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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...
March 8, 2018: British Journal of Mathematical and Statistical Psychology
Yanlou Liu, Tao Xin, Björn Andersson, Wei Tian
Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J...
March 6, 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...
March 3, 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...
February 15, 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...
January 11, 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...
January 11, 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...
January 9, 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...
January 9, 2018: British Journal of Mathematical and Statistical Psychology
Nicolas Gauvrit, Fabien Mathy
The time-based resource sharing (TBRS) model is a prominent model of working memory that is both predictive and simple. TBRS is a mainstream decay-based model and the most susceptible to competition with interference-based models. A connectionist implementation of TBRS, TBRS*, has recently been developed. However, TBRS* is an enriched version of TBRS, making it difficult to test general characteristics resulting from TBRS assumptions. Here, we describe a novel model, TBRS2, built to be more transparent and simple than TBRS*...
February 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...
November 20, 2017: British Journal of Mathematical and Statistical Psychology
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No abstract text is available yet for this article.
November 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...
November 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...
November 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...
November 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...
November 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...
November 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...
November 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...
November 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 QB (P) and QB (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...
November 2017: British Journal of Mathematical and Statistical Psychology
Oscar L Olvera Astivia, Bruno D Zumbo
The purpose of this paper is to highlight the importance of a population model in guiding the design and interpretation of simulation studies used to investigate the Spearman rank correlation. The Spearman rank correlation has been known for over a hundred years to applied researchers and methodologists alike and is one of the most widely used non-parametric statistics. Still, certain misconceptions can be found, either explicitly or implicitly, in the published literature because a population definition for this statistic is rarely discussed within the social and behavioural sciences...
November 2017: British Journal of Mathematical and Statistical Psychology
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