A modification of REMLF90 for estimating variances with the Average-Information algorithm. Initially written by Shogo Tsuruta in 03/99-07/99.
AIREMLF90 uses a second derivative REML algrithm with extra heuristics, as is described in Jensen et al. (1996-7). For most models, it converges in far fewer rounds than EM-REML as implemented in REMLF90. While typically REMLF90 takes 50-300 rounds to converge, AIREMLF90 converges in 5-15 rounds and to a higher accuracy. For selected models, AI-REML may fail to converge when the covariance matrix is close to non-positive definite. Adjust sensitivity of the program by setting the appropriate tolerance or setting good starting values. The final results will be saved in “AIREMLF90.log”.
See PREGSF90 with genotypes (SNP) for options.

OPTION conv_crit 1d-12

Convergence criterion (default 1d-10).

OPTION maxrounds 1000

Maximum rounds (default 5000). When the number < 2, the program calculates BLUP without iterating REML.

OPTION EM-REML 10

Run EM-REML (REMLF90) for first 10 rounds to get initial variances within the parameter space (default 0).

OPTION use_yams

Run the program with YAMS (modified FSPAK). The computing time can be dramatically improved.

OPTION tol 1d-12

Tolerance (or precision) (default 1d-14) for positive definite matrix and g-inverse subroutines.
Convergence may be much faster by changing this value.

OPTION sol se

Store solutions and those s.e.

OPTION residual

y-hat and residuals will be included in “yhat_residual”.

OPTION missing -999

Specify the missing value (default 0).

Heterogeneous residual variances for a single trait

OPTION hetres_pos 10 11

Specify the position of covariables.

OPTION hetres_pol 4.0 0.1 0.1

Initial values of coefficients for heterogeneous residual variances using ln(a0, a1, a2, …) to make these values.

Heterogeneous residual variances for multiple traits
Convergence will be very slow with multiple trait heterogeneous residual variances

OPTION hetres_pos 10 10 11 11

or

OPTION hetres_pos 10 11 12 13

Specify the position of covariables (trait first). “10 10” or “10 11” could be linear for first and second traits.
“11 11” or “12 13” could be quadratic.

OPTION hetres_pol 4.0 4.0 0.1 0.1 0.01 0.01

Initial values of coefficients for heterogeneous residual variances using ln(a0, a1, a2, …) to make these values (trait first).
“4.0 4.0” are intercept for first and second traits.
“0.1 0.1” could be linear and “0.01 0.01” could be quadratic.
To transform back to the original scale, use exp(a0+a1*X1+a2*X2).

OPTION SNP_file snp

Specify the SNP file name to use genotype data.

OPTION se_covar_function <label> <function>

Calculate SD for function of (co)variances by repeated sampling of parameters estimates from their asymptotic, multivariate normal distribution, following Meyer and Houle 2013.

OPTION se_covar_function P G_2_2_1_1+G_2_3_1_1+G_3_3_1_1+G_4_4_1_1+R_1_1

OPTION samples_se_covar_function <n>

Set the number of samples to calculate SE for function of (co)variances.
default value 5000

OPTION out_se_covar_function

Indicate to store in file samples of (co)variances function for postprocessing (histogram, etc.)