Application of the EM algorithm for estimation in the generalized mixe
d model has been largely unsuccessful because the E-step cannot be det
ermined in most instances. The E-step computes the conditional expecta
tion of the complete data log-likelihood and when the random effect di
stribution is normal, this expectation remains an intractable integral
. The problem can be approached by numerical or analytic approximation
s; however, the computational burden imposed by numerical integration
methods and the absence of an accurate analytic approximation have lim
ited the use of the EM algorithm. In this paper, Laplace's method is a
dapted for analytic approximation within the E-step. The proposed algo
rithm is computationally straightforward and retains much of the conce
ptual simplicity of the conventional EM algorithm, although the usual
convergence properties are not guaranteed. The proposed algorithm acco
mmodates multiple random factors and random effect distributions besid
es the normal, e.g., the log-gamma distribution. Parameter estimates o
btained for several data sets and through simulation show that this mo
dified EM algorithm compares favorably with other generalized mixed mo
del methods.