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Abstract
A simulation study was conducted to compare methods to estimate variance components for ovulation rate and litter size in mice. Both traits are ordinal, categorical variables, so the results are generally applicable to similar problems. The data were arranged in one of the following three-stage nested designs: completely balanced; Anderson staggered, nested; or Bainbridge staggered, nested. One set of methods treated the traits as if they were continuous; REML using a reparameterization, REML using pseudo expectations, and Henderson's Method 3. The other treated them as threshold traits; Bayesian analysis using a flat prior, Bayesian analysis using an informative prior and a generalized linear model analysis. The variance components were used to estimate heritabilities and realized values of random effects. Methods were compared using MSE as a criterion. For both traits and all three designs the MSE for heritability was the smallest for the Bayesian analysis using an informative prior. The Bayesian analysis with an informative prior also produced the best random effects estimates and required the fewest number of iterations to reach convergence for all but the.10 heritability level (litter size) for the balanced design.
A two-trait pseudo expectation method and a two-trait Bayesian method using a flat prior were developed for a three-stage nested model to estimate variance and covariance components for ordinal, categorical data. The Bayesian method is based on a threshold model, while the pseudo expectation method is based on the use of normal, continuous data. The two procedures were compared using simulation. The Bayesian method had smaller MSE's for the heritability and correlation estimates, produced similar rank correlations and required substantially less total computer time than the pseudo expectation method.
