Question: Lush (1945, 95) discusses different estimates of heritability for milk-fat percentage in dairy cattle herds. Heritability is defined to be the percentage of variability in fat percentage that is attributable to differences in the heredity of different individuals; the remainder of the variability is attributed to differences in environment.
He notes that when the herd was treated as an SRS, the estimate of heritability was about 0.8; when fat percentage for daughters was regressed on fat percentage for dams and where each dam was represented by only one record, the estimate of heritability decreased to below 0.3. From a sampling perspective, why are these estimates so different? Discuss how you would analyze the full-herd data from both a design-based and a model-based perspective.