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British Journal of Mathematical and Statistical Psychology

Herbert Hoijtink, Xin Gu, Joris Mulder
The software package Bain can be used for the evaluation of informative hypotheses with respect to the parameters of a wide range of statistical models. For pairs of hypotheses the support in the data is quantified using the approximate adjusted fractional Bayes factor (BF). Currently, the data have to come from one population or have to consist of samples of equal size obtained from multiple populations. If samples of unequal size are obtained from multiple populations, the BF can be shown to be inconsistent...
October 21, 2018: British Journal of Mathematical and Statistical Psychology
Marie-Ann Sengewald, Peter M Steiner, Steffi Pohl
The average causal treatment effect (ATE) can be estimated from observational data based on covariate adjustment. Even if all confounding covariates are observed, they might not necessarily be reliably measured and may fail to obtain an unbiased ATE estimate. Instead of fallible covariates, the respective latent covariates can be used for covariate adjustment. But is it always necessary to use latent covariates? How well do analysis of covariance (ANCOVA) or propensity score (PS) methods estimate the ATE when latent covariates are used? We first analytically delineate the conditions under which latent instead of fallible covariates are necessary to obtain the ATE...
October 21, 2018: British Journal of Mathematical and Statistical Psychology
Xueying Tang, Yunxiao Chen, Xiaoou Li, Jingchen Liu, Zhiliang Ying
Personalized learning refers to instruction in which the pace of learning and the instructional approach are optimized for the needs of each learner. With the latest advances in information technology and data science, personalized learning is becoming possible for anyone with a personal computer, supported by a data-driven recommendation system that automatically schedules the learning sequence. The engine of such a recommendation system is a recommendation strategy that, based on data from other learners and the performance of the current learner, recommends suitable learning materials to optimize certain learning outcomes...
September 12, 2018: British Journal of Mathematical and Statistical Psychology
Ken A Fujimoto
Many item response theory (IRT) models take a multidimensional perspective to deal with sources that induce local item dependence (LID), with these models often making an orthogonal assumption about the dimensional structure of the data. One reason for this assumption is because of the indeterminacy issue in estimating the correlations among the dimensions in structures often specified to deal with sources of LID (e.g., bifactor and two-tier structures), and the assumption usually goes untested. Unfortunately, the mere fact that assessing these correlations is a challenge for some estimation methods does not mean that data seen in practice support such orthogonal structure...
November 2018: British Journal of Mathematical and Statistical Psychology
Hyeon-Ah Kang, Ya-Hui Su, Hua-Hua Chang
A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models...
November 2018: British Journal of Mathematical and Statistical Psychology
Po-Hsien Huang
In the past two decades, statistical modelling with sparsity has become an active research topic in the fields of statistics and machine learning. Recently, Huang, Chen and Weng (2017, Psychometrika, 82, 329) and Jacobucci, Grimm, and McArdle (2016, Structural Equation Modeling: A Multidisciplinary Journal, 23, 555) both proposed sparse estimation methods for structural equation modelling (SEM). These methods, however, are restricted to performing single-group analysis. The aim of the present work is to establish a penalized likelihood (PL) method for multi-group SEM...
November 2018: British Journal of Mathematical and Statistical Psychology
Fien Gistelinck, Tom Loeys, Mieke Decuyper, Marieke Dewitte
When considering dyadic data, one of the questions is whether the roles of the two dyad members can be considered equal. This question may be answered empirically using indistinguishability tests in the actor-partner interdependence model. In this paper several issues related to such indistinguishability tests are discussed: the difference between maximum likelihood and restricted maximum likelihood based tests for equality in variance parameters; the choice between the structural equation modelling and multilevel modelling framework; and the use of sequential testing rather than one global test for a set of indistinguishability tests...
November 2018: British Journal of Mathematical and Statistical Psychology
Oscar L Olvera Astivia, Bruno D Zumbo
The Fleishman third-order polynomial algorithm is one of the most-often used non-normal data-generating methods in Monte Carlo simulations. At the crux of the Fleishman method is the solution of a non-linear system of equations needed to obtain the constants to transform data from normality to non-normality. A rarely acknowledged fact in the literature is that the solution to this system is not unique, and it is currently unknown what influence the different types of solutions have on the computer-generated data...
November 2018: British Journal of Mathematical and Statistical Psychology
R Philip Chalmers
An efficient and accurate numerical approximation methodology useful for obtaining the observed information matrix and subsequent asymptotic covariance matrix when fitting models with the EM algorithm is presented. The numerical approximation approach is compared to existing algorithms intended for the same purpose, and the computational benefits and accuracy of this new approach are highlighted. Instructive and real-world examples are included to demonstrate the methodology concretely, properties of the estimator are discussed in detail, and a Monte Carlo simulation study is included to investigate the behaviour of a multi-parameter item response theory model using three competing finite-difference algorithms...
