Genet. Sel. Evol. 38 (2006) 343-358
DOI: 10.1051/gse:2006008

Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

Kaarina Vuori, Ismo Strandén, Marja-Liisa Sevón-Aimonen and Esa A. Mäntysaari

MTT Agrifood Research Finland, Biotechnology and Food Research, Biometrical Genetics, FIN-31600 Jokioinen, Finland

(Received 6 July 2005; accepted 27 January 2006; published online 23 June 2006)

Abstract - A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.

Key words: Gompertz function / non-linear mixed effects / variance components / breeding values / likelihood approximation

Correspondence and reprints: kaarina.vuori@mtt.fi

© INRA, EDP Sciences 2006