I address two issues that were inspired by my work on the Dutch Committee on Tests and Testing (COTAN). The first issue is the understanding of problems test constructors and researchers using tests have of psychometric knowledge. I argue that this understanding is important for a field, like psychometrics, for which the dissemination of psychometric knowledge among test constructors and researchers in general is highly important. The second issue concerns the identification of psychometric research topics that are relevant for test constructors and test users but in my view do not receive enough attention in psychometrics. I discuss the influence of test length on decision quality in personnel selection and quality of difference scores in therapy assessment, and theory development in test construction and validity research. I also briefly mention the issue of whether particular attributes are continuous or discrete.

The issue of compensation in multidimensional response modeling is addressed. We show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone. In addition, a minimal set of assumptions is presented under which the MLEs of the ability parameters are also compensatory. In a recent series of articles, beginning with Hooker, Finkelman, and Schwartzman (2009) in this journal, the second type of compensation was presented as a paradoxical result for certain multidimensional response models, leading to occasional unfairness in maximum-likelihood test scoring. First, it is indicated that the compensation is not unique and holds generally for any multiparameter likelihood with monotone score functions. Second, we analyze why, in spite of its generality, the compensation may give the impression of a paradox or unfairness.

Latent trait models for response times in tests have become popular recently. One challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests. In order to reduce the need for tailor-made models, a model is proposed that unifies two popular approaches to response time modeling: Proportional hazard models and the accelerated failure time model with log–normally distributed response times. This is accomplished by resorting to discrete time. The categorization of response time allows the formulation of a response time model within the framework of generalized linear models by using a flexible link function. Item parameters of the proposed model can be estimated with marginal maximum likelihood estimation. Applicability of the proposed approach is demonstrated with a simulation study and an empirical application. Additionally, means for the evaluation of model fit are suggested.

Starting with Kenny and Judd (Psychol. Bull. 96:201–210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to adding just a selection of the third-order moments. The key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third-order moments in assessing interaction terms of the model. To select the third-order moments, we propose to be guided by the power of the goodness-of-fit test of a model with no interactions, which varies with each selection of third-order moments. A theorem is presented that relates the power of the usual goodness-of-fit test of the model with the power of a moment test for the significance of third-order moments; the latter has the advantage that it can be computed without fitting a model. The main conclusion is that the selection of third-order moments can be based on the power of a moment test, thus assessing the relevance in the analysis of different sets of third-order moments can be computationally simple. The paper gives an illustration of the method and argues for the need of refraining from adding into the analysis an excess of higher-order moments.

We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the method solves a matrix eigen-analysis problem through the adoption of a basis expansion approach to approximating data and weight functions. We apply the proposed method to functional magnetic resonance imaging (fMRI) data to identify networks of neural activity that are commonly activated across subjects while carrying out a working memory task.

In many psychological research domains stimulus-response profiles are explained by conjecturing a sequential process in which some variables mediate between stimuli and responses. Charting sequential processes is often a complex task because (1) many possible mediating variables may exist, and (2) interindividual differences may occur in the relationship between these mediating variables and the response. Recently, Ceulemans and Van Mechelen (Psychometrika 73(1):107–124, 2008) addressed these challenges by developing the CLASSI model. A major drawback of CLASSI is that it requires information about the same set of stimuli for all participants (i.e., crossed data), whereas recently a number of data gathering techniques have been proposed in which the set of stimuli differs across participants, yielding nested data. Therefore we present the CLASSI-N model, which extends the CLASSI model to nested data. A simulated annealing algorithm is proposed. The results of a simulation study are discussed as well as an application to data concerning depression.

Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and sensitivities arising from different studies might vary just because the underlying cut-off value had been different. To cope with the cut-off value problem interest is usually directed towards the receiver operating characteristic (ROC) curve which consists of pairs of sensitivities and false-positive rates (1-specificity). In the context of meta-analysis one pair represents one study and the associated diagram is called an SROC curve where the S stands for “summary”. In meta-analysis of diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC curve. Here, we focus instead on finding sub-groups or components in the data representing different diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which is characterised by one parameter only. Each single study can be represented by a specific value of that parameter. Hence we focus on the distribution of these parameter estimates and suggest modelling a potential heterogeneous or cluster structure by a mixture of specifically parameterised normal densities. We point out that this mixture is completely nonparametric and the associated mixture likelihood is well-defined and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies to be analysed. Several meta-analytic applications on diagnostic studies, including AUDIT and AUDIT-C for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders, as well as diagnostic accuracy inspection data on metal fatigue of aircraft spare parts, are discussed to illustrate the methodology.

Maximum likelihood and Bayesian ability estimation in multidimensional item response models can lead to paradoxical results as proven by Hooker, Finkelman, and Schwartzman (Psychometrika 74(3): 419–442, 2009): Changing a correct response on one item into an incorrect response may produce a higher ability estimate in one dimension. Furthermore, the conditions under which this paradox arises are very general, and may in fact be fulfilled by many of the multidimensional scales currently in use. This paper tries to emphasize and extend the generality of the results of Hooker et al. by (1) considering the paradox in a generalized class of IRT models, (2) giving a weaker sufficient condition for the occurrence of the paradox with relations to an important concept of statistical association, and by (3) providing some additional specific results for linearly compensatory models with special emphasis on the factor analysis model.

Assuming item parameters on a test are known constants, the reliability coefficient for item response theory (IRT) ability estimates is defined for a population of examinees in two different ways: as (a) the product-moment correlation between ability estimates on two parallel forms of a test and (b) the squared correlation between the true abilities and estimates. Due to the bias of IRT ability estimates, the parallel-forms reliability coefficient is not generally equal to the squared-correlation reliability coefficient. It is shown algebraically that the parallel-forms reliability coefficient is expected to be greater than the squared-correlation reliability coefficient, but the difference would be negligible in a practical sense.

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys’ prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under the three-parameter logistic model, the JM estimator returns larger estimates than the WL estimator. Several implications of this result are outlined.