# [R-sig-ME] Need help with Random Effect specification: nested Random Effects and a_priori known regimes (MCMCglmm)

Linus Holtermann holtermann at hwwi.org
Mon Nov 24 16:21:53 CET 2014

```Dear list members,

I need some advices with the specification of the Random Effects in my Mixed model.
I got Panel data from 500 (i) district nested in 50 (j) towns over 10 (t) years.
There are 3 ex-ante known regimes (r) that are district specific and vary with t. So every district is in regime 1 or 2 or 3 and that might change over
time. I know a priori in which regime the districts are at time point t.
My goal is to analyse asymetric impacts of covariates X on y. y is growth of Output. I apply a simple dummy specification, which uses regime 1 as reference.
I estimated a mixed model via MCMCglmm (pooled mixed model):

prior_1 <- list(R = list(V = 1, nu=0.002), G = list(G1 = list(V = diag(1), nu = 0.002)))
model1 <- MCMCglmm(y~ int + D2:int + D3:int + X + D2:X + D3:X ,random=~town,prior=prior_1)
int = intercept
D2 and D3 are dummy-variables indicating that district i is in regime 2 or 3

The random intercept for towns controls for the town specific impacts on growth of districts. But in the specification above, only "int" posseses a random intercept. So only the town specific impact on growth in the reference regime 1 is captured by the random intercept. If i assume that the town specific influence is different between the 3 regimes, can I fit the model as:

prior_2 <- list(R = list(V = 1, nu=0.002), G = list(G1 = list(V = diag(1), nu = 0.002),G2 = list(V = diag(1), nu = 0.002),G3 = list(V = diag(1), nu = 0.002)))))
model2 <- MCMCglmm(y~ int + D2:int + D3:int + X + D2:X + D3:X ,random=~town + D2:town + D3:town, prior=prior_2)

Or are there better solutions to take care of the different town specific influence on district growth during the 3 regimes?
Alternatively:

prior_3 <- list(R = list(V = 1, nu=0.002), G = list(G1 = list(V = diag(3), nu = 0.002)))
model3 <- MCMCglmm(y~ int + D2:int + D3:int + X + D2:X + D3:X ,random=~ idh(as.factor(regime)):town, prior=prior_3)

This time the Random Effects are correlated, which is not the case in model2, right?

Linus Holtermann
Hamburgisches WeltWirtschaftsInstitut gemeinnützige GmbH (HWWI)
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