Modeling global and local person dependence for clustered samples in Rasch models

Cluster sampling is widely applied in social science. Respondents recruited from the same clusters may behave more similarly than those from different clusters in terms of their general proficiency, as well as their response patterns. The homogeneity of general proficiency refers to global person dependence (GPD), which can be adequately accounted for by means of multilevel modeling. Local person dependence (LPD) describes some kinds of interpersonal interactions that are conditional on respondents' proficiency levels, implying that person residuals are not locally independent when fitting a standard (e.g., Rasch) model. Many item response theory (IRT) models have been developed to create a multilevel structure for describing GPD, but few address the occurrence and influence of LPD.
This study was intended to develop a new class of Rasch models for clustered samples to account for GPD and LPD jointly so that the two kinds of dependence can be quantified. In brief, I developed a new set of IRT models for integrating multilevel structures on the measured latent trait(s) and a component of random item difficulty across person clusters. The simple models for dichotomous and polytomous responses were displayed in sequence, and the extensions to multiple tests and many-faceted data were illustrated on top of the basic forms. These models can be easily implemented by means of WinBUGS, a freeware application used for Bayesian analysis. A series of simulations were carried out to examine the parameter recovery of the new models, as well as the consequences of fitting standard models without considering LPD. The results indicated that the parameters of the new models can be recovered very well, and that ignoring LPD by fitting standard models elicits biased estimation and inflated GPD.
The technique of cluster analysis is to group subjects in accordance with the homogeneity among a set of variables. Therefore, it may be helpful to assess the occurrence of LPD, and how respondents within a cluster are grouped together, especially when the magnitude of LPD is substantial. The effectiveness of hierarchical cluster analysis (HCA) in exploring the dependence of person residuals was examined. It was found that HCA was useful for recovering respondents’ true membership by means of the homogeneity information among person residuals, but it was not always sensitive to LPD.
Four empirical examples – the National Longitudinal Study of Adolescent Health (Add Health) project, the Impact of Community Policing Training and Program Implementation on Police Personnel in Arizona study, the International Civic and Citizenship Study in 2009, and the Love Relationship Scale for couples – were used to demonstrate the new models. In the first and second examples particularly, items were designed to measure a single latent trait, whereas in the third and fourth examples, items were assembled as different subtests measuring distinct, but correlated, latent traits. It was found that, in these four examples, the clustered samples exhibited various degrees of LPD on items. As for the findings in the simulations, fitting simpler models without regarding the influence of LPD yielded shrunken scales and inflated GPD.
Finally, conclusions were drawn based on the findings, in which the importance of the consideration of LPD when dealing with clustered samples was emphasized, and the implications of how to interpret LPD were discussed. Limitations in the LPD modeling approach and in HCA for accessing LPD also were addressed. Suggestions for future studies also were provided. All rights reserved.