Multivariate Probit Analysis of Binary Time Series Data with Missing Responses

Abstract

The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, Laird and Harrington (1991) and Liang, Zeger and Qaqish (1992)) and likelihood (see for example Fitzmaurice and Laird (1993) and Molenberghs and Lesaffre (1994)) based methods have been proposed. The number of parameters required for the full specification of these models grows exponentially with the length of the binary time series. Therefore, the analysis is often focused on marginal and first order parameters. In this case, the multivariate probit model (Ashford and Sowden (1970)) becomes an attractive alternative to the above models. The application of the multivariate probit model has been hampered by the intractability of the maximum likelihood estimator, when the length of the binary time series is large. This paper shows that this difficulty can be overcome by the use of Markov Chain Monte Carlo methods. This analysis also allows for valid point and interval estimates of the parameters in small samples. In addition, the analysis is adopted to handle the case of missing at random responses. The approach is illustrated on data involving binary responses measured at unequally spaced time points. Finally, this data analysis is compared to a GEE analysis given in Fitzmaurice and Lipsitz (1995).