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British Journal of Mathematical and Statistical Psychology

Guogen Shan, Charles Bernick, Sarah Banks
This research was motivated by a clinical trial design for a cognitive study. The pilot study was a matched-pairs design where some data are missing, specifically the missing data coming at the end of the study. Existing approaches to determine sample size are all based on asymptotic approaches (e.g., the generalized estimating equation (GEE) approach). When the sample size in a clinical trial is small to medium, these asymptotic approaches may not be appropriate for use due to the unsatisfactory Type I and II error rates...
June 30, 2017: British Journal of Mathematical and Statistical Psychology
Wolf Schwarz, Dennis Reike
Using a standard repeated measures model with arbitrary true score distribution and normal error variables, we present some fundamental closed-form results which explicitly indicate the conditions under which regression effects towards (RTM) and away from the mean are expected. Specifically, we show that for skewed and bimodal distributions many or even most cases will show a regression effect that is in expectation away from the mean, or that is not just towards but actually beyond the mean. We illustrate our results in quantitative detail with typical examples from experimental and biometric applications, which exhibit a clear regression away from the mean ('egression from the mean') signature...
June 30, 2017: British Journal of Mathematical and Statistical Psychology
Maria Bolsinova, Jesper Tijmstra
By considering information about response time (RT) in addition to response accuracy (RA), joint models for RA and RT such as the hierarchical model (van der Linden, 2007) can improve the precision with which ability is estimated over models that only consider RA. The hierarchical model, however, assumes that only the person's speed is informative of ability. This assumption of conditional independence between RT and ability given speed may be violated in practice, and ignores collateral information about ability that may be present in the residual RTs...
June 21, 2017: British Journal of Mathematical and Statistical Psychology
Tamar Kennet-Cohen, Dvir Kleper, Elliot Turvall
A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation...
June 20, 2017: British Journal of Mathematical and Statistical Psychology
Yoosun Jamie Kim, Robert A Cribbie
Valid use of the traditional independent samples ANOVA procedure requires that the population variances are equal. Previous research has investigated whether variance homogeneity tests, such as Levene's test, are satisfactory as gatekeepers for identifying when to use or not to use the ANOVA procedure. This research focuses on a novel homogeneity of variance test that incorporates an equivalence testing approach. Instead of testing the null hypothesis that the variances are equal against an alternative hypothesis that the variances are not equal, the equivalence-based test evaluates the null hypothesis that the difference in the variances falls outside or on the border of a predetermined interval against an alternative hypothesis that the difference in the variances falls within the predetermined interval...
June 1, 2017: British Journal of Mathematical and Statistical Psychology
Ke-Hai Yuan, Ge Jiang, Ying Cheng
Data in psychology are often collected using Likert-type scales, and it has been shown that factor analysis of Likert-type data is better performed on the polychoric correlation matrix than on the product-moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice...
May 26, 2017: British Journal of Mathematical and Statistical Psychology
Frank Goldhammer, Merle A Steinwascher, Ulf Kroehne, Johannes Naumann
Completing test items under multiple speed conditions avoids the performance measure being confounded with individual differences in the speed-accuracy compromise, and offers insights into the response process, that is, how response time relates to the probability of a correct response. This relation is traditionally represented by two conceptually different functions: the speed-accuracy trade-off function (SATF) across conditions relating the condition average response time to the condition average of accuracy, and the conditional accuracy function (CAF) within a condition describing accuracy conditional on response time...
May 2017: British Journal of Mathematical and Statistical Psychology
Ingmar Visser, Rens Poessé
The linear ballistic accumulator (LBA) model (Brown & Heathcote, , Cogn. Psychol., 57, 153) is increasingly popular in modelling response times from experimental data. An R package, glba, has been developed to fit the LBA model using maximum likelihood estimation which is validated by means of a parameter recovery study. At sufficient sample sizes parameter recovery is good, whereas at smaller sample sizes there can be large bias in parameters. In a second simulation study, two methods for computing parameter standard errors are compared...
May 2017: British Journal of Mathematical and Statistical Psychology
Jochen Ranger, Jörg-Tobias Kuhn, Carsten Szardenings
Cognitive psychometric models embed cognitive process models into a latent trait framework in order to allow for individual differences. Due to their close relationship to the response process the models allow for profound conclusions about the test takers. However, before such a model can be used its fit has to be checked carefully. In this manuscript we give an overview over existing tests of model fit and show their relation to the generalized moment test of Newey (Econometrica, 53, 1985, 1047) and Tauchen (J...
