Population mean-uncentered and mean-centered

Simulation parameters ( informal summary)

• A sire mate 40 dams for 15 generations.
• Heritability for Fat percent is 00.35 and milk volume is 0.22
• Fat yield is the product of fat percent and milk volume.
• Ten chromosome, each chromosome has 2000 loci.
• Each of the trait was controlled by 1000 loci.
• BayesC model was run with ID and genotype as an input.
• The 15 generation phenotypes were masked and their EBV were computed using single trait, multi-trait and structural equation for two circumstance.

1. Mean un-centered (mean phenotypic value for milk volume was -1.5 and fat percent is0.188)
2. Mean centered (mean value for milk volume: 13.08 and fat percent: 5.16 was added to the simulated phenotype).

The result of the correlation between the EBV and the masked phenotype is displayed in the following Table. Column 3 is the correlation between the mean-centered phenotype and the EBV , column 4 is the correlation between the mean-centered phenotype and EBV.

Mean un-centerred and mean centered correlation Table for three traits and three methods

Summary

1. For a given method, the accuracy of the un-centered mean is larger than the mean centered phenotype. I expect to get similar result. I am looking into it again. I do not get the reason why mean centering has an effect.
2. For a given method, the accuracy of fat yield is substantially lower for centered mean than un-centered mean. This makes sense because centering for fat yield is different for the two traits ( 13.08 and 5.16). I expect if both traits were centered with the same value the difference in accuracy between centered and un-centered would be lower.
3. The accuracy for structural equation modeling for fat yield is lower particularly for mean centered phenotype than the un-centered phenotype. This also makes sense because the fat yield in this analysis is non-linear function of the milk volume and fat percent( product of milk volume and fat percent, non-linear function).The non-linearity increases when the two phenotypes are centered with different values. Structural equation modeling extracts primarily linear information. The structural equation model might become better when we transform the phenotypes in to log scale. I am working on this.

Next task

1.At the moment, I am running with log transformation for mean centered phenotype. Summarize the log transformed result, if the result makes sense move to simulation with crossbred population. 2. Fit Deep learning models. I need to read a bit on this topic.