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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
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
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
Pasquale Anselmi, Luca Stefanutti, Debora de Chiusole, Egidio Robusto
The gain-loss model (GaLoM) is a formal model for assessing knowledge and learning. In its original formulation, the GaLoM assumes independence among the skills. Such an assumption is not reasonable in several domains, in which some preliminary knowledge is the foundation for other knowledge. This paper presents an extension of the GaLoM to the case in which the skills are not independent, and the dependence relation among them is described by a well-graded competence space. The probability of mastering skill s at the pretest is conditional on the presence of all skills on which s depends...
February 17, 2017: British Journal of Mathematical and Statistical Psychology
María Rubio-Aparicio, Julio Sánchez-Meca, José Antonio López-López, Juan Botella, Fulgencio Marín-Martínez
Subgroup analyses allow us to examine the influence of a categorical moderator on the effect size in meta-analysis. We conducted a simulation study using a dichotomous moderator, and compared the impact of pooled versus separate estimates of the residual between-studies variance on the statistical performance of the Q B(P) and Q B(S) tests for subgroup analyses assuming a mixed-effects model. Our results suggested that similar performance can be expected as long as there are at least 20 studies and these are approximately balanced across categories...
February 6, 2017: British Journal of Mathematical and Statistical Psychology
Ping Chen, Chun Wang, Tao Xin, Hua-Hua Chang
Multidimensional computerized adaptive testing (MCAT) has received increasing attention over the past few years in educational measurement. Like all other formats of CAT, item replenishment is an essential part of MCAT for its item bank maintenance and management, which governs retiring overexposed or obsolete items over time and replacing them with new ones. Moreover, calibration precision of the new items will directly affect the estimation accuracy of examinees' ability vectors. In unidimensional CAT (UCAT) and cognitive diagnostic CAT, online calibration techniques have been developed to effectively calibrate new items...
February 2017: British Journal of Mathematical and Statistical Psychology
Xinru Li, Elise Dusseldorp, Jacqueline J Meulman
In the framework of meta-analysis, moderator analysis is usually performed only univariately. When several study characteristics are available that may account for treatment effect, standard meta-regression has difficulties in identifying interactions between them. To overcome this problem, meta-CART has been proposed: an approach that applies classification and regression trees (CART) to identify interactions, and then subgroup meta-analysis to test the significance of moderator effects. The previous version of meta-CART has its shortcomings: when applying CART, the sample sizes of studies are not taken into account, and the effect sizes are dichotomized around the median value...
February 2017: British Journal of Mathematical and Statistical Psychology
Michael J Brusco, Emilie Shireman, Douglas Steinley, Susan Brudvig, J Dennis Cradit
The emergence of Gaussian model-based partitioning as a viable alternative to K-means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model-based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple-restart (multistart) approach commonly used for K-means partitioning less effective as a heuristic solution strategy...
February 2017: British Journal of Mathematical and Statistical Psychology
Ulf Böckenholt, Thorsten Meiser
Two different item response theory model frameworks have been proposed for the assessment and control of response styles in rating data. According to one framework, response styles can be assessed by analysing threshold parameters in Rasch models for ordinal data and in mixture-distribution extensions of such models. A different framework is provided by multi-process item response tree models, which can be used to disentangle response processes that are related to the substantive traits and response tendencies elicited by the response scale...
February 2017: British Journal of Mathematical and Statistical Psychology
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