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.

翻译：当依赖性可以通过潜在变量来解释时,物品反应数据的因子合金模型比(修剪的)因子合金模型更易解释,更适合(修剪的)因子合金模型,但对于违反有条件独立性的情况则不强。为绕过这些问题,将项目反应数据的缺省葡萄和因子合金模型合并起来,以界定一个综合模型,即所谓的因子树合金模型,从这两种方法中每种方法都有个别的好处。我们建议采用示范选择算法,选择一个合理的因子树合金模型,以了解项目反应中的(累合)依赖性,而不是增加因素和造成计算问题和困难。这一结构可以更好地解释为有条件依赖性,因为有几个可解释的潜在变量。一方面,要素模型的偏差特征保持不变,而任何剩余依赖性均得到考虑。我们讨论与模型选择的估算,特别是,我们建议采用示范选择算法,选择一个合理的因子树合金模型,以了解项目反应的(累合)依赖性。我们的一般方法通过广泛的模拟研究加以示范,并通过分析后向压力分析来说明。