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British Journal of Mathematical and Statistical Psychology

José Fernando Vera
Stability or sensitivity analysis is an important topic in data analysis that has received little attention in the application of multidimensional scaling (MDS), for which the only available approaches are given in terms of a coordinate-based analytical jackknife methodology. Although in MDS the prime interest is in assessing the stability of the points in the configuration, this methodology may be influenced by imprecisions resulting from the inherently necessary Procrustes method. This paper proposes an analytical distance-based jackknife procedure to study stability and cross-validation in MDS in terms of the jackknife distances, which is not influenced by the Procrustes method...
December 20, 2016: 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...
December 13, 2016: British Journal of Mathematical and Statistical Psychology
Klaas Sijtsma, L Andries van der Ark
Over the past decade, Mokken scale analysis (MSA) has rapidly grown in popularity among researchers from many different research areas. This tutorial provides researchers with a set of techniques and a procedure for their application, such that the construction of scales that have superior measurement properties is further optimized, taking full advantage of the properties of MSA. First, we define the conceptual context of MSA, discuss the two item response theory (IRT) models that constitute the basis of MSA, and discuss how these models differ from other IRT models...
December 13, 2016: British Journal of Mathematical and Statistical Psychology
Tom Loeys, Wouter Talloen, Liesbet Goubert, Beatrijs Moerkerke, Stijn Vansteelandt
It is well known from the mediation analysis literature that the identification of direct and indirect effects relies on strong no unmeasured confounding assumptions of no unmeasured confounding. Even in randomized studies the mediator may still be correlated with unobserved prognostic variables that affect the outcome, in which case the mediator's role in the causal process may not be inferred without bias. In the behavioural and social science literature very little attention has been given so far to the causal assumptions required for moderated mediation analysis...
November 2016: British Journal of Mathematical and Statistical Psychology
Ying Cheng, Haiyan Liu
The aim of this paper is to derive the maximal point-biserial correlation under non-normality. Several widely used non-normal distributions are considered, namely the uniform distribution, t-distribution, exponential distribution, and a mixture of two normal distributions. Results show that the maximal point-biserial correlation, depending on the non-normal continuous variable underlying the binary manifest variable, may not be a function of p (the probability that the dichotomous variable takes the value 1), can be symmetric or non-symmetric around p = ...
November 2016: British Journal of Mathematical and Statistical Psychology
Jason D Rights, Sonya K Sterba
Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions...
November 2016: British Journal of Mathematical and Statistical Psychology
Gongjun Xu, Chun Wang, Zhuoran Shang
There has recently been much interest in computerized adaptive testing (CAT) for cognitive diagnosis. While there exist various item selection criteria and different asymptotically optimal designs, these are mostly constructed based on the asymptotic theory assuming the test length goes to infinity. In practice, with limited test lengths, the desired asymptotic optimality may not always apply, and there are few studies in the literature concerning the optimal design of finite items. Related questions, such as how many items we need in order to be able to identify the attribute pattern of an examinee and what types of initial items provide the optimal classification results, are still open...
November 2016: 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...
September 12, 2016: British Journal of Mathematical and Statistical Psychology
Mark Hansen, Li Cai, Scott Monroe, Zhen Li
Despite the growing popularity of diagnostic classification models (e.g., Rupp et al., 2010, Diagnostic measurement: theory, methods, and applications, Guilford Press, New York, NY) in educational and psychological measurement, methods for testing their absolute goodness of fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics such as Pearson's X(2) and the likelihood ratio statistic G(2) suffer from sparseness in the underlying contingency table from which they are computed...
July 12, 2016: British Journal of Mathematical and Statistical Psychology
Sharon X Lin, Leanne Morrison, Peter W F Smith, Charlie Hargood, Mark Weal, Lucy Yardley
N-of-1 study designs involve the collection and analysis of repeated measures data from an individual not using an intervention and using an intervention. This study explores the use of semi-parametric and parametric bootstrap tests in the analysis of N-of-1 studies under a single time series framework in the presence of autocorrelation. When the Type I error rates of bootstrap tests are compared to Wald tests, our results show that the bootstrap tests have more desirable properties. We compare the results for normally distributed errors with those for contaminated normally distributed errors and find that, except when there is relatively large autocorrelation, there is little difference between the power of the parametric and semi-parametric bootstrap tests...
June 24, 2016: British Journal of Mathematical and Statistical Psychology
Wenchao Ma, Jimmy de la Torre
This paper proposes a general polytomous cognitive diagnosis model for a special type of graded responses, where item categories are attained in a sequential manner, and associated with some attributes explicitly. To relate categories to attributes, a category-level Q-matrix is used. When the attribute and category association is specified a priori, the proposed model has the flexibility to allow different cognitive processes (e.g., conjunctive, disjunctive) to be modelled at different categories within a single item...
