Analytic Standard Errors for Latent Gaussian Discrete-Valued Multivariate Time Series

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Unlike their continuous-valued counterpart, there are no universally preferred methodologies for modeling count and discrete-valued time series. This is especially problematic in fields like psychology and education, where repeated measures data often take the form of count, dichotomous, and ordered categorical variables. To address the need for flexible methodology to analyze discrete-valued time series data, a multivariate model defined via deterministic functions of a latent Gaussian series has been proposed. This model has several promising features, including the ability to accommodate a wide variety of marginal distributions within the same model (e.g., overdispersed and zero-inflated distributions) while also allowing for the most flexible autocorrelations possible. In this presentation we extend the work on this model by developing analytic standard errors to support inference on the latent dynamics and parameters associated with the marginal distributions. Properties of these analytic standard errors are examined and discussed.