This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course. The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative “validation” of the factor model, using auxiliary information about the popularity of items consulted during an open-book examination in the course.

In this paper, a theoretical index of dimensionality, called the theoretical DETECT index, is proposed to provide a theoretical foundation for the DETECT procedure. The purpose of DETECT is to assess certain aspects of the latent dimensional structure of a test, important to practitioner and research alike. Under reasonable modeling restrictions referred to as “approximate simple structure”, the theoretical DETECT index is proven to be maximized at the correct dimensionality-based partition of a test, where the number of item clusters in this partition corresponds to the number of substantively separate dimensions present in the test and by “correct” is meant that each cluster in this partition contains only items that correspond to the same separate dimension. It is argued that the separation into item clusters achieved by DETECT is appropriate from the applied perspective of desiring a partition into clusters that are interpretable as substantively distinct between clusters and substantively homogeneous within cluster. Moreover, the maximum DETECT index value is a measure of the amount of multidimensionality present. The estimation of the theoretical DETECT index is discussed and a genetic algorithm is developed to effectively execute DETECT. The study of DETECT is facilitated by the recasting of two factor analytic concepts in a multidimensional item response theory setting: a dimensionally homogeneous item cluster and an approximate simple structure test.

While negative local item dependence (LID) has been discussed in numerous articles, its occurrence and effects often go unrecognized. This is due in part to confusion over what unidimensional latent trait is being utilized in evaluating the LID of multidimensional testing data. This article addresses this confusion by using an appropriately chosen latent variable to condition on. It then provides a proof that negative LID must occur when unidimensional ability estimates (such as number right score) are obtained from data which follow a very general class of multidimensional item response theory models. The importance of specifying what unidimensional latent trait is used, and its effect on the sign of the LIDs are shown to have implications in regard to a variety of foundational theoretical arguments, to the simulation of LID data sets, and to the use of testlet scoring for removing LID.

Some nonparametric dimensionality assessment procedures, such as DIMTEST and DETECT, use nonparametric estimates of item pair conditional covariances given an appropriately chosen subtest score as their basic building blocks. Such conditional covariances given some subtest score can be regarded as an approximation to the conditional covariances given an appropriately chosen unidimensional latent composite, where the composite is oriented in the multidimensional test space direction in which the subtest score measures best. In this paper, the structure and properties of such item pair conditional covariances given a unidimensional latent composite are thoroughly investigated, assuming a semiparametric IRT modeling framework called a generalized compensatory model. It is shown that such conditional covariances are highly informative about the multidimensionality structure of a test. The theory developed here is very useful in establishing properties of dimensionality assessment procedures, current and yet to be developed, that are based upon estimating such conditional covariances.

In particular, the new theory is used to justify the DIMTEST procedure. Because of the importance of conditional covariance estimation, a new bias reducing approach is presented. A byproduct of likely independent importance beyond the study of conditional covariances is a rigorous score information based definition of an item's and a score's direction of best measurement in the multidimensional test space.

Observed-score equating using the marginal distributions of two tests is not necessarily the universally best approach it has been claimed to be. On the other hand, equating using the conditional distributions given the ability level of the examinee is theoretically ideal. Possible ways of dealing with the requirement of known ability are discussed, including such methods as conditional observed-score equating at point estimates or posterior expected conditional equating. The methods are generalized to the problem of observed-score equating with a multivariate ability structure underlying the scores.

Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh and Bolt in Psychometrika 75:454–473, 2010) and possess a mathematical structure that naturally lends itself to evaluating the incremental information provided by attending to distractor selection in scoring. One potential concern in attending to distractors is the possibility that distractor selection reflects a different trait/ability than that underlying the correct response. This paper illustrates a multidimensional extension of a nested logit item response model that can be used to evaluate such distinctions and also defines a new framework for incorporating collateral information from distractor selection when differences exist. The approach is demonstrated in application to questions faced by a university testing center over whether to incorporate distractor selection into the scoring of its multiple-choice tests. Several empirical examples are presented.

This paper extends the theory of conditional covariances to polytomous items. It has been proven that under some mild conditions, commonly assumed in the analysis of response data, the conditional covariance of two items, dichotomously or polytomously scored, given an appropriately chosen composite is positive if, and only if, the two items measure similar constructs besides the composite. The theory provides a theoretical foundation for dimensionality assessment procedures based on conditional covariances or correlations, such as DETECT and DIMTEST, so that the performance of these procedures is theoretically justified when applied to response data with polytomous items. Various estimators of conditional covariances are constructed, and special attention is paid to the case of complex sampling data, such as those from the National Assessment of Educational Progress (NAEP). As such, the new version of DETECT can be applied to response data sets not only with polytomous items but also with missing values, either by design or at random. DETECT is then applied to analyze the dimensional structure of the 2002 NAEP reading samples of grades 4 and 8. The DETECT results show that the substantive test structure based on the purposes for reading is consistent with the statistical dimensional structure for either grade.

Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption, essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriate statistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using any Balanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

Why should ‘better than’ be transitive? The leading answer in ethics is that values do not change with context. But this cannot be the entire source of transitivity, I argue, since transitivity can fail even if values never change, so long as they are complex, with multiple dimensions combined non-additively. I conclude by exploring a new hypothesis: that all alleged cases of nontransitive betterness, such as Parfit’s Repugnant Conclusion, can and should be modelled as the result of complexity, not context-relativity.

This study is a careful examination of the relationships between different components of the alexithymia construct and state versus trait anxiety. In order to study the relations between anxiety and alexithymia in a subclinical population, we administered to 125 female college students a test battery including measures of alexithymia (TAS26), state and trait anxiety (STAI) and depression (QD2A). Results indicated positive correlations between depression, anxiety (state and trait) and alexithymia scores. Partial correlations revealed a tight link between trait anxiety and alexithymia. Furthermore, in agreement with the view that alexithymia is a multidimensional construct, the various alexithymia dimensions were found to be diversely correlated with anxiety. On the basis of partial correlation analyses, a descriptive model of the relationships between depression, state anxiety, trait anxiety and alexithymia was postulated. This model was confirmed by pathways analyses.

The failure of the Supreme Court of Canada to give more than lip service to “context” when considering claims under s. 15 of the Canadian Charter of Rights and Freedoms arises largely from the Court's analytic framework, which resists recognizing the social relations of power inherent in complex cases of oppression. The precise nature of the flaws in the Court's analysis is demonstrated in a number of thoughtful feminist critiques that received recognition in the recent decision in R. v. Kapp. While it is too soon to tell whether the Court intends to depart completely from the past decade of s. 15 jurisprudence, equality-seeking groups now have greater opportunities to advance alternative theoretical frameworks for Charter interpretation. This article discusses one such framework, multidimensionality theory, which focuses on the interaction of systems of oppression, conceptualized as an invisible matrix—a vast network of complex, overlapping, interactive, and mutually reinforcing systems. The operation of the systems obscures their effects, and their complexity renders outcomes difficult to predict when they interconnect at sites of subordination and privilege. One can expose the operation of the systems by looking at particular sites of oppression/privilege and considering the contradictions or “inexplicability” of the circumstances based on one system alone. The author argues that the failure of the Charter claim at the heart of the Supreme Court's decision in Native Women's Association of Canada v. Canada demonstrates the need for courts to employ multidimensionality theory in cases of complex oppression. In NWAC, multidimensionality theory reveals that the “dominant” Aboriginal groups were involved in the negotiation/performance of hegemonic masculinities within a racial/colonial context that provided them with justification to suppress NWAC's independent promotion of the interests of Aboriginal women in constitutional negotiations with the government, and that the government was complicit in this performance. By framing the freedom of expression issue as whether NWAC had a “special” right to a speaking platform, and the equality issue as exclusively one of determining whether NWAC could prove the other groups were “male dominated,” the Court fragmented considerations of patriarchy from those of racism and colonization, distorting the synergistic effect of the systems of oppression and reinforcing colonial ideology.

Although intersectionality analysis originates in a critique of legal doctrine and its confining approach to subject formation, intersectionality has been adopted widely outside of legal scholarship—nationally and internationally—to explain how fields of power operate and interact to produce hierarchy for any limitless combination of identities. Yet, within law, some scholars have raised questions precisely about the capacity of intersectionality to grapple with subjects who occupy multiple social positions and those with “partially privileged” identities in particular. Thus, over roughly a decade, a critique took shape about the theoretical capacity and normative commitment of intersectionality theory to address particular subgroups.

This essay tells part of the curious story about how a race-sexuality critique of intersectionality emerged, what may have motivated it, and how it has facilitated an emerging progressive masculinities literature that is “post-intersectional,” i.e., positioned over and against intersectionality. Like other post-intersectionality approaches, multidimensionality theorists decidedly seek to ‘get beyond’ something, and that ‘something’ that underwrites the turn away from intersectionality appears not as substantive theoretical or analytical content, or as political strategy, but rather, as identity-driven and engendered.

The aim of this study was to analyze the reliability and validity evidence of scores on the Spanish version of Self-Description Questionnaire II (SDQ-II). The instrument was administered in a sample of 2022 Spanish students (51.1% boys) from grades 7 to 10. Confirmatory factor analysis (CFA) was used to examine validity evidence based on internal structure drawn from the scores on the SDQ-II. CFA replicated the correlated 11 first-order factor structure. Furthermore, hierarchical confirmatory factor analysis (HCFA) was used to examine the hierarchical ordering of self-concept, as measured by scores on the Spanish version of the SDQ-II. Although a series of HCFA models were tested to assess academic and non-academic components organization, support for those hierarchical models was weaker than for the correlated 11 first-order factor structure. Results also indicated that scores on the Spanish version of the SDQ-II had internal consistency and test-retest reliability estimates within an acceptable range.