    

DOI:10.1111/j.2044-8317.1992.tb00996.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY