AIREMLF90

A modification of REMLF90 with computing by the Average-Information
Algorithm.

Written by Shogo Tsuruta, University of Georgia, 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. 


Several options are avaiable:


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 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.

OPTION sol se

    store solutions and s.e.

OPTION residual

    y-hat and residual will be shown in yhat_residual.

OPTION missing -1

    set the missing observation (default 0).

OPTION constant_var 5 1 2

    The effect number (5), the first trait number (1), and the second trait number (2), implying the covariance between traits 1 and 2 for effect 5.


# 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 mutiple 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).