Likelihood inference in a correlated probit regression model

Maximum Likelihood Variance Components Estimation for Binary Data

“…The Table 25.10, n=10). We noticed none of the accuracy problems reported in Ochi and Prentice (1984) and, in fact, were able to reproduce the true values in their Table 1 with those of Ochi and Prentice; slight differences are to be expected because they used the approximation due to Mendell and Elston (1974). For example in group 2, Ochi and Prentice obtain .Y 2 = ~ = .651, whereas our estimates give i' 2 = .661.…”

“…We applied the methods derived in Section 3 to the data analyzed by Ochi and Prentice (1984), from Weil (1970), and to the salamander data from McCullagh and Neider (1989, Section 14.5).…”

“…However, like the beta-binomial models, his models are also difficult to generalize to multiple random effects. For -2-these reasons we consider in this paper correlated probit models which are generalizations of those of Ochi and Prentice (1984). These are similar to the logit normal models of Pierce and Sands (1975), Wong and Mason (1984) and Stiratelli, Laird and Ware (1984), though Stiratelli, Laird and Ware's models are intended only for the longitudinal data setting.…”

“…If we set X = diag{ 1m} i = 1,2,· · ·,G, Z = diag{ 1niJ' j = 1,2,· · ·,m;, P = J.L, this reduces to the Ochi and Prentice (1984) model, with the restriction that negative correlations cannot be modeled. Model (2.1) has the advantage over the Ochi and Prentice model that it does not require the mean to be constant within levels of the random effect.…”

Statistical methods for the beta-binomial model in teratology.

“…Kupper and Haseman (7) introduced the correlated binomial model by considering the correlation between two binary responses within the same litter. A different approach was used by Ochi and Prentice (8). In their model, binary responses within the same litter are defined according to whether the corresponding components of a multivariate normal variate with common mean, variance, and correlation exceed a common threshold.…”