Application of a Mixed Normal Mixture Model for the Estimation of Mastitis-Related Parameters

The current methodology for estimating genetic parameters for SCC (SCS) does not account for the difference in SCS between healthy cows and cows with an intramammary infection (IMI). We propose a two-component finite mixed normal mixture model to estimate IMI prevalence, separate SCS subpopulation means, individual posterior probabilities of IMI, and SCS variance components. The theory is presented and the expectation-conditional maximization algorithm is utilized to compute maximum likelihood estimates. The methodology is illustrated on two simulated data sets based on the current knowledge of SCS parameters. Maximum likelihood estimates of IMI prevalence and SCS subpopulation means were close to simulated values, except for the estimate of IMI prevalence when both subpopulations were almost confounded. Individual posterior probabilities of IMI were always higher among infected than among healthy cows. Error and additive variance components obtained under the mixture model were closer to simulated values than restricted maximum likelihood estimates obtained assuming a homogeneous SCS distribution, especially when subpopulations were completely separated and when mixing proportion was highest. Convergence was linear and rapid when priors were chosen with caution. The advantages of the methodology are demonstrated, and its feasibility for large data sets is discussed.