### Table of Contents

# THRGIBBS3F90

## Summary

The GIBBS3F90 version with heterogenous residual variances for THRGIBBS1F90.

## Parameters

The parameter file is the same as for THRGIBBS1F90 except for heterogeneity.

## Options

OPTION cat 0 0 2 5

“0” indicate that the first and second traits are linear. “2” and “5” indicate that the third and fourth traits are categorical with 2 (binary) and 5 categories.

OPTION fixed_var all

Store all samples for solutions in “all_solutions” and posterior means and SD for all effects in “final_solutions”, assuming that (co)variances in the parameter file are known.

OPTION fixed_var all 1 2 3

Store all samples for solutions in “all_solutions” and posterior means and SD for 1, 2, and 3 effects in “final_solutions”.

OPTION fixed_var mean

Only posterior means and SD for solutions are calculated for all effects in “final_solutions”.

OPTION fixed_var mean 1 2 3 Only posterior means and SD for solutions are calculated for effects 1, 2, and 3 in "final_solutions".

OPTION solution all

Caution: this option will create a huge output solution file when you run many rounds and/or use a large model. Store all samples for solutions in “all_solutions” and posterior means and SD for all effects. The file “all_solutions” could be very large.

OPTION solution all 1 2 3

Caution: this option will create a huge output solution file when you run many rounds and/or use a large model. Store all samples for solutions in “all_solutions” and posterior means and SD for 1, 2, and 3 effects. The file “all_solutions” could be very large.

OPTION solution mean

Only posterior means and SD for solutions are calculated for all effects in “final_solutions”.

OPTION solution mean 1 2 3

Only posterior means and SD for solutions are calculated for effects 1, 2, and 3 in “final_solutions”.

OPTION cont 10000

“10000” is the number of samples run previously. The user can restart the program from the last run.

OPTION prior 5 2 -1 5

The (co)variance priors are specified in the parameter file.

Degree of belief for all random effects should be specified using the following structure:

OPTION prior eff1 db1 eff2 db2 … effn dbn -1 dbres

effx correspond to the effect number and dbx to the degree of belief for this random effect, -1 corresponds to the degree of belief of the residual variance.

In this example 2 is the degree of belief for the 5th effect, and 5 is the degree of belief for the residual.

OPTION seed 123 -432

Two seeds for a random number generator can be specified.

OPTION thresholds 0.0 1.0 2.0

Set the fixed thresholds. No need to set 0 for binary traits.

OPTION residual 1

Set the residual variance = 1. For binary traits, the residual variance is automatically set to 1, so no need to use this option.

OPTION pos_def

Specify checking pos-def for fixed effects.

OPTION censored 1 0

Negative values for the categorical trait in the data set indicate censored records. “1 0” determines that the first categorical trait is censored and the second uncensored.

OPTION SNP_file snp

Specify the SNP file name to use genotype data.

OPTION hetres_int col nlev

where col is column in the data file that selects which residual (co)variance to select, and nlev is the maximum number of levels. Different residual (co)variances need to be numbered consecutively starting from 1.

Initially, all residual (co)variances are assigned identical (co)variances as in the parameter file. During the estimation, (co)variances that are 0 in the parameter file will not be estimated.

The number of observations per each subset must be large enough to allow the estimation, and the missing-trait pattern should be similar. The program has not been tested in multiple-trait situations when one trait is present in some subclasses but always missing in another subclass.

number of samples and length of burn-in?

In the first run, if you have no idea about the number of samples and burn-in, just type your guess (10000 or whatever) for samples and (0) for burn-in. You may need 2 or 3 runs to figure out the convergence.

Give n to store every n-th sample?

Gibbs samples are usually highly correlated, so you do not have to keep all samples. Maybe every 10th,20th, 50th, …

To check the convergence and to calculate posterior means and SD, run postgibbsf90.

OPTION hetres_int 5 10

The position “5” to identify the interval in the data file and the number of intervals “10” for heterogeneous residual variances.

OPTION hetres_var x11 x12 x13 x21 x22 x23 x31 x32 x33 y11 y12 y13 y21 y22 y23 y31 y32 y33 : : : z11 z12 z13 z21 z22 z23 z31 z32 z33

Give residual covariances for each interval (e.g., x, y, and z).