Heteroscedastic Latent Trait Models for Dichotomous Data

Abstract

Effort has been devoted to account for heteroscedasticity with respect to observed or latent moderator variables in item or test scores. For instance, in the multi-group generalized linear latent trait model, it could be tested whether the observed (polychoric) covariance matrix differs across the levels of an observed moderator variable. In the case that heteroscedasticity arises across the latent trait itself, existing models commonly distinguish between heteroscedastic residuals and a skewed trait distribution. These models have valuable applications in intelligence, personality and psychopathology research. However, existing approaches are only limited to continuous and polytomous data, while dichotomous data are common in intelligence and psychopathology research. Therefore, in present paper, a heteroscedastic latent trait model is presented for dichotomous data. The model is studied in a simulation study, and applied to data pertaining alcohol use and cognitive ability.

An Alternative to the 3PL: Using Asymmetric Item Characteristic Curves to Address Guessing Effects

“…Note that if δ 1 = 0, then the residual variance is homoscedastic with = δ 0 ; if δ 1 > 0, then the residual variance is increasing with θ; if δ 1 < 0, the residual variance is decreasing with θ as we can see in upper panels of Figure . After setting δ 0 to an arbitrary constant, the resulting item response model for dichotomous data (Molenaar, ) can be written as …”

“…It should be emphasized that the only difference between the model in Equation and the 2PNO is the term in the denominator, which reduces to 1 if = 0, making the 2PNO a special case. Consistent with Molenaar (), we use the slope/intercept notation for the IRT parameters (i.e., α i , β i ) recognizing that the model could also be written using Lord's () parameterization. Note that more positive values of β mean less difficulty in this notation.…”

“…(). In this article, we examine one such asymmetric model, namely, the residual heteroscedasticity (RH) IRT model (Molenaar, ), and compare its fit to the 3PL/3PNO using several real as well as simulated multiple‐choice test data sets.…”

“…We consider the use of a residual heteroscedasticity (RH) model as an alternative, and compare its performance to the 3PL with real test data sets and through simulation analyses. Our results suggest advantages to the RH approach, including closer fit to real data, more interpretable parameter estimates, and greater psychological plausibility.An Alternative to the 3PL residual heteroscedasticity (RH) IRT model (Molenaar, 2014), and compare its fit to the 3PL/3PNO using several real as well as simulated multiple-choice test data sets.…”

Capturing Context-Related Change in Emotional Dynamics via Fixed Moderated Time Series Analysis

“…Traditionally, multivariate modeling solutions to the problem of heterogeneity have been proposed in the context of studying between-person differences, encompassing, for instance, multiple-group structural equation modeling (SEM) (e.g., Jöreskog, 1971), finite and infinite mixture SEM (Bauer, 2007;Dolan, 2009;Hessen & Dolan, 2009;Lubke & Muthén, 2005;D. Molenaar, 2015;Sterba, 2013), SEM with fixed moderators (e.g., Bauer & Hussong, 2009;Curran et al, 2014;D.…”