Multivariate Probit Analysis of Binary Time Series Data with Missing Responses

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).