Estimating Spatial Econometrics Models with Integrated Nested Laplace Approximation
Round 1
Reviewer 1 Report
The paper presents an application/ extension of the R package R-INLA to a class of model called "slm". This kind of model include several spatial econometrics models described in the paper like SEM, SLM, SDM, SDEM. Although it seems interesting for the readers, the paper is somehow like a software implementation introduction. In details, they show how to use functions in R-INLA software to perform statistics inference for the "slm" model.
Although the authors provide good application examples, no evidence is shown to illustrate that the proposed method will work well. For example, Table 1 and 2 do not show which estimates are good or not. Probably, some simulations are needed.
From my opinion, this manuscript should be submitted to a more statistical "software" journal.
Author Response
Please, see attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper introduces the integrated Nested Laplace Approximation (INLA) in the spatial autoregressive models by adding a new package implementation in R-INLA.
Tackling a problem to find a hidden correlation between variables in a dynamic setting is still very challenging. In this sense, I think the main contribution of this paper is applying the INLA method in Spatial autoregressive models and investigating the performance. Although the article focuses on the spatial correlation between variables (without considering the time), the contribution seems to be enough to accept for publication.
Major Comments.
- Figure 6 and Figure 8 show approximation performances for four different methods. It might be good to show some statistics (like mean and variance) for each technique (INLA vs. MCMC).
- In Section 6, there is a discussion about the model selection. It would also be instructive which model can be selected in Sections 7.
- It would also be instructive to discuss in what conditions this INLA method shows higher differences between INLA and MCMC to apply.
Minor Comments:
- Equation (11), the proportional sign, seems to be redundant to me.
- line 413, the punctuation '.' is missing at the end of the sentence.
- Table 11 (on page 28), the INLASEM column, shows all zero values. If this is true, I think it needs more explanations. If this was not filled by mistake, the column needs to be filled out.
- Page 29, 30 needs to be removed.
Author Response
Please, see attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors discussed a new class of latent models in INLA for model fitting, model selection and inference in spatial econometrics. Spatial econometric models are receiving increasing interest these days, and this work is a timely effort on developing appropriate tools for such research. The paper is very well written, and the quality is high. I recommend this paper to be accepted as is.
Author Response
Please, see attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Sorry, but it is not shown how good the INLA method works in 'slm' model.
I do not expect comparison with MCMC. I would rather expect at least some simulations to show that the method can work well with a given "underlying/true" model.
As this is my main concern, I strongly reject this paper.
Author Response
We have included a simulation study in the paper.
