12.1 Introduction to PolyEM programs

PolyEM is a set of programs to evaluate the likelihood and compute MLEs for polygenic models of quantitative traits by EM algorithms. There are four main programs whose features are summarized below:

• univar: This program fits a univariate trait model. It is primarily for test purposes. The likelihood is computed by three methods including polygenic peeling, which does not extend to looped pedigrees, and by a matrix method which does not extend to large pedigrees.

• unibig: An extension of univar to big pedigrees that implements a method compute the likelihood for large looped pedigrees too.

• bivar: An extension of unibig for bivariate traits.

• multivar: An extension of bivar for multivariate traits.

All programs can work with looped pedigrees. The exception is that looped pedigrees cannot be used for the polygenic peeling algorithm in univar. The other programs do not use polygenic peeling to evaluate the likelihood.

Only examples and statement references for multivar are given since it has the most complete features. The statements for other programs are similar with some exceptions (e.g., any statements with covariances do not apply to univar or unibig).