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Abstract:
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Partially ordered set (poset) responses are prevalent in fields including psychology, education, and health. For example, the psychopathologic classification of no anxiety (NA), mild anxiety (MA), anxiety with depression (AwD), and severe anxiety (SA) form a poset. Partly because of the lack of analytic tools, poset responses are often collapsed into other data forms such as ordinal data. During such process, subtle information within poset is inevitably lost. In this presentation a longitudinal latent variable model for poset responses and its application to health data will be described. It is argued that latent variable modeling enables the integration of information from both ordinal and nominal components in poset. Using the above example, NA>{MA,AwD}>SA form the ordinal component, and MA and AwD form the nominal component. Specifically, it will be demonstrated that the latent variable model “discovers” implicit ordering within the nominal categories. This is possible because both intra-person and inter-person information are borrowed to reinforce inference. Additionally, the relationship between poset inference and semi-supervised learning will also be highlighted.
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