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

[Linus Holtermann]

Hello Jarrod,

I guess, that your suggestion a) might be the best choice for my model:

 prior_a <- list(R = list(V = 1, nu=0.002), G = list(G1 = list(V =diag(3), nu = 0.002)))
model_a <- MCMCglmm(y~ int + D2:int + D3:int + X + D2:X + D3:X,random=~us(regime):town, prior=prior_1a

int = intercept
D2 and D3 are dummy-variables indicating that district i is in regime 2 or 3

in this specification, we have random intercepts for int, D2:int and D3:int. So we can show the difference in town sepficic impact on district growth between the 3 regimes. The covariances give further Iiformation about the correlation between these impacts.

Is it possible to estimate an addidtional idependent random effect, that captures the unobservable county specific time-invariant effect? That is similiar to a classical random effect in Panel data models. It is important that both types of random effects are independent of each other and among themselves.

Bests,


Linus Holtermann
Hamburgisches WeltWirtschaftsInstitut gemeinnützige GmbH (HWWI)
Heimhuder Straße 71
20148 Hamburg
Tel +49-(0)40-340576-336
Fax+49-(0)40-340576-776
Internet: www.hwwi.org
Email: holtermann at hwwi.org

Amtsgericht Hamburg HRB 94303
Geschäftsführer: PD Dr. Christian Growitsch | Prof. Dr. Henning Vöpel
Prokura: Dipl. Kauffrau Alexis Malchin
Umsatzsteuer-ID: DE 241849425
________________________________________
Von: Jarrod Hadfield [j.hadfield at ed.ac.uk]
Gesendet: Dienstag, 25. November 2014 10:31
An: Linus Holtermann
Cc: r-sig-mixed-models at r-project.org
Betreff: Re: [R-sig-ME] Need help with Random Effect specification: nested Random Effects and a_priori known regimes (MCMCglmm)

Hi Linus,

In model 2 they are correlated, but its a bit weird. The 3x3
covariance matrix looks like

V1   V1   V1
V1 V1+V2  V1
V1   V1  V1+V3

where V1, V2 and V3 are the variances associated with town, D2:town
and D3:town. Amongst other things this model does not allow the
influence of town under regimes 2 and 3 to be less than that in regime
1.

In model 3 the effects are not correlated (because an idh structure is
used) and the 3x3 covariance matrix looks like:

V1 0  0
0  V2 0
0  0  V3

model 1 has constant variance and perfect correlation:

V1   V1  V1
V1   V1  V1
V1   V1  V1

Perhaps better options would be

a) us(regime):town which is a completely unstructured covariance
matrix with 6 parameters (3 variances and 3 covariances)

or

b) town+regime:town which has covariance matrix:

V1+V2  V1    V1
   V1  V1+V2  V1
   V1   V1   V1+V2

giving constant variance and constant (non-zero) correlation.

Cheers,

Jarrod

Quoting Linus Holtermann <holtermann at hwwi.org> on Mon, 24 Nov 2014
16:21:53 +0100:

> 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?
>
>
> Thanks in advance,
>
>
> Linus Holtermann
> Hamburgisches WeltWirtschaftsInstitut gemeinnützige GmbH (HWWI)
> Heimhuder Straße 71
> 20148 Hamburg
> Tel +49-(0)40-340576-336
> Fax+49-(0)40-340576-776
> Internet: www.hwwi.org
> Email: holtermann at hwwi.org
>
> Amtsgericht Hamburg HRB 94303
> Geschäftsführer: PD Dr. Christian Growitsch | Prof. Dr. Henning Vöpel
> Prokura: Dipl. Kauffrau Alexis Malchin
> Umsatzsteuer-ID: DE 241849425
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>



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