[R-sig-Geo] Question impacts lagged independent variables lagsarlm

[Roger Bivand]

On Sat, 4 Jun 2016, Jorge Cárcamo wrote:

> Dear all,
>
> I am working with a lagsarlm "mixed" model I executed:
> library(spdep)
> library(coda)
> dsts15 <- nbdists(nbs15, data.xy)
> idw15 <- lapply(dsts15, function(x) 1/(x))
> sy15 <- nb2listw(nbs15, glist=idw15, style="W")
> mod.sdm.15<-lagsarlm(AR32 ~ SD46 + Totaland + PC18 + PC22 + sra + sla + saa
> + owue + yearrain + yearfdi, data=data, listw=sy15, type="mixed",
> tol.solve=1.0e-12)
> summary(mod.sdm.15)
>
> And got following results (abridged table):
>
>               Estimate Std. Error z value Pr(>|z|)
> (Intercept)   1.4255019  0.4824828  2.9545 0.003132
> SD46          0.0149057  0.0116146  1.2834 0.199365
> Totaland     -0.0217556  0.0072475 -3.0018 0.002684
> ...
> yearrain      0.0557373  0.0485612  1.1478 0.251062
> yearfdi      -0.0109979  0.0069536 -1.5816 0.113741
> lag.SD46      0.0262273  0.0278045  0.9433 0.345539
> lag.Totaland  0.0060992  0.0141515  0.4310 0.666474
> ...
> lag.yearrain -0.2083118  0.0772751 -2.6957 0.007024
> lag.yearfdi   0.0111460  0.0081562  1.3666 0.171761
> Rho: -0.54702, LR test value: 10.052, p-value: 0.0015215
>
> Immediatly, I exectued impacts(mod.sdm.15, R=1000), to get the impacts:
>
>               Direct     Indirect         Total
> SD46      0.013136761  0.013451739  0.0265884995
> Totaland -0.023517332  0.013397014 -0.0101203177
> ...
> yearrain  0.079110119 -0.177734631 -0.0986245121
> yearfdi  -0.012677636  0.012773412  0.0000957761
>
> Through simulation I manage to get credible intervals for direct, indirect
> and total impacts (HPDinterval(impacts, choice="XXX")).

As you must know from the references on the help page for impacts methods, 
these are the combined impacts of the variables:

S_r(W) = (I - \rho W)^{-1} (\beta_r I - \gamma_r W)

where the direct impacts are sum(S_r(W))/n, etc. The \gamma_r are the 
coefficients on W x_r.

>
> However, how can I get the impacts of the lagged variables? I have seen
> some publications such as: Läpple, D., & Kelley, H. (2014). Spatial
> dependence in the adoption of organic drystock farming in Ireland. That
> report a posterior mean and credible intervals for the lagged variables.

Given the above, either you are misreading Läpple & Kelley (I do not have 
access), or both you and they are wrong. There are by definition on 
separable impacts for the lagged X variables.

Hope this clarifies,

Roger

>
> All suggestions are welcome.
>
> Best regards,
>
> *Ing. Jorge Alfredo Cárcamo, M. Sc., Ph. D. (c)*
> Agriculture economics
> Georg-August-Universität Göttingen
>
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>
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-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 91 00
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