Multiple traits model

Multiple traits model is used for estimating genetic correlation among traits of one population or the same traits of multiple populations, both balanced or unbalanced records (v 1.5.0 or later) are now acceptable and there is no limitation on the number of traits used in analysis for HIBLUP. Moreover, users can appoint different covariates, fixed and random effects for different traits. PBLUP, GBLUP, SSGBLUP are all available for multiple traits model, HIBLUP can automatically switch to one of them according to the provided file. Always remember that there is no need to adjust the order of individuals or markers to be consistent among different files, HIBLUP can do it automatically.
Taking GBLUP for an example, the multiple model can be achieved by following command:

./hiblup --multi-trait
         --pheno demo.phe
         --pheno-pos 8 9 10
         --qcovar 4,5 5 4
         --dcovar 2,3 0 2
         --rand 6,7 7 0
         --xrm demo.GA,demo.GD  # same with --bfile demo --add --dom
         --vc-method AI
         --ai-maxit 30
         --threads 32
         --out demo

The detailed format of input files please refer to phenotype, genotype. The way of how to set covariates (--qcovar), fixed (--dcovar) and random (--rand) effect for multiple traits, please refer to here.

There are 5 types of algorithms for variance components estimation:
“AI”, “EM”, “HE”, “EMAI”, “HI”, where “AI” is AIREML,”EM” is EMREML, and “HE” represents HE regression, “HI” is “HE+AI”, which uses the outcome of HE regression as the start values of AIREML, users can choose one of them by flag --vc-method, and change the maximum iteration number for AIREML and EMREML by flag --ai-maxit and --em-maxit respectively. For “HE” regression, if covariates for fixed effects are provided, HIBLUP will first regress the phenotype on these, then perform HE Regression using the residuals, the standard error(SE) of HE is computed by Jackknife resampling strategy at 100 repeats. By default, HIBLUP doesn’t calculate the random effects for HE regression, user can add a flag --he-pred to output it, and only in this situation, the flag --pcg can be used for fast computing on very large dataset, which we call it as “HE+PCG” strategy.

By default, HIBLUP fits the covariance of residuals among traits, users can add the flag --ignore-cove to ignore residual covariance for multiple traits model.

Several files will be generated:

demo.vars: the variance, heritability and SE of all random effects for all traits:

Item	Var	Var_SE	h2	h2_SE
tr1_loc	13.73854	9.9309	0.11739	0.07538
tr1_dam	2.29288	3.18932	0.01959	0.02731
tr1_demo.GA	61.35173	9.57171	0.52423	0.06964
tr1_demo.GD	29.93077	6.27996	0.25575	0.06022
tr1_e	9.71917	1.67088	0.08305	0.01696
tr2_dam	3.42172	3.80424	0.02971	0.03308
tr2_demo.GA	63.59	10.52058	0.55219	0.06017
tr2_demo.GD	38.14332	7.27491	0.33122	0.06696
tr2_e	10.00395	1.63578	0.08687	0.01578
tr3_demo.GA	21.03906	6.94184	0.2203	0.0668
tr3_demo.GD	15.25593	10.56861	0.15974	0.10919
tr3_e	59.20689	9.04084	0.61996	0.09801

demo.covars: the co-variance, correlation and SE of all traits for all genetic random effects:

Item	COVar	COVar_SE	r	r_SE
tr1:tr2_demo.GA	46.6899	8.56852	0.747524	0.171364
tr1:tr3_demo.GA	16.3376	5.96333	0.454749	0.185599
tr2:tr3_demo.GA	12.3489	6.21401	0.337612	0.157671
tr1:tr2_demo.GD	26.9273	4.65452	0.796922	0
tr1:tr3_demo.GD	-2.25039	4.95673	-0.105301	0.23413
tr2:tr3_demo.GD	8.23124	5.21494	0.341194	0.259133
tr1:tr2_e	0.24039	1.17428	0.024379	0.119333
tr1:tr3_e	-1.10713	2.87487	-0.0461537	0.11985
tr2:tr3_e	-4.80127	2.85341	-0.197284	0.128375

demo.*.anova: the variance analysis table of covariates, fixed effects for different traits.
demo.*.beta: the estimated coefficients and SE of covariates, fixed effects for different traits.
demo.*.rand: the estimated environmental random effects, genetic random effects (the column named “PA”, “GA”, or “HA” is the list of breeding values for phenotypic and non-phenotypic individuals) and residuals for different traits.

Users can specify the start values for all unknown variance and co-variance to --vc-priors and --covc-priors, the way of how to input the genetic components can be found at here.

HIBLUP only estimates co-variance for genetic random effect and residual effect, not for environmental random effect, therefore at least one genetic random effect should be included in the model, which can be from pedigree (--pedigree), genotype (--bfile) or XRMs (--xrm). If users insist on estimating correlation for environmental random effects, just make relationship matrix for those random effects by the flag --make-xrm (see the chapter “XRM for environmental random effect” here), then assign it to the option --xrm.