Application of an approximate EM type algorithm and some devices for estimation of (Co) variances into the data set with combinations of measurements on a continuous and a binary trait
1992
Togashi, K. (Hokkaido National Agricultural Experiment Station, Sapporo (Japan)) | Smith, S.P. | Hammond, K.
A method for estimating location and dispersion parameters is presented for situations with 3 classes of animals: animals with records of continuous and binary responses, and animals with records of continuous or binary traits. An underlying normal distribution is assumed with a fixed threshold. Location parameters of the fixed and random effects are taken as the mode of posterior distribution resulting from a combination of normal density, a prior, and product of binomial likelihood function. These estimates are obtained with the Newton-Raphson algorithm. The ratio of residual covariance for continuous and underlying varieties to residual variance for the underlying variate is estimated by applying approximate EM type algorithm which needs not to treat fixed and random effects as known. The elements of a coefficient matrix based on ordering traits within animals are obtained by summing up individual values without matrix multiplication and it is suggested that this procedure makes inversion much easier. The inverse elements of a coefficient matrix to estimate (co)variance components are given by absorbing fixed effects into random effects and are obtained by application of tridiagonalization. The idea presented in the part of an approximate EM type algorithm is introduced into MLF algorithm to estimate (co)variance components. The estimation procedure based on an approximate EM type algorithm is developed into a specific data set, i.e. a sequential data structure. The estimated location parameters were almost the same for the two computations, one is the iteration until convergence and the other to limit the number of iterations on satisfying set of dispersion parameters
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