AIC wrong in weighted SEM/SDEM

[rsbivand]

When observation weights are used the reported AIC is the standard AIC. When observation weights are used a dAIC measure might be more appropriate, see http://www.isr.umich.edu/src/smp/asda/J%20Surv%20Stat%20Methodol-2015-Lumley-jssam_smu021.pdf. Moved from r-spatial/spdep#13

[rsbivand]

Emails:
Sat, 14 Apr 2018
Tue, 10 Apr 2018

I have recently been introduced to the spdep package and I am highly
impressed with it! Thank you very much for the work that you and your
contributors have put into it.

I have a question. I noticed the function "errorsarLM" and "spautolm"
have options for observation weights but "sacsarlm" function does not. Is
there a reason why that function cannot handle observation weights. Is
there some work around that you are aware of for including observation
weights? Thank you for your time!

They were in spautolm() from the inception, and later added to errorsarlm()

• which fits the SAR error model from spautolm() using a different
  implementation. The weights= argument was not added to lagsarlm(), nor
  sacsarlm(). I haven't seen a theoretical development that would show how to
  do this in terms of the variance-covariance matrix of the error. If you know
  of such a development, please let me know. We had thought that the INLA slm
  model might help, and it may indeed for the spatial lag model with weights
  (with a little brutality), but we need a good theoretical basis first. What
  is your use case?

16 Apr 2018

I agree. No causal relation. My analysis at this point is more descriptive
than counterfactual.

I'll check out SLX and SDEM.

I have not looked for theoretical developments yet. If I find something I'll
be sure to let you know. Thank you for your time

Thank you Roger. I am estimating the relationship between suicide rates
and policy variables at the county level. I would like to weigh by county
population.

So you are able to use those in the only models you should consider. County
suicide rates cannot influence each other causally simultaneously. Look too
at SLX and SDEM models, both take case weights. Did you find relevant
theoretical developments (in statistics or spatial econometrics) for spatial
lag case weights? Please consider using R-sig-geo - this is privatising my
replies to your questions.

24 Apr 2018

Thanks for getting back to me, happy that SDEM is helpful.

Thank you for the tip. The SDEM model is much more appropriate for my
specific analysis!

I noticed that when observation weights are used the reported AIC is the
standard AIC. When observation weights are used a dAIC measure might be
more appropriate,
http://www.isr.umich.edu/src/smp/asda/J%20Surv%20Stat%20Methodol-2015-Luml
ey-jssam_smu021.pdf.

This is a good point, I'll open an issue on the spdep github repo to remind
myself (or others) of the problem. Maybe in the near term I should block
reporting AIC for the weighted cases for SEM and SDEM in errorsarlm(), and
possibly spautolm() SEM too.