British Journal of Mathematical and Statistical Psychology

Shi, Yuying; Leite, Walter; Algina, James

doi: 10.1348/000711008X398968pmid: 19243680

Cross‐classified random effects modelling (CCREM) is a special case of multi‐level modelling where the units of one level are nested within two cross‐classified factors. Typically, CCREM analyses omit the random interaction effect of the cross‐classified factors. We investigate the impact of the omission of the interaction effect on parameter estimates and standard errors. Results from a Monte Carlo simulation study indicate that, for fixed effects, both coefficients estimates and accompanied standard error estimates are not biased. For random effects, results are affected at level 2 but not at level 1 by the presence of an interaction variance and/or a correlation between the residual of level two factors. Results from the analysis of the Early Childhood Longitudinal Study and the National Educational Longitudinal Study agree with those obtained from simulated data. We recommend that researchers attempt to include interaction effects of cross‐classified factors in their models.

Poon, Wai‐Yin; Wang, Hai‐Bin

doi: 10.1348/000711008X401314pmid: 19364445

We develop a method for the analysis of multivariate ordinal categorical data with misclassification based on the latent normal variable approach. Misclassification arises if a subject has been classified into a category that does not truly reflect its actual state, and can occur with one or more variables. A basic framework is developed to enable the analysis of two types of data. The first corresponds to a single sample that is obtained from a fallible design that may lead to misclassified data. The other corresponds to data that is obtained by double sampling. Double sampling data consists of two parts: a sample that is obtained by classifying subjects using the fallible design only and a sample that is obtained by classifying subjects using both fallible and true designs, which is assumed to have no misclassification. A unified expectation–maximization approach is developed to find the maximum likelihood estimate of model parameters. Simulation studies and examples that are based on real data are used to demonstrate the applicability and practicability of the proposed methods.

Tunney, Richard J.

doi: 10.1348/000711009X416416pmid: 19341516

Two experiments examined the nature of recognition memory by asking how subjective reports of remembering change over time. In Experiment 1, participants were asked to report their experience of remembering using the well‐known remember–know–guess procedure. Estimates of recollection declined over a 14‐day period, but estimates of familiarity remained constant, suggesting that the processes are independent. In Experiment 2, participants were asked to report their confidence in their recognition decisions. Subjective reports of confidence were analysed via receiver operating characteristics and also indicated different rates of decline for recollection and familiarity. Superficially, the data appear to support a dual‐process account of recognition, but close inspection shows the data to be consistent with a simple signal detection model. The conclusion is that although the phenomenal experience of remembering changes over time this is most likely to be predicated on a single process.

Kowalchuk, Rhonda K.; Headrick, Todd C.

doi: 10.1348/000711009X423067pmid: 19358745

The Tukey family of g‐and‐h distributions is often used to model univariate real‐world data. There is a paucity of research demonstrating appropriate multivariate data generation using the g‐and‐h family of distributions with specified correlations. Therefore, the methodology and algorithms are presented to extend the g‐and‐h family from univariate to multivariate data generation. An example is provided along with a Monte Carlo simulation demonstrating the methodology. In addition, algorithms written in Mathematica 7.0 are available from the authors for implementing the procedure.

García‐Pérez, Miguel A.

doi: 10.1348/000711009X424057pmid: 19422731

Observers in a two‐alternative forced‐choice (2AFC) detection task face the need to produce a response at random (a guess) on trials in which neither presentation appeared to display a stimulus. Observers could alternatively be instructed to use a ‘guess’ key on those trials, a key that would produce a random guess and would also record the resultant correct or wrong response as emanating from a computer‐generated guess. A simulation study shows that ‘denoising’ 2AFC data with information regarding which responses are a result of guesses yields estimates of detection threshold and spread of the psychometric function that are far more precise than those obtained in the absence of this information, and parallel the precision of estimates obtained with yes–no tasks running for the same number of trials. Simulations also show that partial compliance with the instructions to use the ‘guess’ key reduces the quality of the estimates, which nevertheless continue to be more precise than those obtained from conventional 2AFC data if the observers are still moderately compliant. An empirical study testing the validity of simulation results showed that denoised 2AFC estimates of spread were clearly superior to conventional 2AFC estimates and similar to yes–no estimates, but variations in threshold across observers and across sessions hid the benefits of denoising for threshold estimation. The empirical study also proved the feasibility of using a ‘guess’ key in addition to the conventional response keys defined in 2AFC tasks.

