## The Annals of Applied Statistics

### Local adaptation and genetic effects on fitness: Calculations for exponential family models with random effects

#### Abstract

Random effects are implemented for aster models using two approximations taken from Breslow and Clayton [J. Amer. Statist. Assoc. 88 (1993) 9–25]. Random effects are analytically integrated out of the Laplace approximation to the complete data log likelihood, giving a closed-form expression for an approximate missing data log likelihood. Third and higher derivatives of the complete data log likelihood with respect to the random effects are ignored, giving a closed-form expression for second derivatives of the approximate missing data log likelihood, hence approximate observed Fisher information. This method is applicable to any exponential family random effects model. It is implemented in the CRAN package aster (R Core Team [R: A Language and Environment for Statistical Computing (2012) R Foundation for Statistical Computing], Geyer [R package aster (2012) http://cran.r-project.org/package=aster]). Applications are analyses of local adaptation in the invasive California wild radish (Raphanus sativus) and the slender wild oat (Avena barbata) and of additive genetic variance for fitness in the partridge pea (Chamaecrista fasciculata).

#### Article information

Source
Ann. Appl. Stat., Volume 7, Number 3 (2013), 1778-1795.

Dates
First available in Project Euclid: 3 October 2013

https://projecteuclid.org/euclid.aoas/1380804816

Digital Object Identifier
doi:10.1214/13-AOAS653

Mathematical Reviews number (MathSciNet)
MR3127968

Zentralblatt MATH identifier
06237197

#### Citation

Geyer, Charles J.; Ridley, Caroline E.; Latta, Robert G.; Etterson, Julie R.; Shaw, Ruth G. Local adaptation and genetic effects on fitness: Calculations for exponential family models with random effects. Ann. Appl. Stat. 7 (2013), no. 3, 1778--1795. doi:10.1214/13-AOAS653. https://projecteuclid.org/euclid.aoas/1380804816

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