gllamm estimates Generalized Linear Latent And Mixed Models. These models include multilevel (hierarchical) regression models with an arbitrary number of levels, generalized linear mixed models, multilevel factor models and some types of latent class models. We refer to the random effects (random intercepts, slopes or coefficients), factors, etc. as latent variables or random effects.
If the latent variables are assumed to be multivariate normal, gllamm uses Gauss-Hermite quadrature, or adaptive quadrature if the adapt option is also specified. Adaptive quadrature can be considerably more accurate than ordinary quadrature, see first reference at the bottom of this help file.
With the ip(f) option, the latent variables are specified as discrete with freely estimated probabilities (masses) and locations.
More information on the models is available from www.gllamm.org