Extending the Basic Local Independence Model to Polytomous Data

Psychometrika - A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model,...     

On the empirical indistinguishability of knowledge structures

In recent years a number of articles have focused on the identifiability of the basic local independence model. The identifiability issue usually concerns two model parameter sets predicting an identical probability distribution on the response patterns. Both parameter sets are applied to the same knowledge structure. However, nothing is known about cases where different knowledge structures predict the same probability distribution. This situation is referred to as ʻempirical indistinguishabilityʼ between two structures and is the main subject of the present paper. Empirical indistinguishability is a stronger form of unidentifiability, which involves not only the parameters, but also the structural and combinatorial properties of the model. In particular, as far as knowledge structures are concerned, a consequence of empirical indistinguishability is that the existence of certain knowledge states cannot be empirically established. Most importantly, it is shown that model identifiability cannot guarantee that a certain knowledge structure is empirically distinguishable from others. The theoretical findings are exemplified in a number of different empirical scenarios.     

An iterative procedure for extracting skill maps from data

The methodologies for the construction of a knowledge structure mainly refer to the query to experts, the skill maps, and the data-driven approaches. This last method is of growing interest in recent literature. In this paper, an iterative procedure for building a skill map from a set of data is introduced. This procedure is based on the minimization of the distance between the knowledge structure delineated by a given skill map and the data. The accuracy of the proposed method is tested through a number of simulation studies where the amount of noise in the data is manipulated as well as the kind of structure to be reconstructed. Results show that the procedure is accurate and that its performance tends to be sufficiently stable even with high error rates. The procedure is compared to two already-existing methodologies to derive knowledge structures from a set of data. The use of the corrected Akaike Information Criterion (AICc) as a stopping criterion of the iterative reconstruction procedure is tested against the app criterion introduced by Schrepp. Moreover, two empirical applications on clinical data are reported, and their results show the applicability of the procedure.     

A class of k-modes algorithms for extracting knowledge structures from data

One of the most crucial issues in knowledge space theory is the construction of the so-called knowledge structures. In the present paper, a new data-driven procedure for large data sets is described, which overcomes some of the drawbacks of the already existing methods. The procedure, called k-states, is an incremental extension of the k-modes algorithm, which generates a sequence of locally optimal knowledge structures of increasing size, among which a “best” model is selected. The performance of k-states is compared to other two procedures in both a simulation study and an empirical application. In the former, k-states displays a better accuracy in reconstructing knowledge structures; in the latter, the structure extracted by k-states obtained a better fit.     

Experiencing whole type: living into the archetypal Self

Expanding on Jung’s use of the role of the superior and inferior functions, Angelo Spoto advances a new typological model based on ‘whole type’ that utilizes a typological perspective on the archetypal Self. In this new model four cognitive modes taking superior positions are developed in the first half of life and four cognitive modes taking inferior positions are encountered in the second half of life. This model indicates that type development and type dynamics take place through the holding of the tension of opposites between superior and inferior functions, helped by the transcendent function operating differently in the first and second halves of life. Specifically, in the first half of life, the transcendent function produces a tertium that moves typological development along to consolidate an ego-pattern. In the second half of life, the transcendent function takes the individual into encounters having to do with an appreciation of sacrifice, transformation, and symbol-making, as the personality advances towards a greater awareness of wholeness, by way of the inferiors.     

Beyond the Score: Clinical Evaluation Through Formal Psychological Assessment

Questionnaires generate numerical scores, but endorsing different sets of items could produce the same score despite reflecting qualitatively different configurations of clinical features. Formal psychological assessment (FPA) attempts to overcome this by identifying the clinical features entailed by observed response patterns. This study illustrates an application of FPA to the cleaning subscale of a questionnaire assessing obsessive–compulsive symptoms and DSM–IV–TR diagnostic criteria for obsessive–compulsive disorder. A deterministic model of the items–criteria relationships was constructed by mapping each item to each diagnostic criterion. The resulting model was tested on a large community sample (N = 4,412). Results indicate that the theoretical model has adequate fit; item error rates and probabilities for each of the criteria are examined. Clinically relevant examples of the items–criteria relationships are discussed. Possible applications of FPA to personality assessment are also discussed, including long multidimensional questionnaires and questionnaires that use subtle item content.     

On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures

In the process of fitting a probabilistic knowledge structure to data, standard goodness-of-fit statistics only partially describe the correctness of the fitted model. Irrespectively of how good the fit is, a too-high value of the error rates (careless error and lucky guess probabilities) might be a symptom of a misspecification of the model. In this situation, it could be critical to interpret those values as error rates. A more reasonable solution would be to hypothesize that some modifications have to be introduced in the model. In this paper, we show that in specific cases, these modifications yield basic local independence model parameterizations that are not identifiable. The applicative consequences of the theoretical results are displayed by means of an example carried out on a set of clinical data collected through the Maudsley Obsessional-Compulsive Questionnaire.     

Knowledge space theory, formal concept analysis, and computerized psychological assessment

In the present study, the use of knowledge space theory (KST), jointly with formal concept analysis (FCA), is proposed for developing a formal representation of the relations between the items of a questionnaire and a set of psychodiagnostic criteria. This formal representation can be used to develop an efficient adaptive tool for psychological assessment. Rusch and Wille (1996) have shown some interesting connections between KST and FCA; these connections are applied in the construction of knowledge structures, starting from a formal context representing the relations between items and criteria. The proposed general methodology was applied, as an example, to the Maudsley Obsessional-Compulsive Questionnaire. We used a data set provided by a sample of patients with a diagnosis of obsessive-compulsive disorder to validate the obtained structures. The parameters of the basic local independence model (BLIM) were estimated for the obtained knowledge structures. The fit of each model was tested by parametric bootstrap because of the sparseness of the derived data matrix. The results are discussed in light of both psychological and methodological relapses. In particular, we propose a reinterpretation of the BLIM parameters that seems suitable for testing reliability and construct validity; furthermore, it is pointed out how the obtained structures could represent the starting point for the development of a computerized assessment tool.     

On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory

Psychometrika - Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is...