Supported features

Supported operations

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

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

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

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 $$C$$