## Mixed linear model solver

### Description

Given known variance components, Best Linear Unbiased Estimators (BLUE) of fixed effects and Best Linear Unbiased Predictors (BLUP) of random effects are obtained using Henderson's mixed model equations.

### Usage

 1 ghap.mme(fixed,random,weights=NULL,env.eff=FALSE,data,K,varcomp,verbose=TRUE) 

### Arguments

 fixed Formula describing the fixed effects part of the model, e.g. y ~ a + b + c ... If the model does not include any covariate simply state the response variable with an intercept, i.e. y ~ 1. random A character value with name of the column containing labels for the random effects. weights A numeric vector with residual weights. If not supplied, all residual weights are set to 1. env.eff A logical value indicating if permanent environmental effects should be included (default=FALSE). data A dataframe containing the data. K A covariance matrix for random effects. varcomp A numeric vector specifying the known variance components, in the following order: residual, correlated (e.g., additive genetic) and uncorrelated (e.g., permanent environmental) random effects variances, respectively. If env.eff=FALSE, the third variance component is ignored. verbose A logical value specfying whether log messages should be printed (default = TRUE).

### Details

Consider the model described in ghap.blmm and ghap.lmm. In the special case where variance components are known, this function uses Henderson's mixed model equations to solve for fixed and random effects.

### Value

The returned GHap.blmm object is a list with the following items:

 b A numeric vector containing the BLUE of fixed effects. u A numeric vector containing BLUP of correlated random effects. p A numeric vector containing the BLUP of permanent environmental effects. This vector is suppressed if env.eff=FALSE. varu A numeric value for the known variance of correlated random effects. varp A numeric value for the known variance of permanent environmental effects. This value is suppressed if env.eff=FALSE. vare A numeric value for the known residual variance. h2 A numeric value for the known variance explained by correlated random effects only. H2 A numeric value for the known variance explained by random effects. This value is suppressed if env.eff=FALSE. k A numeric vector containing the solutions for \mathbf{K}^{-1}\mathbf{\hat{u}}. This vector is used by the ghap.blup function. y A numeric vector containing the records used to fit the model. weights A numeric vector containing the residual weights used to fit the model. residuals A numeric vector containing residuals computed based on the BLUE and BLUP solutions. pdev Deviance evaluated at the BLUE and BLUP solutions.

### Author(s)

Yuri Tani Utsunomiya <ytutsunomiya@gmail.com>

### References

C. R. Henderson. Sire evaluation and genetic trends. Journal of Animal Science. 1973. Symposium: 10-41.

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 # #### DO NOT RUN IF NOT NECESSARY ### # # # Copy the example data in the current working directory # ghap.makefile() # # # Load data # phase <- ghap.loadphase("human.samples", "human.markers", "human.phase") # # # Subset data - randomly select 3000 markers with maf > 0.02 # maf <- ghap.maf(phase, ncores = 2) # set.seed(1988) # markers <- sample(phase$marker[maf > 0.02], 3000, replace = FALSE) # phase <- ghap.subsetphase(phase, unique(phase$id), markers) # rm(maf,markers) # # # Generate block coordinates based on windows of 10 markers, sliding 5 marker at a time # blocks <- ghap.blockgen(phase, 10, 5, "marker") # # # Generate matrix of haplotype genotypes # ghap.haplotyping(phase, blocks, batchsize = 100, ncores = 2, freq = 0.05, outfile = "example") # # # Load haplotype genotypes # haplo <- ghap.loadhaplo("example.hapsamples", "example.hapalleles", "example.hapgenotypes") # # # Compute kinship matrix # K <- ghap.kinship(haplo, batchsize = 100) # # # Quantitative trait with 50% heritability # # One major haplotype accounting for 30% of the genetic variance # sim <- ghap.simpheno(haplo = haplo, K = K, h2 = 0.5, g2 = 0.3, major = 1000,seed=1988) # # ### RUN ### # # # Solving for effects # model <- ghap.mme(fixed = phenotype ~ 1, random = "individual", data = sim$data, K = K # varcomp = c(sim$vare,sim$varu)) # plot(model$u,sim$u, ylab="True Breeding Value", xlab="Estimated Breeding Value") # cor(model$u,sim\$u) 

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