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Factor tree copula models for item response data | | Sayed H. Kadhem
; Aristidis K. Nikoloulopoulos
; | | Date: |
2 Jan 2022 | | Abstract: | Factor copula models for item response data are more interpretable and fit
better than (truncated) vine copula models when dependence can be explained
through latent variables, but are not robust to violations of conditional
independence. To circumvent these issues, truncated vines and factor copula
models for item response data are joined to define a combined model, the
so-called factor tree copula model, with individual benefits from each of the
two approaches. Rather than adding factors and causing computational problems
and difficulties in interpretation and identification, a truncated vine
structure is assumed on the residuals conditional on one or two latent
variables. This structure can be better explained as a conditional dependence
given a few interpretable latent variables. On the one hand, the parsimonious
feature of factor models remains intact and any residual dependencies are being
taken into account on the other. We discuss estimation along with model
selection. In particular, we propose model selection algorithms to choose a
plausible factor tree copula model to capture the (residual) dependencies among
the item responses. Our general methodology is demonstrated with an extensive
simulation study and illustrated by analyzing Post Traumatic Stress Disorder. | | Source: | arXiv, 2201.00339 | | Services: | Forum | Review | PDF | Favorites | |
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