Table 4.
Best-fit models chosen based on the maximum DIC criterion described in the text.
| Variable | Model1 | Variance |
|---|---|---|
| Production | mu[k] <− a + b*pca2[j,i] + b1[j]* pow(pca2[j,i],2) | sig.e |
| Mortality | mu[k] <− a + b*pca2[j,i] | sig.e |
| Egg Weight | mu[k] <− a + b*pca1[j,i] + b1[j]* pow(pca1[j,i],2) + c[j]*pca2[j,i] + c1*pow(pca2[j,i],2) | sig.e |
| Haugh Unit | mu[k] <− a[j] + b[j]*pca1[j,i] + b1* pow(pca1[j,i],2) + c*pca2[j,i] + c1[j]*pow(pca2[j,i],2) | sig.e[j] |
| Whole Egg Solids | mu1[j,i] <− a + b*pca1[j,i] + c[i]*pca2[j,i] + c1[i]*pow(pca2[j,i],2) | sig.e |
| Vitelline Membrane - Force | mu[k] <− a + b*pca1[j,i] + b1[j]* pow(pca1[j,i],2) + c[j]*pca2[j,i] | sig.e |
| Vitelline Membrane - Deformation | mu[k] <− a + b[j]*pca2[j,i] | sig.e |
| Shell Strength - Force | mu[k] <− a + b*pca1[j,i] + c[j]*pca2[j,i] | sig.e |
| Shell Dynamic Stiffness | mu1[j,i] <− a + b*pca1[j,i] + b1[i]* pow(pca1[j,i],2) + c[i]*pca2[j,i] | sig.e |
| Shell Thickness | mu1[j,i] <− a + b*pca1[j,i] + b1* pow(pca1[j,i],2) + c*pca2[j,i] + c1[i]*pow(pca2[j,i],2) | sig.e |
Y is the response; i, refers to the housing system (Aviary, Enriched or Conventional); j, refers to the time period (week in production or month for quality); k, l, refer to the replicate, and replicate measurement per replicate, respectively, per time period and housing system; PC1, the first principal component; PC2, the second principal component; α, intercept; αi, represents a different intercept per housing system; b, c, linear slope in association with PC1 and PC2, respectively; bi, ci variable linear slope per housing system in association with PC1 and PC2, respectively; b1, c1, regression coefficient representing the non-linear, quadratic, trend in association with PC1 and PC2, respectively; b1i, c1i, variable regression coefficient representing the non-linear, quadratic, trend per housing system in association with PC1 and PC2, respectively; σ2, 
, the residual variance and its version when assumed different between housing systems; DIC, the Deviance Information Criterion used for model selection (please refer to the text).