D.5 Milk Yield

D.5 Brown Swiss: Milk Yield

D.5.1: Full Period: 1982-2023

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	12.9694	0.7576	17.1190	\(< 0.0001\)
parityprimiparous	-2.5964	0.0086	-301.9207	\(< 0.0001\)
year1983	1.9968	0.5636	3.5432	0.0004
year1984	2.5867	0.7005	3.6927	0.0002
year1985	3.0365	0.7138	4.2538	\(< 0.0001\)
year1986	3.0073	0.7181	4.1878	\(< 0.0001\)
year1987	2.8618	0.7298	3.9212	0.0001
year1988	2.8946	0.7369	3.9279	0.0001
year1989	3.4588	0.7441	4.6483	\(< 0.0001\)
year1990	3.6510	0.7641	4.7781	\(< 0.0001\)
year1991	3.9590	0.7684	5.1519	\(< 0.0001\)
year1992	4.0727	0.7695	5.2926	\(< 0.0001\)
year1993	4.1564	0.7719	5.3844	\(< 0.0001\)
year1994	4.1695	0.7816	5.3344	\(< 0.0001\)
year1995	4.3510	0.7962	5.4648	\(< 0.0001\)
year1996	4.3577	0.7996	5.4499	\(< 0.0001\)
year1997	4.9766	0.8017	6.2072	\(< 0.0001\)
year1998	5.6956	0.8013	7.1077	\(< 0.0001\)
year1999	5.5569	0.8014	6.9344	\(< 0.0001\)
year2000	5.7601	0.8018	7.1842	\(< 0.0001\)
year2001	6.4392	0.8024	8.0250	\(< 0.0001\)
year2002	6.6584	0.7975	8.3487	\(< 0.0001\)
year2003	6.9133	0.7978	8.6650	\(< 0.0001\)
year2004	7.4849	0.8011	9.3438	\(< 0.0001\)
year2005	7.4077	0.8009	9.2494	\(< 0.0001\)
year2006	7.4445	0.8009	9.2951	\(< 0.0001\)
year2007	7.4704	0.8002	9.3360	\(< 0.0001\)
year2008	7.7316	0.8007	9.6564	\(< 0.0001\)
year2009	7.9143	0.8012	9.8778	\(< 0.0001\)
year2010	7.8865	0.8044	9.8047	\(< 0.0001\)
year2011	8.1415	0.8138	10.0046	\(< 0.0001\)
year2012	8.4769	0.8247	10.2784	\(< 0.0001\)
year2013	8.2752	0.8316	9.9513	\(< 0.0001\)
year2014	8.6468	0.8244	10.4891	\(< 0.0001\)
year2015	8.7346	0.8189	10.6665	\(< 0.0001\)
year2016	8.9358	0.8185	10.9170	\(< 0.0001\)
year2017	9.4246	0.8234	11.4456	\(< 0.0001\)
year2018	9.7763	0.8237	11.8692	\(< 0.0001\)
year2019	9.8116	0.8319	11.7948	\(< 0.0001\)
year2020	9.9146	0.8356	11.8650	\(< 0.0001\)
year2021	10.1348	0.8437	12.0121	\(< 0.0001\)
year2022	9.9886	0.8499	11.7524	\(< 0.0001\)
year2023	10.3002	0.8540	12.0610	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	7.8318	7.8318	301.8503	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	5.6701	5.6701	39.5730	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.6580	14.6580	115662.1015	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	14.2764	14.2764	14852.7179	\(< 0.0001\)

Table 25: Brown Swiss: Milk Yield - 1982-2023 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	-0.0329	0.0751	-0.44	0.6613
s(thi_mean_t0_3d):primiFx1	-0.1460	0.0792	-1.84	0.0653
s(days_in_milk_):multiFx1	3.1329	0.3803	8.24	\(< 1e-15\)
s(days_in_milk_):primiFx1	4.9629	0.5562	8.92	\(< 1e-18\)

Variance Component	Estimated \( \sigma \)
\(\sigma_\alpha\)	2.5454
\(\sigma_\iota\)	1.0788
\(\sigma_\phi\)	2.6594
s(thi_mean_t0_3d):multi	1.1793
s(days_in_milk_):primi	8.9385
s(days_in_milk_):multi	8.7987
s(thi_mean_t0_3d):primi	0.7122
Residual	3.0960

Table 26: Brown Swiss: Milk Yield - 1982-2023 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure 25: Brown Swiss: Milk Yield - 1982-2023 - Diagnostic Plot

THI Effect and Lactation Curve

Figure 26: Brown Swiss: Milk Yield - 1982 - 2023 - THI Effect and Lactation Curve

