A log‐linear multidimensional Rasch model for capture–recapture

Abstract

In this paper, a log-linear multidimensional Rasch model is proposed for capture-recapture analysis of registration data. In the model, heterogeneity of capture probabilities is taken into account, and registrations are viewed as dichotomously scored indicators of one or more latent variables that can account for correlations among registrations. It is shown how the probability of a generic capture profile is expressed under the log-linear multidimensional Rasch model and how the parameters of the traditional log-linear model are derived from those of the log-linear multidimensional Rasch model. Finally, an application of the model to neural tube defects data is presented.

Asymptotic Posterior Normality of Multivariate Latent Traits in an IRT Model

“…We shall verify the proposed conditions (CS1') to (CS5') for a multidimensional version of a model by Lee and Bolt (2018) and discuss them also for the models of Pelle et al (2016) and a logit model with interaction of the latent variables (Rizopoulos, 2006).…”

“…Conditions (CS1') to (CS5') for other models can be verified similarly. For example, the multidimensional Rasch model implemented in Pelle et al (2016) is the logit model…”

“…For example, the multidimensional Rasch model implemented in Pelle et al. ( 2016 ) is the logit model where is the probability of inclusion in registration i , given the vector of latent variables. In this case, would replace ( 23 ) for , while the subsequent arguments are the same as above.…”

“…As far as we know, APN of multivariate LTs has not been proved so far for IRT models of a general context, although posterior normality or APN is assumed quite often under various IRT setups (e.g., Anderson & Vermunt, 2000;Anderson & Yu, 2017;Anderson et al, 2007;Hessen, 2012;Li, 2010;Paek, 2016). For example, Pelle et al (2016) assume posterior multivariate normality for the latent variable vector of a log-linear multidimensional Rasch model for capturerecapture analysis of registration data.…”

“…For example, Pelle et al. ( 2016 ) assume posterior multivariate normality for the latent variable vector of a log-linear multidimensional Rasch model for capture–recapture analysis of registration data.…”