Christensen, Karl Bang; Kreiner, Svend

doi: 10.1348/000711009X424200pmid: 19341515

For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non‐parametric item response theory a natural starting‐point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using p‐values computed using Markov chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.

Boik, Robert J.; Panishkan, Kamolchanok; Hyde, Scott K.

doi: 10.1348/000711009X428189pmid: 19534846

A flexible class of models is proposed for principal component (PCs) of covariance matrices. The models allow constraints to be imposed on the eigenvalues and/or the eigenvectors and yield simplified PCs that retain their variance maximization and orthogonality properties. The models are fitted to sample covariance matrices by minimizing a discrepancy function. Asymptotic distributions of estimators are obtained under the assumption that fourth‐order moments of the parent distribution are finite. Hypothesis tests are obtained by comparing discrepancy functions that are minimized under different constraints. An Edgeworth expansion is used to obtain second‐order accurate confidence intervals for differentiable eigenfunctions. The techniques are illustrated on a real data set.

Solanas, Antonio; Leiva, David; Salafranca, Lluís

doi: 10.1348/000711009X426253pmid: 19486549

The directional consistency and skew‐symmetry statistics have been proposed as global measure of social reciprocity. Although both measures can be useful for quantifying social reciprocity, researchers need to know whether these estimators are biased in order properly to assess descriptive results. That is, if estimators are biased, researchers should compare actual values with expected values under the specified null hypothesis. Furthermore, standard errors are needed to enable suitable assessment of discrepancies between actual and expected values. This paper aims to derive some exact and approximate expressions in order to obtain bias and standard error values for both estimators for round‐robin designs, although the results can also be extended to other reciprocal designs.

Penev, Spiridon; Raykov, Tenko

doi: 10.1348/000711009X429494pmid: 19397846

This paper is concerned with the reliability of weighted combinations of a given set of dichotomous measures. Maximal reliability for such measures has been discussed in the past, but the pertinent estimator exhibits a considerable bias and mean squared error for moderate sample sizes. We examine this bias, propose a procedure for bias correction, and develop a more accurate asymptotic confidence interval for the resulting estimator. In most empirically relevant cases, the bias correction and mean squared error correction can be performed simultaneously. We propose an approximate (asymptotic) confidence interval for the maximal reliability coefficient, discuss the implementation of this estimator, and investigate the mean squared error of the associated asymptotic approximation. We illustrate the proposed methods using a numerical example.

Long, Jeffrey; Ryoo, Jihoon

doi: 10.1348/000711009X431509pmid: 19486548

Non‐linear growth curves are discussed within the context of the linear mixed model. Non‐linearity is modelled with time transformations known as fractional polynomials (FPs) having power terms that can be negative values and fractions with conventional polynomials (CPs) as a special case. Issues of interpretation are discussed with a focus on the instantaneous rate of change in models with and without static correlates. Methods for model selection are presented with emphasis on penalized and non‐penalized indices of global fit based on the maximized likelihood and fitted models. Two empirical examples are presented with psychological data in which FPs were fitted along with CPs of equal and next highest order. The results show that the FPs had equal or better fit than the higher‐order CPs and had prediction curves with as favourable or more favourable characteristics, such as less extreme behaviour at the edges of the observed time intervals. The results illustrate some of the potential advantages of FPs relative to CPs, which include parsimony, flexibility of curve shape, and the ability to approximate asymptotes. Though FPs are not necessarily suggested as replacements for CPs or other transformations (e.g. piecewise models), they might be useful when the goal is to model non‐linear growth trends with smooth curves.