June 18, 2016: British Journal of Mathematical and Statistical Psychology
Sandip Sinharay
Snijders (2001, Psychometrika, 66, 331) suggested a statistical adjustment to obtain the asymptotically correct standardized versions of a specific class of person-fit statistics. His adjustment has been used to obtain the asymptotically correct standardized versions of several person-fit statistics including the lz statistic (Drasgow et al., 1985, Br. J. Math. Stat. Psychol., 38, 67), the infit and outfit statistics (e.g., Wright & Masters, 1982, Rating scale analysis, Chicago, IL: Mesa Press), and the standardized extended caution indices (Tatsuoka, 1984, Psychometrika, 49, 95)...
May 2016: British Journal of Mathematical and Statistical Psychology
Michael J Brusco, Hans-Friedrich Köhn, Douglas Steinley
The maximum cardinality subset selection problem requires finding the largest possible subset from a set of objects, such that one or more conditions are satisfied. An important extension of this problem is to extract multiple subsets, where the addition of one more object to a larger subset would always be preferred to increases in the size of one or more smaller subsets. We refer to this as the multiple subset maximum cardinality selection problem (MSMCSP). A recently published branch-and-bound algorithm solves the MSMCSP as a partitioning problem...
May 2016: British Journal of Mathematical and Statistical Psychology
Robert A Cribbie, Chantal Ragoonanan, Alyssa Counsell
Researchers often want to demonstrate a lack of interaction between two categorical predictors on an outcome. To justify a lack of interaction, researchers typically accept the null hypothesis of no interaction from a conventional analysis of variance (ANOVA). This method is inappropriate as failure to reject the null hypothesis does not provide statistical evidence to support a lack of interaction. This study proposes a bootstrap-based intersection-union test for negligible interaction that provides coherent decisions between the omnibus test and post hoc interaction contrast tests and is robust to violations of the normality and variance homogeneity assumptions...
May 2016: British Journal of Mathematical and Statistical Psychology
Sangbeak Ye, Georgios Fellouris, Steven Culpepper, Jeff Douglas
In order to look more closely at the many particular skills examinees utilize to answer items, cognitive diagnosis models have received much attention, and perhaps are preferable to item response models that ordinarily involve just one or a few broadly defined skills, when the objective is to hasten learning. If these fine-grained skills can be identified, a sharpened focus on learning and remediation can be achieved. The focus here is on how to detect when learning has taken place for a particular attribute and efficiently guide a student through a sequence of items to ultimately attain mastery of all attributes while administering as few items as possible...
May 2016: British Journal of Mathematical and Statistical Psychology
Jochen Ranger, Jörg-Tobias Kuhn, Carsten Szardenings
Psychological tests are usually analysed with item response models. Recently, some alternative measurement models have been proposed that were derived from cognitive process models developed in experimental psychology. These models consider the responses but also the response times of the test takers. Two such models are the Q-diffusion model and the D-diffusion model. Both models can be calibrated with the diffIRT package of the R statistical environment via marginal maximum likelihood (MML) estimation. In this manuscript, an alternative approach to model calibration is proposed...
May 2016: British Journal of Mathematical and Statistical Psychology
Iris A M Smits, Marieke E Timmerman, Alwin Stegeman
Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew-normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew-normal factor are equivalent to those under a quadratic model up to third-order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew-normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general...
May 2016: British Journal of Mathematical and Statistical Psychology
Rand R Wilcox
Let r1 and r2 be two dependent estimates of Pearson's correlation. There is a substantial literature on testing H0  : ρ1  = ρ2 , the hypothesis that the population correlation coefficients are equal. However, it is well known that Pearson's correlation is not robust. Even a single outlier can have a substantial impact on Pearson's correlation, resulting in a misleading understanding about the strength of the association among the bulk of the points. A way of mitigating this concern is to use a correlation coefficient that guards against outliers, many of which have been proposed...
April 26, 2016: British Journal of Mathematical and Statistical Psychology
Alwin Stegeman, Tam T T Lam
We consider multi-set data consisting of Nk observations, k = 1,…, K (e.g., subject scores), on J variables in K different samples. We introduce a factor model for the J × J covariance matrices Σk, k = 1,…, K, where the common part is modelled by Parafac2 and the unique variances Uk, k = 1,…, K, are diagonal. The Parafac2 model implies a common loadings matrix that is rescaled for each k, and a common factor correlation matrix. We estimate the unique variances Uk by minimum rank factor analysis on Σk for each k...
November 3, 2015: British Journal of Mathematical and Statistical Psychology
Kathleen Scalise, Diane D Allen
No abstract text is available yet for this article.
November 2015: British Journal of Mathematical and Statistical Psychology
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