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Random regression (RR) models have become a popular choice for the analysis of longitudinal data or 'repeated' records. Typically, analyses require numerous parameters, i.e. (co)variances between RR coefficients and measurement error variances, to be estimated, especially if the model of analysis includes additional random effects such as maternal effects. Programs for RR model analysis using restricted maximum likelihood (REML) are available. However, the high computational demands of REML analyses for RR models severely limit the feasibility of RR analyses for data sets sufficiently large to support estimation of the pertaining (co)variance components, in particular for models fitting many RR coefficients.

Bayesian analyses using Gibbs sampling provide an alternative which is markedly simpler to implement than REML. Whilst the range of models which can be accommodated via Gibbs sampling may be more restrictive and the total computing time required may be longer than for corresponding REML analyses, memory requirements are substantially less. Hence Bayesian methodology readily facilitates large scale analyses. Apart from these practical advantages, of course, it provides estimates of complete sampling distributions rather than just simple point estimates.

Purpose

RRGIBBS performs a single task : the analysis of a simple class of RR models using Bayesian methodology. Models may involve :

• multiple fixed effects, including cross-classified effects and 'standard' covariables, as well as fixed regression(s) on Legendre polynomials of the meta-meter;
• sets of random regression coefficients, regressing on orthogonal polynomials or user-defined functions of a single, continuous covariable, the so-called 'meta-meter';
• multiple random effects, distributed proportionally to an identity matrix or the numerator relationship matrix between animals,
• different orders of polynomial fit for each random effect,
• homogeneous or heterogeneous measurement error variances modelled as a step function of the covariable,
• a single trait only.

Model specification is via a parameter file. The run time behaviour of RRGIBBS can be modified by a number of command line options. RRGIBBS is a 'no-frills' program. It basically offers little more than a reasonably efficient Gibbs sampler for a range of random regression analyses. The main output are files with the successive samples of (co)variance components drawn, ready for your favourite post-Gibbs analysis. In addition, limited summary information is produced, including estimates of covariance matrices among RR coefficients and measurement error variances obtained as means over samples (after 'burn-in'), and approximate 95% highest posterior density regions.

Computing environment

RRGIBBS is written in standard Fortran 95 and self-contained, except for routines to generate random numbers. The source code is available for downloading. Compiled versions are available for : Linux, Compaq Alpha stations and SUN work stations.

Availability

RRGIBBS is available free of charge to the scientific community under the conditions that it remains my copyright, that it is not modified other than to adapt it to the local computing environment or for personal research, and that its use is credited in any publications.

Reference

Meyer, K. (2002). RRGIBBS - A program for simple random regression analyses via Gibbs sampling. Seventh World Congress on Genetics Applied to Livestock Production, Montpellier, France, August 19-23, 2002, Paper No. 28-27, 2pp. View summary - Download paper (2 pages, pdf file, 0.1Mb)