From peterchi at u.washington.edu  Thu Mar  1 23:56:54 2012
From: peterchi at u.washington.edu (Peter Chi)
Date: Thu, 1 Mar 2012 14:56:54 -0800 (PST)
Subject: [Inla-commits] Heritability under a zero-inflated Poisson model
Message-ID: <alpine.LRH.2.01.1203011456540.7863@hymn12.u.washington.edu>



Hello all,

I am trying to estimate heritability of a trait under the assumption of a zero-inflated Poisson distribution, using the AnimalINLA extension package.

I am a bit confused about the specification of lambda as described in the Holand 2011 paper. They suggest estimating lambda as \sum{y_i} / \sum{n_i} which I think for me amounts simply to the mean of my trait value, as each of my n_i's are 1. 

So, 2 questions:
1) Can anyone explain the justification for this choice of lambda? I've looked at one of the reference papers (Vazquez 2009) but I'm still unclear. Holand et al. state in their eqn (5) that heritability is estimated as: 
\sigma^2_u / (\sigma^2_u + \lambda^{-1})

So I guess \lambda^{-1} is supposed to represent the environmental variance, but I'm not sure why this would be the case.

2) As shown above, the denominator has \lambda^{-1} in it. But, I have suspicions that the estimated posterior distributions of heritability from animal.inla have been calculated with simply \lambda in the denominator, not \lambda^{-1}... Does anyone have experience with this?

Thanks!


Peter