Bi-factor and Second-Order Copula Models for Item Response Data

Bi-factor and second-order models based on copulas are proposed for item response data, where the items are sampled from identified subdomains of some larger domain such that there is a homogeneous dependence within each domain. Our general models include the Gaussian bi-factor and second-order models as special cases and can lead to more probability in the joint upper or lower tail compared with the Gaussian bi-factor and second-order models. Details on maximum likelihood estimation of parameters for the bi-factor and second-order copula models are given, as well as model selection and goodness-of-fit techniques. Our general methodology is demonstrated with an extensive simulation study and illustrated for the Toronto Alexithymia Scale. Our studies suggest that there can be a substantial improvement over the Gaussian bi-factor and second-order models both conceptually, as the items can have interpretations of discretized maxima/minima or mixtures of discretized means in comparison with discretized means, and in fit to data.

Hierarchical models of psychopathology: empirical support, implications, and remaining issues

There is an ongoing revolution in psychology and psychiatry that will likely change how we conceptualize, study and treat psychological problems.- Many theorists now support viewing psychopathology as consisting of continuous dimensions rather than discrete diagnostic categories. Indeed, recent papers have proposed comprehensive taxonomies of psychopathology dimensions to replace the DSM and ICD taxonomies of categories. The proposed dimensional taxonomies, which portray psychopathology as hierarchically organized correlated dimensions, are now well supported at phenotypic levels. Multiple studies show that both a general factor of psychopathology at the top of the hierarchy and specific factors at lower levels predict different functional outcomes. Our analyses of data on a large representative sample of child and adolescent twins suggested the causal hypothesis that phenotypic correlations among dimensions of psychopathology are the result of many familial influences being pleiotropic. That is, most genetic variants and shared environmental factors are hypothesized to non-specifically influence risk for multiple rather than individual dimensions of psychopathology. In contrast, person-specific experiences tend to be related to individual dimensions. This hierarchical causal hypothesis has been supported by both large-scale family and molecular genetic studies. Current research focuses on three issues. First, the field has not settled on a preferred statistical model for studying the hierarchy of causes and phenotypes. Second, in spite of encouraging progress, the neurobiological correlates of the hierarchy of dimensions of psychopathology are only partially described. Third, although there are potentially important clinical implications of the hierarchical model, insufficient research has been conducted to date to rec-ommend evidence-based clinical practices.

Criterion validity and relationships between alternative hierarchical dimensional models of general and specific psychopathology

[Correction Notice: An Erratum for this article was reported in Vol 129(7) of Journal of Abnormal Psychology (see record 2020-72912-001). In the article (http://dx.doi.org/10.1037/abn0000601), an acknowledgment is missing from the author note. The missing acknowledgement is included in the erratum.] Psychopathology can be viewed as a hierarchy of correlated dimensions. Many studies have supported this conceptualization, but they have used alternative statistical models with differing interpretations. In bifactor models, every symptom loads on both the general factor and 1 specific factor (e.g., internalizing), which partitions the total explained variance in each symptom between these orthogonal factors. In second-order models, symptoms load on one of several correlated lower-order factors. These lower-order factors load on a second-order general factor, which is defined by the variance shared by the lower-order factors. Thus, the factors in second-order models are not orthogonal. Choosing between these valid statistical models depends on the hypothesis being tested. Because bifactor models define orthogonal phenotypes with distinct sources of variance, they are optimal for studies of shared and unique associations of the dimensions of psychopathology with external variables putatively relevant to etiology and mechanisms. Concerns have been raised, however, about the reliability of the orthogonal specific factors in bifactor models. We evaluated this concern using parent symptom ratings of 9-10 year olds in the ABCD Study. Psychometric indices indicated that all factors in both bifactor and second-order models exhibited at least adequate construct reliability and estimated replicability. The factors defined in bifactor and second-order models were highly to moderately correlated across models, but have different interpretations. All factors in both models demonstrated significant associations with external criterion variables of theoretical and clinical importance, but the interpretation of such associations in second-order models was ambiguous due to shared variance among factors. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Response Surface Methodology Using a Fullest Balanced Model: A Re-Analysis of a Dataset in the Korean Journal for Food Science of Animal Resources

Response surface methodology (RSM) is a useful set of statistical techniques for modeling and optimizing responses in research studies of food science. In the analysis of response surface data, a second-order polynomial regression model is usually used. However, sometimes we encounter situations where the fit of the second-order model is poor. If the model fitted to the data has a poor fit including a lack of fit, the modeling and optimization results might not be accurate. In such a case, using a fullest balanced model, which has no lack of fit, can fix such problem, enhancing the accuracy of the response surface modeling and optimization. This article presents how to develop and use such a model for the better modeling and optimizing of the response through an illustrative re-analysis of a dataset in Park et al. (2014) published in the Korean Journal for Food Science of Animal Resources.

Nonlinear Growth Models as Measurement Models: A Second-Order Growth Curve Model for Measuring Potential

Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.