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Title: Goodness-of-fit in multilevel latent class analysis Authors:  Erwin Nagelkerke - Tilburg University (Netherlands) [presenting]
Daniel Oberski - Tilburg University (Netherlands)
Jeroen Vermunt - Tilburg University (Netherlands)
Abstract: In the context of latent class models that deal with nested data, the goodness-of-fit depends on multiple aspects, amongst which several local independence assumptions. However, due to a lack of local fit statistics, the issues related to model fit can only be inspected jointly through global fit statistics. Given the number of possible model specifications, and potential areas for model misfit, the reliance on global fit poses several problems. Most notably, in case of a badly fitting model, there is no indication of the source of the misfit, which can prove valuable theoretical information. This is especially true for the fit of more complex models such as the multilevel model latent class model and the time dependencies in hidden Markov models. Vice versa, in case of an overall adequate fit, particular assumption violations may go unnoticed. For example, a multilevel latent class model may well be suited for the large majority of observed groups, leading to an overall good fit of the model, but could fail to model the dependencies of several extreme groups. New fit statistics are proposed to improve the understanding of the model, allow individual testing of the local independence assumptions, and inspect the fit of the model locally to pinpoint misfit and provide additional substantive insight.