May 2017: British Journal of Mathematical and Statistical Psychology
Peter W van Rijn, Usama S Ali
We compare three modelling frameworks for accuracy and speed of item responses in the context of adaptive testing. The first framework is based on modelling scores that result from a scoring rule that incorporates both accuracy and speed. The second framework is the hierarchical modelling approach developed by van der Linden (2007, Psychometrika, 72, 287) in which a regular item response model is specified for accuracy and a log-normal model for speed. The third framework is the diffusion framework in which the response is assumed to be the result of a Wiener process...
May 2017: British Journal of Mathematical and Statistical Psychology
Dylan Molenaar, Maria Bolsinova
In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times...
May 2017: British Journal of Mathematical and Statistical Psychology
Paul De Boeck, Haiqin Chen, Mark Davison
Based on data from a cognitive test presented in a condition with time constraints per item and a condition without time constraints, the effect of speed on accuracy is investigated. First, if the effect of imposed speed on accuracy is negative it can be explained by the speed-accuracy trade-off, and if it can be captured through the corresponding latent variables, then measurement invariance applies between a condition with and a condition without time constraints. The results do show a negative effect and a lack of measurement invariance...
May 2017: British Journal of Mathematical and Statistical Psychology
Dylan Molenaar, Ingmar Visser
No abstract text is available yet for this article.
May 2017: British Journal of Mathematical and Statistical Psychology
Hyeon-Ah Kang
The Cox proportional hazards model with a latent trait variable (Ranger & Ortner, 2012, Br. J. Math. Stat. Psychol., 65, 334) has shown promise in accounting for the dependency of response times from the same examinee. The model allows flexibility in shapes of response time distributions using the non-parametric baseline hazard rate while allowing parametric inference about the latent variable via exponential regression. The flexibility of the model, however, comes at the price of a significant increase in the complexity of estimating the model...
May 2017: British Journal of Mathematical and Statistical Psychology
Maria Bolsinova, Jesper Tijmstra, Dylan Molenaar
It is becoming more feasible and common to register response times in the application of psychometric tests. Researchers thus have the opportunity to jointly model response accuracy and response time, which provides users with more relevant information. The most common choice is to use the hierarchical model (van der Linden, 2007, Psychometrika, 72, 287), which assumes conditional independence between response time and accuracy, given a person's speed and ability. However, this assumption may be violated in practice if, for example, persons vary their speed or differ in their response strategies, leading to conditional dependence between response time and accuracy and confounding measurement...
May 2017: British Journal of Mathematical and Statistical Psychology
Chen-Wei Liu, Wen-Chung Wang
Examinee-selected item (ESI) design, in which examinees are required to respond to a fixed number of items in a given set, always yields incomplete data (i.e., when only the selected items are answered, data are missing for the others) that are likely non-ignorable in likelihood inference. Standard item response theory (IRT) models become infeasible when ESI data are missing not at random (MNAR). To solve this problem, the authors propose a two-dimensional IRT model that posits one unidimensional IRT model for observed data and another for nominal selection patterns...
April 8, 2017: British Journal of Mathematical and Statistical Psychology
Michael Smithson, Yiyun Shou
This paper introduces a two-parameter family of distributions for modelling random variables on the (0,1) interval by applying the cumulative distribution function of one 'parent' distribution to the quantile function of another. Family members have explicit probability density functions, cumulative distribution functions and quantiles in a location parameter and a dispersion parameter. They capture a wide variety of shapes that the beta and Kumaraswamy distributions cannot. They are amenable to likelihood inference, and enable a wide variety of quantile regression models, with predictors for both the location and dispersion parameters...
March 17, 2017: British Journal of Mathematical and Statistical Psychology
Maria Umlauft, Frank Konietschke, Markus Pauly
Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null...
March 15, 2017: British Journal of Mathematical and Statistical Psychology
Joe W Tidwell, Michael R Dougherty, Jeffrey S Chrabaszcz, Rick P Thomas
Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties...
February 27, 2017: British Journal of Mathematical and Statistical Psychology
Siwei Liu
This paper compares the multilevel modelling (MLM) approach and the person-specific (PS) modelling approach in examining autoregressive (AR) relations with intensive longitudinal data. Two simulation studies are conducted to examine the influences of sample heterogeneity, time series length, sample size, and distribution of individual level AR coefficients on the accuracy of AR estimates, both at the population level and at the individual level. It is found that MLM generally outperforms the PS approach under two conditions: when the sample has a homogeneous AR pattern, namely, when all individuals in the sample are characterized by AR processes with the same order; and when the sample has heterogeneous AR patterns, but a multilevel model with a sufficiently high order (i...
February 22, 2017: British Journal of Mathematical and Statistical Psychology
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