Negative binomial integer-valued auto-regressive process for longitudinal count data

Abstract

This paper proposes a longitudinal integer-valued auto-regressive model of order one with Negative-Binomial marginals. The proposed model is suitable for analyzing repeated count data that exhibits significant over-dispersion at each time point and that is exposed to sev- eral time-dependent covariates. The estimation of the model parameters is handled by two non-likelihood approaches: The Generalized Quasi-likelihood (GQL) and the adaptive Quadratic Inference function (AQIF). The consistency of the model estimators is assessed via Monte Carlo simulation experiments and application to the epileptic seizures is made. The results demonstrate that both approaches GQL and AQIF yield reliable estimates but GQL provides better standard errors.

Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 243-257.