Table 3.

Goodness of fit of models MA, MG, and MGD and likelihood ratio test (χ ² -value and P-value) between models MG and MGD

	-2 log likelihood			Likelihood ratio test
	MA	MG	MGD	χ 2 -value	P-value
Milk yield	31531.5	31488.1	31484.3	3.8	0.026
Fat yield	18363.1	18299.5	18295.9	3.6	0.029
Protein yield	17852.5	17824.6	17817.6	7.0	0.004
Somatic cell score	6072.9	6055.0	6050.6	4.4	0.018
Milkability	-1243.5	-1297.6	-1323.9	26.3	1.46*10-7
Stature	9979.0	9907.9	9908.4	-0.5	1.000
Udder score	9916.5	9902.4	9902.5	-0.1	1.000
Udder depth	5287.9	5239.7	5238.5	1.2	0.137
Feet and legs score	9884.9	9880.9	9880.9	0.0	1.000

The measures of goodness of fit (-2 log likelihood) for models MA, MG and MGD are reported as well as the likelihood ratio test statistics ($\mathit{\chi ²}-\mathit{\text{value}}=-2ln\frac{\mathit{\text{likelihood}}\mathit{\text{for}}\mathit{MG}}{\mathit{\text{likelihood}}\mathit{\text{for}}\mathit{MGD}}$) between models MG and MGD and the corresponding P-values.