Using a Multivariate Multilevel Polytomous Item Response Theory Model to Study Parallel Processes of Change: The Dynamic Association Between Adolescents' Social Isolation and Engagement With Delinquent Peers in the National Youth Survey

Abstract

The application of multidimensional item response theory models to repeated observations has demonstrated great promise in developmental research. It allows researchers to take into consideration both the characteristics of item response and measurement error in longitudinal trajectory analysis, which improves the reliability and validity of the latent growth curve (LGC) model. The purpose of this study is to demonstrate the potential of Bayesian methods and the utility of a comprehensive modeling framework, the one combining a measurement model (e.g., a multidimensional graded response model, MGRM) with a structural model (e.g., an associative latent growth curve analysis, ALGC). All analyses are implemented in WinBUGS 1.4.3 ( Spiegelhalter, Thomas, Best, & Lunn, 2003 ), which allows researchers to use Markov chain Monte Carlo simulation methods to fit complex statistical models and circumvent intractable analytic or numerical integrations. The utility of this MGRM-ALGC modeling framework was investigated with both simulated and empirical data, and promising results were obtained. As the results indicate, being a flexible multivariate multilevel model, this MGRM-ALGC model not only produces item parameter estimates that are readily estimable and interpretable but also estimates the corresponding covariation in the developmental dimensions. In terms of substantive interpretation, as adolescents perceived themselves more socially isolated, the chance that they are engaged with delinquent peers becomes profoundly larger. Generally, boys have a higher initial exposure extent than girls. However, there is no gender difference associated with other latent growth parameters.

Sample Size Requirements for Estimation of Item Parameters in the Multidimensional Graded Response Model

“…A recent study (Thomas et al, 2013 ) used the multidimensional GRM (MGRM) to score the responses to the Penn Face Memory Test, a measure of visual episodic memory. Hsieh et al ( 2010 ) combined the MGRM with latent growth curve analysis in modeling the longitudinal association between adolescents' social isolation and delinquency. Forero et al ( 2013 ) applied MGRM scoring to the two-dimensional Short Form-12 questionnaire, a widely used measure of physical and mental health status and change.…”

On Longitudinal Item Response Theory Models: A Didactic

“…In these cases, the L-MIRT model and L-UIRT model overlook crucial details. In particular, the L-MIRT model (Hsieh et al, 2010) essentially assumes a constant set of traits measured over time. For this relatively straightforward example, the domains are designed to change over time.…”

“…Item response theory (IRT) models are useful tools to model the relationship between the categorical outcome variables and the latent continuous traits. Recent work has extended IRT models to model changes in latent traits, leading to the family of longitudinal IRT (L-IRT) models (e.g., Andersen, 1985; Cai, 2010; Hsieh, von Eye, & Maier, 2010; Huang, 2013; McArdle, Grimm, Hamagami, Bowles, & Meredith, 2009; Paek, Li, & Park, 2016; von Davier, Xu, & Carstensen, 2011; Wang, Kohli, & Henn, 2016; Wilson, Zheng, & McGuire, 2012). Within this family, models differ mainly in the following aspects: (1) the measurement model that implies the factor structure of the primary latent traits measured repeatedly, which could either be unidimensional, multidimensional (Hsieh et al, 2010), or hierarchical (Huang, 2013); (2) the relationship of the latent traits over time, which could either be captured by a completely unstructured covariance matrix (Andrade & Tavares, 2005; Cai, 2010; Paek et al, 2016) or by linear/nonlinear change patterns via the latent growth curve (LGC) models (Bollen & Curran, 2006; Duncan, Duncan, & Strycker, 2006); and (3) whether nuisance factors are in place to account for the dependency of the same items administered over time (e.g., two-tier model; Cai, 2010; Paek et al, 2016; Wang et al, 2016).…”

“…Three specific types of models will be the focus of discussion. In order of complexity, these models include the longitudinal unidimensional IRT (L-UIRT) model (Wang et al, 2016; Wilson et al, 2012), longitudinal multidimensional IRT (L-MIRT) model (Hsieh et al, 2010), and longitudinal higher-order IRT (L-HO-IRT) model (Huang, 2013). All of these models are variations of the general LGC model and the respective measurement model: The UIRT model assumes that a single latent trait is measured by all the items; MIRT models posit that item responses are probabilistically determined by multiple, usually correlated, latent traits; the HO-IRT models (de la Torre & Song, 2009; Sheng & Wikle, 2008) capture the hierarchical nature of factor structure (e.g., Huang & Wang, 2014; Sawaki, Stricker, & Oranje, 2009), whereby a general factor (such as math aptitude) informs domain-specific factors (such as algebra, geometry, calculus, or subsets thereof).…”

Modeling Response Time and Responses in Multidimensional Health Measurement

“…When the instruments include multiple scales measuring different constructs or different aspects of the same construct (e.g., Zickar and Robie, 1999; Fraley et al, 2000; Fletcher and Hattie, 2004; Zagorsek et al, 2006; Pilkonis et al, 2014), the multidimensional extension of the GRM, namely, the MGRM (Hsieh et al, 2010; Jiang et al, 2016), is appropriate. Let θ be a vector of length H representing the latent traits of interest, and let h = 1, 2, …, H .…”