Calculating the ICC

[SamPassmore]

Hi @rdinnager,

I was just reviewing the calculation for ICC and wanted to double check something with you.

Via email you suggested this formula: phylo_sd^2 / (spatial_var^2 + phylo_sd^2 + 1 + (pi^2)/3)

But upon reviewing Repeatability for Gaussian and non-Gaussian data, Nakagawa & Schielzeth (2010). The mention that residual error for a binomial model to be

sigma^2_e = w * pi^2/3

And then go on to say that w should be constrained to 1.

So my question is, should it be 1 * (pi^2)/3? not 1 + (pi^2)/3

[SamPassmore]

Ah i see now that under additive overdispersion model residual variance is calculated as sigma^2_e = sigma^2_e + (pi^2)/3

And then we constrain sigma^2_e to 1 because it needs to be something.

[HedvigS]

Ok, understood.

Please make changes in extract_INLA_posteriors.R if necessary

See also #43

[HedvigS]

this issue should be closed when #46 is merged, afaik.

[SamPassmore]

I was just asking Russell a question because I was discussing the ICC calculation with someone else, who used a different denominator.

They do not have a 1 in their denominator: i.e. they use phylo_sd^2 / (spatial_var^2 + phylo_sd^2 + (pi^2)/3)

I think they may have used the multiplicative calculation for residual variance from Nakagawa & Schielzeth (2010), whereas we used the additive, and set sigma^2_e to 1. But I also see here that Jarrod Hadfield is reccomending setting the observational residual variance to zero - although it's not entirely clear if that is the same situation as us.

In any case, it will have a constant difference on the results, and we shouldn't be interpretting the value of the estimates too closely anyway. So, this was just an interest question I thought @rdinnager might be clued up on.

[HedvigS]

Sure, no worries. I just thought that it might be closed by his PR, my bad. Please go on discussing as you will :)