The paper is very interesting and I recommend the publication in RME provided some corrections are made. Most of the corrections are indicated directly in the manuscript. Special attention must be given to the section “Resultados e Discussão”, where results are basicallydescribed, without a discussion. Furthermore references must follow the journal normatization.
The authors study, using simulations, the propertiesof the pseudo-maximum likelihood estimator for the autologistic regression model. The simulations cover scenarios with two covariates with and without correlation among them and also with and without spatial correlation. Differesnt probability of success for each plant was considered (low, medium and high infestation) and also the autocorrelation parameter γ as varied. An numerical illustration is also provided with data from plant disease.
The paper is well written and the subject is relevant. A previous work which also access the properties of the pseudo-maximum likelihood estimator is: Johansson (2001) Parameter estimation in the auto-binomial model using the coding and the pseudo likelihood method approached with simmulated annealing and numarical optimization. Pattern Recognition Lettters, 22, 1233-1246.
I have found some problems which require action from the authors. The major one is the generationg procress for the simulated data. I don't think the process adopted by the authors ensures a joint distribution for the vector y which is from the autologistic model. If this is the case a proof is required. This would be a major theoretical result worthing a paper on its own. For sure the third phase do not ensures a autologistic model. Unfortunately this makes invalid all the authors conclusions since we do not know whether the true model for the generated data is in fact the assumed model, the autologistic regression model.
A simple way to generate a observation vector for which the joint distribution is of a autoligistic model is as follows:
In what follows I list minor comments which may be useful for the authors.
References cited by the referee – Denise add the PDF files below
At the moment I am not sure what is in the paper about the pseudo-likelihood method and about the generation of simulated data. I tried to download the pdf version of the paper from the wiki site but there was some problem and it did not work. Can you please send me a copy of the paper? I know it is in Portuguese, but I will get an idea about the structure, which I don't have at the moment. Also at the moment I don't understand "they want to know why we use p for the intermediate steps of the algorithm to get pi". I guess that the simulated data are an approximation to the usual autologistic model, where (if I remember right) the probability of a presence at a location depends on the expected values of presences and absences around it, rather than the actual 0s and 1s. That seems to make it an autologistic model, but perhaps not the usual one.
I agree that the generation process does not produce the usual autologistic model, but it does produce an interesting model where the probability of an occurrence depends on the probabilities for surrounding cells. Is that model a new idea? I don't know. What I think is interesting is that if we suppose that is the correct model then we might wonder how usual autologistic regression estimation works at estimating the model. I guess that is what Denise's simulations show. Also, it seems that the iterative method used to fit the model fits the model used to generate the data if we use the surrounding cell probabilities in the model even when we know the presences and absences. It is so long since I thought about all of this that I cannot remember exactly what Denise did. But am I right that we have a new type of autologistic model, with a simple iterative method fof fitting it that apparently works quite well?