Maximum likelihood and an approximate expectation and maximization procedures to estimate dispersion parameters in a data set of combination of censored and uncensored traits

A method for estimating variance and covariance components for both uncensored and censored traits is described. The paper considers two cases: An uncensored trait and a right-censored trait; and two uncensored traits. A multivariate normal distribution is assumed for these traits and Bayesian arguments are employed to derive estimation procedures for dispersion parameters such as genetic variance and environmental variance. Observations are transformed by a Cholesky decomposition of the residual variance-covariance matrix so that residual covariance becomes zero. The residual variance for a right-censored trait and the residual covariance of a right-censored trait and an uncensored trait are estimated by two methods: maximum likelihood (ML) approach and an approximate expectation and maximization (EM) algorithm which is equivalent to restricted maximum likelihood (REML). A numerical example is used to illustrate the steps involved in applying the proposed methods. Comparison of the size of dispersion parmeters in both between ML and an approximate EM procedures and between ignoring and accounting for censoring is tested in a numerical example.