A comparison of normal and nonnormal mixed models for number of lambs born in Norwegian sheep

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Abstract
A comparison of linear (LM), threshold (TM), and Poisson (PM) mixed models for genetic analysis of number of lambs born (NLB) from 1-yr-old ewes was conducted using 37,718 and 18,633 records of two Norwegian breeds, Da1a and Spaslsau, respectively. Models fitted included flock-year as a fixed effect and the random effect of sire. In the Poisson model, the residual variation was assumed to be Poisson, whereas it was normal in LM and multinomial in TM. The models were compared with respect to goodness of fit, predictive ability, and ranking of sires. Goodness of fit and predictive ability were assessed via the mean squared error and the correlation between observed NLB and fitted (predicted) values. Predictive ability was evaluated by estimating effects of sire and flock-year using a random half of the data and then using these estimates to predict records on the other half of the data. The heritability of NLB for Dala was estimated to be .20, .39, and .08 with LM, TM, and PM, respectively. For Spælsau, corresponding estimates were .12, .26, and .00, respectively. In the PM, problems of low or zero estimates of sire variances were encountered. Hence, an alternative sire variance (PM-L) was approximated from the heritability estimated on the outward scale by REML. All models performed similarly with respect to goodness of fit, predictive ability, and ranking of sires. The TM was very slightly better for both breeds, but the PM and PM-L seemed clearly poorer than TM and LM. An approximate test rejected the hypothesis that the conditional distribution of NLB was Poisson.

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