British Journal of Mathematical and Statistical Psychology

Ulrich, Rolf; Giray, Markus

doi: 10.1111/j.2044-8317.1989.tb01111.xpmid: N/A

This paper investigates the measurement of reaction times (RTs) with clocks of limited time resolution. The questions raised are: (a) What is the relationship between measured and true RT? (b) Are mean and variance of measured RT biased, and if so, (c) how does this bias depend on the clock's time resolution? (d) Is it possible to correct this bias? It is concluded that the bias is practically negligible even if the time resolution of a clock is only 30 ms. The results show that a clock of limited time resolution biases mean and variance of measured RT. Furthermore it is shown that the effect of time resolution on detecting a true mean RT difference is negligible if the variance of true RT is relatively large. Formulae are provided to correct the bias of mean and variance of measured RT. In addition the implication of time resolution on measured RT for paired observations is analysed. It is shown that the product moment correlation coefficient but not the covariance of paired RT measures is affected by time resolution. A correction formula to remove the bias on the product moment correlation coefficient is provided.

Marley, A. A. J.

doi: 10.1111/j.2044-8317.1989.tb01112.xpmid: N/A

A large class of random utility models can be expressed in terms of multivariate (dependent) Weibull distributions. This class includes Luce's choice model, McFadden's generalized extreme value class, and Tversky's elimination by aspects model. A major advantage of this class is that one can obtain simple closed form representations of the predicted choice probabilities and reaction times. In this paper I develop a ‘process’ model that gives a natural interpretation of the origins of these models, and discuss various limitations, and possible extensions, of such models.

Formann, Anton K.

doi: 10.1111/j.2044-8317.1989.tb01113.xpmid: N/A

Two types of restricted latent class models are known: linearly constrained latent class analysis (LCA), especially models assuming equalities of certain latent parameters, and linear logistic LCA. The present paper shows some new fields for their application, namely, one application of the first model type to non‐monotone dichotomous items and three applications of linear logistic LCA: 1. A model for paired comparisons comparable to that by Bradley and Terry, but providing for a heterogeneous sample composed of subsamples with different scaling values for the objects. 2. A model for repeated measurements on one and the same item, whereby changes over time can be represented by class‐specific change parameters. 3. Two variants of a simple scaling model showing that the unconditional as well as the conditional maximum‐likelihood representation of the Rasch model are special cases of LCA.

Muthén, Bengt

doi: 10.1111/j.2044-8317.1989.tb01114.xpmid: N/A

An estimator is considered for mean and covariance structure analysis of non‐normal continuous variables. This estimator extends the ADF estimator of Browne (1982, 1984) to include structured means. The behaviour of the estimator is compared to that of normal‐theory generalized least‐squares in simulated data.

Kroonenberg, Pieter M.; Berge, Jos M. F.

doi: 10.1111/j.2044-8317.1989.tb01115.xpmid: N/A

In this paper three‐mode principal component analysis and perfect congruence analysis for weights applied to sets of covariance matrices are explained and detailed, and the relationships between the two techniques are explored. It is shown that given several assumptions are made for three‐mode principal component analysis close links between the two techniques exist. The methods are illustrated with data pertaining to a theory of self‐concept.

Muthén, Bengt O.

doi: 10.1111/j.2044-8317.1989.tb01116.xpmid: N/A

A new method is proposed for estimating factor means and factor covariances in a group of individuals selected on their observed scores. The selection variable is, for example, the total score on an admissions test. Given a factor model for the test items based on the group of test takers, we may be interested in the factor structure for those in the top quartile. The differences in factor means and covariances between this selected group and the full group gives useful information both on successful test performance and on test validity. The new method draws on the classic Pearson‐Lawley selection formulas. It avoids the fallacy of factor analysis on the selected group, which would lead to incorrect estimates. The new method is applied to a simple factor structure model for the GMAT test. Although the majority of the GMAT items test verbal skills, it is found that a quantitative factor shows the greatest change in moving from average to top quartile test takers.

Rasmussen, Jeffrey Lee

doi: 10.1111/j.2044-8317.1989.tb01117.xpmid: N/A

The parametric groups by trials analysis of variance F ratio is a widely used statistical test. When the variancc‐covariance assumption of the test is not met, researchers are commonly advised to use an epsilon‐corrected F ratio. A non‐parametric alternative has also been recommended when this assumption is not tenable. The present study compares the Type I error rate and power of the conventional F ratio, the epsilon‐corrected F ratio, and a non‐parametric statistic under various degrees of violation of the variance‐covariance assumption. The results indicate that only under gross violation of the assumption does the non‐parametric test show superior power to the parametric test. Additionally the results indicate that the power of the non‐parametric test is also affected by violation of the variance‐covariance assumption. In general the epsilon‐corrected F ratio is recommended under the conditions investigated.

Rasmussen, Jeffrey Lee

doi: 10.1111/j.2044-8317.1989.tb01118.xpmid: N/A

Computer‐intensive statistical techniques have been suggested as alternatives to standard parametric analysis due to their freedom from normal‐theory assumptions. Two such techniques that may be used for correlational analysis are bootstrap and approximate randomization tests. These techniques were compared with the parametric Pearson's r under composite‐normal conditions in which the test of significance of Pearson's r is known to possess overly liberal Type I error rates. Results indicated that the approximate randomization test had Type I error rates that closely followed the parametric approach. The bootstrap, however, showed good control of the Type I error rates, except on small sample sizes.

Kim, Seock‐ho; Baker, Frank B.; Subkoviak, Michael J.

doi: 10.1111/j.2044-8317.1989.tb01119.xpmid: N/A

Under the minimum logit chi‐square item parameter estimation procedure, observed proportions of correct response of zero or unity result in infinite logits and estimates cannot be obtained. The paper examines the application of three rules (l/2n, l/4n and elimination) for dealing with such cases. A simulation study is conducted in which sample size, number of grouping intervals, underlying item discrimination and difficulty are varied. The outcome variables are the square of the difference between the estimates and the underlying parameter values for item discrimination and difficulty. The results indicate that a complex set of interactions exist among the factors employed in the study. Overall, the 1/4n rule is preferred over the other two rules as it generally yields the smallest RMSE for both item discrimination and difficulty. However, as sample size increases the differences among the three rules decreased.

Gillett, Raphael

doi: 10.1111/j.2044-8317.1989.tb01120.xpmid: N/A

The UGC evaluation of research performance in British universities contained a sampling artifact which potentially contributed to an overestimation of the performance of larger departments. The statistical principles underlying the artifact are elucidated, and the magnitude of the effect is investigated.