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

[Roger Bivand]

On Sun, 5 Jun 2016, Jorge Cárcamo wrote:

> Prof. Bivand,
>
> Many thanks for your clarification. I think that I should read Läpple &
> Kelley again.
>
> One more question, I assume that if I create independent lag variables
> with: data$w_xxx <- lag.listw(sy15,data$xxx) and add them into the model I
> can get the impacts of these lag variables; however, if I add them into the
> model, do I need to change the type="lag" instead of "mixed" when running
> lagsarlm command?

Don't even think about this, it is senseless. The impact of x_r is as 
given in the formula, the only contrast is between the impacts in the 
model="lag" case and the model="mixed" case. Because of the interaction 
between \rho and the \betas (and \gammas) in the y = \rho W y + ... 
models, you only get one set of impacts per x_r per model. You can 
interprete the differences between the three impact components between 
models, but avoid playing with stuff without doing all of the maths first.

Roger

>
> Many thanks for your attention.
>
> Jorge
>
> *Ing. Jorge Alfredo Cárcamo, M. Sc., Ph. D. (c)*
> Agriculture economics
> Georg-August-Universität Göttingen
>
> On Sun, Jun 5, 2016 at 2:17 PM, Roger Bivand <Roger.Bivand at nhh.no> wrote:
>
>> 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
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
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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
>> e-mail: Roger.Bivand at nhh.no
>> http://orcid.org/0000-0003-2392-6140
>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
>> http://depsy.org/person/434412
>

-- 
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
e-mail: Roger.Bivand at nhh.no
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
http://depsy.org/person/434412