# Performs genomic prediction based on SNP codata. The main function of the package. The input includes response values, a design matrix for the fixed effects, a matrix with SNP genotype data and a design matrix for the SNP codata. ```r genomicEBV.w.codata(y, X, Z, X.SNPcodata, Z.test = NULL, max.iter = 100, conv.crit = 1e-5) ``` ## Arguments - `y`: Response values - `X`: Design matrix for the fixed effects - `Z`: Genotype matrix with element values of 0, 1 or 2 - `X.SNPcodata`: Design matrix for the linear predictor of the SNP variances. - `Z.test`: An optional genotype matrix for a test data set. - `max.iter`: The maximum number of iterations - `conv.crit`: The value of the convergence criterion. ## Details By specifying the matrix `Z.test` in the input, the function computes predicted genomic breeding values for an out-of-sample data set. ## Returns - **gEBV**: Genomic breeding values - **predicted.gEBV**: Genomic breeding values based on the genotypes in `Z.test` - **w**: Computed SNP weights - **u**: Fitted SNP effects - **beta**: Fitted fixed effects - **disp.beta**: Fitted coefficients in the linear predictor for the SNP variance model - **Converge**: Shows whether the algorithm has converged or not - **iter**: The number of iterations used ## Author(s) Lars Ronnegard ## Examples ```r ####### #Simulation part set.seed(1234) N <- 200 #Number of individuals k <- 300 #Number of SNPs with all marker positions including a QTL Z1 <- matrix(0, N, k ) Z2 <- matrix(0, N, k ) Z1[1:N, 1] <- rbinom(N, 1, 0.5) #Simulated phased SNP matrices Z2[1:N, 1] <- rbinom(N, 1, 0.5) LD.par <- 0.2 #A parameter to simulate LD. 0 gives full LD, and 0.5 no LD for (j in 2:k) { Z1[1:N, j] <- abs( Z1[1:N, j-1] - rbinom(N, 1, LD.par) ) Z2[1:N, j] <- abs( Z2[1:N, j-1] - rbinom(N, 1, LD.par) ) } Z <- Z1 + Z2 #Genotypic SNP matrix x1 <- c(rep(1,k/2), rep(0,k/2)) #An indicator for the SNPs. #The first k/2 SNPs and the last k/2 have different variances #Simulate linear predictor for the random effect variance lin.pred <- 0 + 2*x1 X.snp <- model.matrix( ~ x1 ) #Corresponding design matrix u <- rnorm(k, 0 , sqrt( exp(lin.pred) )) #Took the square root here because it is the SD that is specified. #and exp() because we are modelling a log link. u.scaled <- u/as.numeric( sqrt( var( crossprod(t(Z), u) )) ) #Scaled by the variance of the breeding values e <- rnorm(N) #A residual variance mu <- 0 y <- mu + crossprod(t(Z),u.scaled) + e ###### #Estimation part mod1 <- genomicEBV.w.codata(y = as.numeric(y), X = matrix(1, N, 1), Z = Z, X.SNPcodata = X.snp) #To fit gBLUP just specify X.SNPcodata = matrix(1, k, 1) cat("Correlation between true and estimated BV for the codata model:") cat(cor(crossprod(t(Z),u.scaled), mod1$gEBV), "\n") ```

genomicEBV.w.codata function