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 problems, 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 problems, AI-REML fails 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.

OPTION conv_crit 1d-12

Convergence criterion (default 1d-10).

OPTION maxrounds 500

Maximum rounds (default 5000). When it is negative, the program calculates BLUP without running REML.

OPTION EM-REML 10

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

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 s.e.

OPTION missing -1

Set 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 use ln(a0, a1, a2, …) to make these values.

Heterogeneous residual variances for multiple traits

OPTION hetres_pos 10 10 11 11

Specify the position of covariables (trait first).

OPTION hetres_pol 4.0 4.0 0.1 0.1 0.01 0.01

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