Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.     

Incommensurability,incomparability, and God’s choice of a world

Anselmian theism holds that there necessarily exists a being, God, who is essentially unsurpassable in power, knowledge, goodness, and wisdom. This being is also understood to be the creator and sustainer of all that is. In contemporary analytic philosophy of religion, this role is generally understood as follows: God surveys the array of possible worlds, and in his wisdom selects exactly one for actualization, based on its axiological properties. In this paper, I discuss an under-appreciated challenge for this account of the Anselmian God’s selection of a world. In particular, I urge that there are failures of comparability between various possible worlds, and I argue that, given certain assumptions, these failures threaten the rationality of God’s choice of a world. To the extent that rationality is deemed necessary for unsurpassability, this result also challenges the core Anselmian notion that God is an unsurpassable being.     

Invariant Ordering of Item-Total Regressions

A new observable consequence of the property of invariant item ordering is presented, which holds under Mokken’s double monotonicity model for dichotomous data. The observable consequence is an invariant ordering of the item-total regressions. Kendall’s measure of concordance W and a weighted version of this measure are proposed as measures for this property. Karabatsos and Sheu proposed a Bayesian procedure (Appl. Psychol. Meas. 28:110–125, 2004), which can be used to determine whether the property of an invariant ordering of the item-total regressions should be rejected for a set of items. An example is presented to illustrate the application of the procedures to empirical data.     

A tutorial on how to do a Mokken scale analysis on your test and questionnaire data

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. Second, we discuss dos and don'ts for MSA; the don'ts include misunderstandings we have frequently encountered with researchers in our three decades of experience with real‐data MSA. Third, we discuss a methodology for MSA on real data that consist of a sample of persons who have provided scores on a set of items that, depending on the composition of the item set, constitute the basis for one or more scales, and we use the methodology to analyse an example real‐data set.     

Detection and validation of unscalable item score patterns using item response theory: an illustration with Harter's Self-Perception Profile for Children

We illustrate the usefulness of person-fit methodology for personality assessment. For this purpose, we use person-fit methods from item response theory. First, we give a nontechnical introduction to existing person-fit statistics. Second, we analyze data from Harter's (1985) Self-Perception Profile for Children (Harter, 1985) in a sample of children ranging from 8 to 12 years of age (N = 611) and argue that for some children, the scale scores should be interpreted with care and caution. Combined information from person-fit indexes and from observation, interviews, and self-concept theory showed that similar score profiles may have a different interpretation. For some children in the sample, item scores did not adequately reflect their trait level. Based on teacher interviews, this was found to be due most likely to a less developed self-concept and/or problems understanding the meaning of the questions. We recommend investigating the scalability of score patterns when using self-report inventories to help the researcher interpret respondents' behavior correctly.     

Reliability Beyond Theory and Into Practice

The critical reactions of Bentler (2009, doi:), Green and Yang (2009a, doi:; 2009b, doi:), and Revelle and Zinbarg (2009, doi:) to Sijtsma’s (2009, doi:) paper on Cronbach’s alpha are addressed. The dissemination of psychometric knowledge among substantive researchers is discussed.     

A direct solution for pairwise rotations in Kaiser's varimax method

The present note contains a completing-the-squares type approach to the varimax rotation problem. This approach yields a direct proof of global optimality of a solution for optimal rotation in a plane. Because varimax rotation can be interpreted as diagonalization of a set of symmetric matrices, the present solution also applies to the diagonalization problem.The author is obliged to Jos M. F. ten Berge for helpful comments.     

On meredith's solution for weighted procrustes rotation

Meredith developed a criterion for weighted procrustes rotation. The solution was given using Lagrange multipliers. We show that the solution can be obtained more simply, and that our approach enables us to transform the orthogonalization problem, also considered by Meredith, to that of minimizing a quadratic form on the unit sphere.     

The effectiveness of family-based cognitive-behavior grief therapy to prevent complicated grief in relatives of suicide victims: the mediating role of suicide ideation

Grief interventions are more effective for high risk individuals. The presence of suicide ideation following suicide bereavement was examined to determine whether it indicates a high risk status. Using data from a randomized controlled trial (n = 122) on the effectiveness of cognitive-behavior therapy, the effect of suicide ideation on the effectiveness of grief therapy on the bereavement outcome at 13 months post loss was examined. Results show that suicide ideators more often have a history of mental disorder and suicidal behavior than non-ideators, and suicide ideation indicates a high risk for adverse bereavement outcome. Grief therapy likely reduces the risk of maladaptive grief reactions among suicide ideators. Therefore, suicide ideators may benefit from grief therapy following a loss through suicide.