Threshold Model

R script: thr.txt
Literature 1: Mrode, R.A. 2005. Linear Models for the Prediction of Animal Breeding Values. CAB International, Oxon, UK.
Literature 2: Gianola, D. and Foulley, J.L. 1983. Sire Evaluation for Ordered Categorical Data with a Threshold Model. Genetic Selection Evolution.

Given the components of MME, fit non-linear (threshold) model for categorical traits.

Here is a numerical application from Mrode (2005), example 10.1, concerning the calving ease scores from 28 male and female calves. Calving ease was scored as 1:normal birth, 2:slight difficulty, 3:extreme difficulty.

# pedigree
> s <- c(0,0,1,3)
> d <- c(0,0,0,0)
> Ainv <- quass(s,d)
>
# X matrix
> X <- matrix(c(rep(0,9), rep(1,11),    0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,1,0    ), ncol=2, nrow=20)
>
> # Z matrix
> Z <- matrix(c(1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0, 0,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0, 
+   0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,     0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1), ncol=4, nrow=20  )
>
> # number of categories
> ncats <- 3
>
> # category of response
> cat <- matrix(c(1,1,1,0,1,3,1,0,1,2,1,0,1,1,0,0,0,1,2,2,    0,0,0,1,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,0,  
+   0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0), ncol=3)
>
> # initial values for solutions
> inits <-  matrix(c(0.468, 1.080, rep(0, 6)))
>
> # variance components ratio
> ratio <- 1/(1/19)
>
> disp <- TRUE

The thr function gives:

> thr(Ainv, X, Z, ncats, cat, inits, ratio, disp)

iteration  1 
            [,1]
[1,]  0.44100858
[2,]  1.04479217
[3,]  0.28686921
[4,] -0.35832281
[5,] -0.04152769
[6,]  0.05785352
[7,]  0.03985081
[8,] -0.06517799

iteration  2 
            [,1]
[1,]  0.43750215
[2,]  1.06613002
[3,]  0.27630322
[4,] -0.35772771
[5,] -0.04305507
[6,]  0.05859682
[7,]  0.04097484
[8,] -0.06532759

iteration  3 
            [,1]
[1,]  0.43781529
[2,]  1.06746240
[3,]  0.27736820
[4,] -0.35891673
[5,] -0.04340028
[6,]  0.05917583
[7,]  0.04121130
[8,] -0.06596911

iteration  4 
            [,1]
[1,]  0.43777081
[2,]  1.06752821
[3,]  0.27735389
[4,] -0.35895477
[5,] -0.04342556
[6,]  0.05920580
[7,]  0.04123036
[8,] -0.06599831

Threshold Model

List

Threshold Model