Application of a finite mixture model to somatic cell scores of Italian goats

The objectives of this study were to apply a finite mixture model (FMM) to data for somatic cell count in goats and to compare the fit of the FMM with that of a standard linear mixed effects model. Bacteriological information was used to assess the ability of the model to classify records from healthy or infected goats. Data were 4518 observations of somatic cell score (SCS) and bacterial infection from both udder halves of 310 goats from 5 herds in Northern Italy. The records were from a complete production season, and were taken monthly from February to November 2000. Explanatory factors in both models included a 3-parameter regression on days in milk (DIM); fixed class effects of herd-test-day, parity group, and udder side (left or right); and random effects of goat and udder half within goat. In addition, the 2-component FMM included a fixed mean for the second component of the model (theoretically corresponding to infected udder halves), as well as an unknown probability of membership to a given putative infection status. A Bayesian statistical approach was used for the analysis with Gibbs sampling used to obtain draws from posterior distributions of parameters of interest. Two sampling chains of 200,000 cycles each were generated for each model. The FMM yielded a much lower estimate of residual variance than the standard model (1.28 vs. 3.02 SCS²), and a slightly higher estimate for the between-goat variance (1.79 vs. 1.48). The deviance information criterion (DIC) was used to compare the fit of the 2 models. The DIC was much lower for the FMM, indicating a better fit to the data. The FMM was able to classify correctly 60 and 48% of the healthy and infected observations, respectively. This was slightly higher than what would be expected from random classification, but not high enough for useful mastitis diagnosis. Nevertheless, increased precision of genetic evaluation is the goal of applying the FMM, rather than timely and accurate mastitis diagnosis. The results suggest that more research on FMM for SCS is merited and necessary for proper application.