General mixture item response models with different item response structures: Exposition with an application to Likert scales

This article proposes a general mixture item response theory (IRT) framework that allows for classes of persons to differ with respect to the type of processes underlying the item responses. Through the use of mixture models, nonnested IRT models with different structures can be estimated for different classes, and class membership can be estimated for each person in the sample. If researchers are able to provide competing measurement models, this mixture IRT framework may help them deal with some violations of measurement invariance. To illustrate this approach, we consider a two-class mixture model, where a person’s responses to Likert-scale items containing a neutral middle category are either modeled using a generalized partial credit model, or through an IRTree model. In the first model, the middle category (“neither agree nor disagree”) is taken to be qualitatively similar to the other categories, and is taken to provide information about the person’s endorsement. In the second model, the middle category is taken to be qualitatively different and to reflect a nonresponse choice, which is modeled using an additional latent variable that captures a person’s willingness to respond. The mixture model is studied using simulation studies and is applied to an empirical example.     

A Cross-Classified CFA-MTMM Model for Structurally Different and Nonindependent Interchangeable Methods

Multirater (multimethod, multisource) studies are increasingly applied in psychology. Eid and colleagues (2008) proposed a multilevel confirmatory factor model for multitrait-multimethod (MTMM) data combining structurally different and multiple independent interchangeable methods (raters). In many studies, however, different interchangeable raters (e.g., peers, subordinates) are asked to rate different targets (students, supervisors), leading to violations of the independence assumption and to cross-classified data structures. In the present work, we extend the ML-CFA-MTMM model by Eid and colleagues (2008) to cross-classified multirater designs. The new C4 model (Cross-Classified CTC[M-1] Combination of Methods) accounts for nonindependent interchangeable raters and enables researchers to explicitly model the interaction between targets and raters as a latent variable. Using a real data application, it is shown how credibility intervals of model parameters and different variance components can be obtained using Bayesian estimation techniques.     

A generalized item response tree model for psychological assessments

A new item response theory (IRT) model with a tree structure has been introduced for modeling item response processes with a tree structure. In this paper, we present a generalized item response tree model with a flexible parametric form, dimensionality, and choice of covariates. The utilities of the model are demonstrated with two applications in psychological assessments for investigating Likert scale item responses and for modeling omitted item responses. The proposed model is estimated with the freely available R package flirt (Jeon et al., 2014b).     

Evaluation on types of invariance in studying extreme response bias with an IRTree approach

In recent years, item response tree (IRTree) approaches have received increasing attention in the response style literature for their ability to partial out response style latent variables as well as associated item parameters. When an IRTree approach is adopted to measure extreme response styles, directional and content invariance could be assumed at the latent variable and item parameter levels. In this study, we propose to evaluate the empirical validity of these invariance assumptions by employing a general IRTree model with relaxed invariance assumptions. This would allow us to examine extreme response biases, beyond extreme response styles. With three empirical applications of the proposed evaluation, we find that relaxing some of the invariance assumptions improves the model fit, which suggests that not all assumed invariances are empirically supported. Specifically, at the latent variable level, we find reasonable evidence for directional invariance but mixed evidence for content invariance, although we also find that estimated correlations between content-specific extreme response latent variables are high, hinting at the potential presence of a general extreme response tendency. At the item parameter level, we find no directional or content invariance for thresholds and no content invariance for slopes. We discuss how the variant item parameter estimates obtained from a general IRTree model can offer useful insight to help us understand response bias related to extreme responding measured within the IRTree framework.     

Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation

Psychometrika - In this paper, we propose a joint modeling approach to analyze dependency in parallel response data. We define two types of dependency: higher-level dependency and within-item...     

CFA Models with a General Factor and Multiple Sets of Secondary Factors

We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model. Furthermore, the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables, decomposition of the variances, and the inclusion of interactions, similar to generalizability theory. We provide two applications to illustrate the utility of the proposed class of models.     

A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data

Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.

     

Perceived physical competence and body image as predictors of perceived peer acceptance in adolescents

The purpose of this study was to investigate the relationships among perceived physical competence, body image, and peer acceptance. Body image was considered as a possible mediator of the relationships between perceived physical competence and peer acceptance. Adolescents (N = 838) completed questionnaires. Direct and indirect effects of perceived physical competence and body image on perceived peer acceptance were explored using structural equation modelling. Gender differences were found and the structural mediation model was a reasonable fit to the data; the pattern of relationships in the model was different for adolescent males and females.     

South Korean counselors’ perceived multicultural counseling competence: Relationship with openness to experience,perceived general counseling competence,and multicultural counseling education/practice

This study investigated variables related to the perceived multicultural counseling competence (MCC) of South Korean counselors. The relationship between perceived MCC and demographic information was explored, and effects of openness to experience, general counseling competence, and multicultural counseling education/practice on perceived MCC were examined.  Results revealed no relationship with demographic information and perceived MCC and significant effects of general counseling competence and multucultural counseling education/practice on perceived MCC. Implications for multicultural counseling training and future research are discussed.