D.5.2: Split Period: Until 2010 - After 2010

D.5.2.1: Split Period: 1982 - 2010

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	12.3247	0.4735	26.0294	\(< 0.0001\)
parityprimiparous	-2.4485	0.0075	-325.8224	\(< 0.0001\)
year1983	2.3555	0.2880	8.1793	\(< 0.0001\)
year1984	3.0902	0.3440	8.9824	\(< 0.0001\)
year1985	3.5151	0.3664	9.5927	\(< 0.0001\)
year1986	3.4948	0.4159	8.4025	\(< 0.0001\)
year1987	3.3965	0.4621	7.3505	\(< 0.0001\)
year1988	3.4378	0.4688	7.3334	\(< 0.0001\)
year1989	4.0267	0.4867	8.2734	\(< 0.0001\)
year1990	4.2713	0.4891	8.7333	\(< 0.0001\)
year1991	4.6013	0.4934	9.3264	\(< 0.0001\)
year1992	4.7541	0.4960	9.5850	\(< 0.0001\)
year1993	4.8388	0.5027	9.6262	\(< 0.0001\)
year1994	4.8777	0.5096	9.5718	\(< 0.0001\)
year1995	5.0237	0.5100	9.8508	\(< 0.0001\)
year1996	5.0527	0.5128	9.8541	\(< 0.0001\)
year1997	5.6594	0.5195	10.8943	\(< 0.0001\)
year1998	6.3969	0.5163	12.3888	\(< 0.0001\)
year1999	6.3501	0.5144	12.3444	\(< 0.0001\)
year2000	6.5902	0.5145	12.8081	\(< 0.0001\)
year2001	7.3556	0.5128	14.3432	\(< 0.0001\)
year2002	7.5783	0.5121	14.7999	\(< 0.0001\)
year2003	7.8819	0.5125	15.3796	\(< 0.0001\)
year2004	8.3994	0.5135	16.3576	\(< 0.0001\)
year2005	8.3719	0.5238	15.9815	\(< 0.0001\)
year2006	8.4540	0.5307	15.9291	\(< 0.0001\)
year2007	8.5350	0.5307	16.0833	\(< 0.0001\)
year2008	8.9487	0.5369	16.6667	\(< 0.0001\)
year2009	9.2918	0.5435	17.0971	\(< 0.0001\)
year2010	9.4000	0.5478	17.1585	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	8.5317	8.5317	348.8165	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	5.9995	5.9995	24.7061	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.5636	14.5636	128068.7551	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	14.0529	14.0529	17306.6859	\(< 0.0001\)

Table 27: Brown Swiss: Milk Yield - 1982-2010 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	0.2406	0.0789	3.05	0.0023
s(thi_mean_t0_3d):primiFx1	0.1624	0.0793	2.05	0.0407
s(days_in_milk_):multiFx1	2.2987	0.3918	5.87	\(< 1e-08\)
s(days_in_milk_):primiFx1	3.1749	0.5430	5.85	\(< 1e-08\)

Variance Component	Estimated \( \sigma \)
\(\sigma_\alpha\)	2.4405
\(\sigma_\iota\)	1.0394
\(\sigma_\phi\)	2.4162
s(thi_mean_t0_3d):multi	1.8846
s(days_in_milk_):primi	7.3526
s(days_in_milk_):multi	7.7494
s(thi_mean_t0_3d):primi	0.7307
Residual	2.8776

Table 28: Brown Swiss: Milk Yield - 1982-2010 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure 27: Brown Swiss: Milk Yield - 1982-2010 - Diagnostic Plot

THI Effect and Lactation Curve

Figure 28: Brown Swiss: Milk Yield - 1982 - 2010 - THI Effect and Lactation Curve

D.5.2.2: Split Period: 2010 - 2023

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	21.2111	0.2414	87.8540	\(< 0.0001\)
parityprimiparous	-2.8924	0.0156	-185.6574	\(< 0.0001\)
year2012	0.2441	0.2084	1.1714	0.2415
year2013	0.0342	0.2784	0.1229	0.9022
year2014	0.4650	0.3250	1.4306	0.1526
year2015	0.5156	0.3134	1.6453	0.0999
year2016	0.7994	0.3036	2.6328	0.0085
year2017	1.1041	0.2984	3.7003	0.0002
year2018	1.6417	0.2974	5.5193	\(< 0.0001\)
year2019	1.8518	0.3009	6.1546	\(< 0.0001\)
year2020	1.8166	0.3105	5.8508	\(< 0.0001\)
year2021	2.0801	0.2758	7.5430	\(< 0.0001\)
year2022	1.7860	0.3374	5.2928	\(< 0.0001\)
year2023	2.0136	0.3992	5.0434	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	8.1345	8.1345	248.1362	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	6.1359	6.1359	53.3577	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.7627	14.7627	96671.5767	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	14.2234	14.2234	9759.0387	\(< 0.0001\)

Table 29: Brown Swiss: Milk Yield - 2011-2023 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	0.0611	0.0815	0.75	0.4535
s(thi_mean_t0_3d):primiFx1	-0.1991	0.0940	-2.12	0.0341
s(days_in_milk_):multiFx1	4.8333	0.3724	12.98	\(< 1e-37\)
s(days_in_milk_):primiFx1	5.2524	0.5628	9.33	\(< 1e-19\)

Variance Component	Estimated \( \sigma \)
\(\sigma_\alpha\)	2.6594
\(\sigma_\iota\)	1.1640
\(\sigma_\phi\)	3.3349
s(thi_mean_t0_3d):multi	1.6731
s(days_in_milk_):primi	9.1749
s(days_in_milk_):multi	10.8600
s(thi_mean_t0_3d):primi	1.0195
Residual	3.5347

Table 30: Brown Swiss: Milk Yield - 2011-2023 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure 29: Brown Swiss: Milk Yield - 2011-2023 - Diagnostic Plot

THI Effect and Lactation Curve

Figure 30: Brown Swiss: Milk Yield - 2011 - 2023 - THI Effect and Lactation Curve