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Selecting linear-score distributions for modelling milk-culture results
H G Allore1, D J Wilson, H N Erb
1Department of Animal Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, NY 14853, USA. hga1@cornell.edu
Preventive Veterinary Medicine
|March 21, 1998
Summary
Weibull and beta distributions effectively model dairy cow somatic cell counts for mastitis research. These models improve simulation accuracy for milk quality by fitting linear score data better than normal distributions.
Area of Science:
- Veterinary Epidemiology
- Dairy Science
- Statistical Modeling
Background:
- Somatic cell count (SCC) is a key indicator of bovine mastitis and milk quality.
- Accurate modeling of SCC distribution is crucial for developing effective mastitis simulation models.
- Previous models often used normal distributions, which may not adequately represent SCC data.
Purpose of the Study:
- To identify appropriate probability distributions for logarithmically transformed somatic cell counts (linear score) in dairy cattle.
- To evaluate the fit of different distributions for use in a mastitis and milk quality simulation model.
- To compare distribution fits based on bacterial culture results and bulk-tank SCC levels.
Main Methods:
- Retrospective analysis of survey data from 65 dairy herds in New York (1993-1995).
- Estimation of probability density functions using maximum-likelihood estimators for individual-cow linear scores.
- Goodness-of-fit tests (Anderson-Darling, Kolmogorov-Smirnov, chi-squared) were used to compare Weibull, beta, and normal distributions.
Main Results:
- The Weibull distribution demonstrated a strong fit, ranking among the top three for 14 out of 15 culture-result-specific bulk-tank SCC groups.
- The beta distribution also showed a good fit, ranking in the top three for nine groups, and has a logical relationship with linear score.
- The normal distribution provided a poorer fit compared to Weibull and other distributions for culture-negative and coagulase-negative staphylococci samples.
Conclusions:
- Weibull and beta distributions provide an adequate fit for modeling individual-cow linear scores in dairy cattle, outperforming the normal distribution.
- These distributions improve the accuracy of simulation models for mastitis and milk quality by better representing SCC data.
- The use of Weibull and beta distributions reduces the need for data truncation and minimizes systematic errors in modeling.