Supported features

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Supported operations[edit]

Currently lmt support the following operations on linear mixed models:

  • Solving for BLUP and BLUE solutions conditional on supplied variances for random and fixed factor, respectively;
  • Gibbs sampling of variance components in single pass and blocked mode;
  • MC-EM-REML estimation of variance components
  • Sampling (block)diagonal elements of the inverse of the mixed model coefficient matrix
  • Solving for (block)diagonal elements of the inverse of the mixed model coefficient matrix

Supported factors and variables[edit]

lmt supports

  • fixed
  • random factors
  • classification variables
  • continuous co-variables, which can be nested. For continuous co-variables lmt support user-defined polynomials and hard coded Legendre polynomials up to order 6.
  • genetic group co-variables

All classification and co-variables can be associated to a fixed or random factor.

Supported variance structures[edit]

For random factor lmt supports variance structures of

  • structure $$\Gamma\otimes\Sigma$$, where $$\Sigma$$ is an dense symmetric positive definite matrix, and
  • $$\Theta_L(\Gamma\otimes I_{\Sigma})\Theta_L^{'}$$, where $$\Theta$$ is symmetric positive definite block-diagonal matrix of $$n$$ symmetric positive definite martices $$\Sigma_i, i=1,..,n$$, $$\Theta_L$$ is the lower Cholesky factor of $$\Theta$$ and $$I_{\Sigma}$$ is an identity matrix of dimension $$\Sigma_i$$.

When solving linear mixed models $$\Sigma$$ and $$\Gamma$$ are user determined constants, whereas when estimating variances $$\Gamma$$ is a user determined constant and $$\Sigma$$ is a function of the data.

Supported type for $$\Gamma$$ are

  • an identity matrix
  • an arbitrary positive definite diagonal matrix
  • a pedigree-based numerator relationship matrix $$A$$ which may contain meta-founders
  • a pedigree- and genotype-based relationship matrix $$H$$ which may contain meta-founders
  • a user-defined(u.d.) symmetric, positive definite matrix of which inverse is supplied
    • as a sparse upper-triangular matrix stored in csr format
    • as a dense matrix
  • a co-variance matrix of a selected auto-regressive process

Further lmt supports special variance structures which are not covered by the above description

  • SNP-BLUP variance for the model of Liu and Goddard 2014 with the option to model marker co-variances as above.

Supported linear mixed model solvers[edit]

lmt supports

  • a direct solver requiring to explicitly build the linear mixed model equations left-hand-side coefficient matrix($$C$$)
  • an iteration-on-data pre-conditioned gradient solver which does not require $$C$$

Supported features related to genomic data[edit]

  • direct use of genomic marker data
  • building of genomic relationship matrices($$G$$) from supplied genomic data
  • uploading of a u.d. $$G$$
  • adjustment of $$G$$ to $$A_{gg}$$ in SS-G-BLUP and SS-SNP-BLUP
  • solving Single-Step-G-BLUP models
  • Variance component estimation for Single-Step-G-BLUP models
  • solving Single-Step-T-BLUP models
  • solving Single-Step-SNP-BLUP models
  • calculation of true H matrix diagonal elements
  • all Single-Step models can be run from "bottom-up", that is the user supplies the genotypes and all necessary ingredients(e.g. $$G$$) are built on the fly.

Supported pedigree types[edit]

  • ordinary pedigrees
  • probabilistic pedigrees with an unlimited number of parent pairs per individual
  • genetic group pedigrees
  • meta-founder pedigrees
  • ignoring of inbreeding
  • iterative derivation of inbreeding coefficients