November 2018: British Journal of Mathematical and Statistical Psychology
Jenő Reiczigel, Márton Ispány, Gábor Tusnády, György Michaletzky, Marco Marozzi
Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the lowest proportion of 'contamination' which, if removed from the population or from the sample, makes the fit of the model perfect. The mixture index of fit has been widely used in psychometric studies. We show that the asymptotic confidence limits proposed by Rudas et al. (1994, J. R Stat Soc. Ser. B, 56, 623) as well as the jackknife confidence interval by Dayton (, Br...
November 2018: British Journal of Mathematical and Statistical Psychology
Jochen Ranger, Anett Wolgast, Jörg-Tobias Kuhn
Van der Linden's (2007, Psychometrika, 72, 287) hierarchical model for responses and response times in tests has numerous applications in psychological assessment. The success of these applications requires the parameters of the model to have been estimated without bias. The data used for model fitting, however, are often contaminated, for example, by rapid guesses or lapses of attention. This distorts the parameter estimates. In the present paper, a novel estimation approach is proposed that is robust against contamination...
July 27, 2018: British Journal of Mathematical and Statistical Psychology
Luca Stefanutti
By generalizing and completing the work initiated by Stefanutti and Albert (2003, Journal of Universal Computer Science, 9, 1455), this article provides the mathematical foundations of a theoretical approach whose primary goal is to construct a bridge between problem solving, as initially conceived by Newell and Simon (1972, Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.), and knowledge assessment (Doignon and Falmagne, 1985, International Journal of Man-Machine Studies, 23, 175; Doignon and Falmagne, 1999, Knowledge spaces...
July 23, 2018: British Journal of Mathematical and Statistical Psychology
Shaobo Jin, Chunzheng Cao
The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small-sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study...
May 2018: British Journal of Mathematical and Statistical Psychology
Sandip Sinharay
Tatsuoka suggested several extended caution indices and their standardized versions, and these have been used as person-fit statistics by various researchers. However, these indices are only defined for tests with dichotomous items. This paper extends two of the popular standardized extended caution indices for use with polytomous items and mixed-format tests. Two additional new person-fit statistics are obtained by applying the asymptotic standardization of person-fit statistics for mixed-format tests. Detailed simulations are then performed to compute the Type I error rate and power of the four new person-fit statistics...
May 2018: British Journal of Mathematical and Statistical Psychology
Douglas Steinley, Michael J Brusco
Two expectations of the adjusted Rand index (ARI) are compared. It is shown that the expectation derived by Morey and Agresti (1984, Educational and Psychological Measurement, 44, 33) under the multinomial distribution to approximate the exact expectation from the hypergeometric distribution (Hubert & Arabie, 1985, Journal of Classification, 2, 193) provides a poor approximation, and, in some cases, the difference between the two expectations can increase with the sample size. Proofs concerning the minimum and maximum difference between the two expectations are provided, and it is shown through simulation that the ARI can differ significantly depending on which expectation is used...
May 2018: British Journal of Mathematical and Statistical Psychology
Hao Wu
In structural equation modelling (SEM), a robust adjustment to the test statistic or to its reference distribution is needed when its null distribution deviates from a χ2 distribution, which usually arises when data do not follow a multivariate normal distribution. Unfortunately, existing studies on this issue typically focus on only a few methods and neglect the majority of alternative methods in statistics. Existing simulation studies typically consider only non-normal distributions of data that either satisfy asymptotic robustness or lead to an asymptotic scaled χ2 distribution...
May 2018: British Journal of Mathematical and Statistical Psychology
Shiyu Wang
The maximum likelihood classification rule is a standard method to classify examinee attribute profiles in cognitive diagnosis models (CDMs). Its asymptotic behaviour is well understood when the model is assumed to be correct, but has not been explored in the case of misspecified latent class models. This paper investigates the asymptotic behaviour of a two-stage maximum likelihood classifier under a misspecified CDM. The analysis is conducted in a general restricted latent class model framework addressing all types of CDMs...
May 2018: British Journal of Mathematical and Statistical Psychology
Dylan Molenaar, Maria Bolsinova, Jeroen K Vermunt
In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times...
May 2018: British Journal of Mathematical and Statistical Psychology
Peida Zhan, Hong Jiao, Dandan Liao
To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first...
May 2018: British Journal of Mathematical and Statistical Psychology
Xin Gu, Joris Mulder, Herbert Hoijtink
Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers' theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior...
May 2018: British Journal of Mathematical and Statistical Psychology
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