Modeling relationships between calving traits: a comparison between standard and recursive mixed models

Table 1 Posterior mean (standard deviation) of structural coefficients for calving traits from the recursive mixed models

Structural coefficients	Model^a	Category of GL
		261-267 d	268-273 d	274-279 d	280-291 d
λ_CD←GL(l. u.^b/1 d GL)	RMM1	0.005 (0.005)	0.020** (0.003)	0.032** (0.005)	0.040** (0.003)
	RMM2	0.006 (0.005)	0.020** (0.003)	0.032** (0.005)	0.040** (0.003)
	RMM3	0.005 (0.005)	0.021** (0.003)	0.033** (0.005)	0.041** (0.003)
Overall effect of GL on SB (l. u./1 d GL)^c	RMM1	-0.044** (0.006)	-0.021** (0.004)	-0.008 (0.006)	0.024** (0.003)
	RMM2	-0.044** (0.0062)	-0.021** (0.0038)	-0.008 (0.0057)	0.025** (0.0031)
	RMM3	-0.044** (0.006)	-0.021** (0.004)	-0.008 (0.006)	0.025** (0.003)
λ_SB←CD(l. u./l. u. CD)	RMM1	0.339** (0.023)	0.331** (0.011)	0.330** (0.007)	0.3311** (0.007)
	RMM2	0.327** (0.023)	0.319** (0.010)	0.317** (0.007)	0.318** (0.007)
	RMM3	0.330** (0.003)	0.321** (0.011)	0.319** (0.007)	0.320** (0.007)

** 99% highest posterior density region, HPD_99%, does not include 0; ^aRMM1: recursive mixed model (RMM) assuming that the relationship between residuals is due to the recursive relationships between the gestation length (GL) phenotype and the liabilities to calving difficulty (CD) and stillbirth (SB); RMM2: RMM assuming that the relationships both between residuals and between herd-years are due to the recursive relationships between the phenotype of GL and the liabilities to CD and SB; RMM3: recursive mixed model assuming that phenotypic correlations of the system are uniquely caused by the recursiveness; ^b l. u.: liability units; ^cThe overall recursive effect of GL on liability to SB is the sum of the direct and indirect recursive effects, λ_SB←GL+ λ_CD←GL× λ_SB←CD

ISSN: 1297-9686