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Artigo

Informações gerais

  1. Título: Uma avaliação do estimador de pseudo-verossimilhança para modelos autologísticos espaciais
  2. Autores:
  3. Periódico:

Submissão inicial

  1. Versões preliminares do texto:
    • artigo2 (Denise, 08/02/2007)
    • artigo2 em PDF e artigo 2 tem TEX (Clarice, 11/02/2007, 13:48)
    • artigo2, primeira parte (1/3), revisado por PJ (PJ, 12/02/2007, 15:35)
    • artigo2, segunda parte (2/3), revisado por PJ (PJ, 12/02/2007, 20:10)
    • artigo2, terceira parte (3/3), revisado por PJ (PJ, 12/02/2007, 23:30)
  2. Texto Submetido:

Revisão do artigo

  1. Revisões no texto após comentários dos revisores:
    1. Revisão Denise 19/08/2007, 21:45
    2. Revisão Clarice 19/03/2008, 16:00
    1. Revisão PJ 12/04/2008, 24:00 (versão parcial, PJ ainda editando o texto)

Referee Reports

Referee 1

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.

Authors discussions/comments on the referre report
  • PJ (21/02/2008): Denise and Clarice have revised the manuscript following the comments written by this referee. I believe there is no action needed from PJ and/or Brian here, unless Clarice and Denise say otherwise.

Referee 2

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:

  • start with whatever configuration. For example, the one generated by the authors procedure or generated by the author's model M3, a logistic without a spatial component
  • Use the Gibbis sample to generate a final configuration (monitoring the convergence which will be quick). For the use of the Sample, use the idea of the COD procedure from Besag in order to generate a Gibbs step in 2 blocks, corresponding to generate the “whites” of a chessboard conditioned on the “blacks” and, next, generate the “blacks” conditioned on the “whites”.

In what follows I list minor comments which may be useful for the authors.

  1. Page 1, line-5: analítico
  2. Page 1, line-5: two key references for the analytical properties of the pseudo-likelihood estimator, although in the context of point procesess are:
    • Jensen and Künsch (1994) Annals of the institute of Statistical Mathematics, 46, 475-486.
    • Jensen and Møller (1991) Annals of applied probability, 1, 445-461
  3. Figure 1 shows before being mentioned
  4. Pag 5, line-5: I do not understand why the term square root of 2 appears
  5. Page 6, line-1: this is the main subject of the paper, it is necessary to provide a reference to the statement about the efficience of the pseudo-likelihood estimators. I thnk it does not exists but I may be wrong.
  6. Page 6, las paragraph: how did the authors reached the conclusion the pseudo likelihood method is more efficient than COD and has reasonable assymptotic properties? What “inneficient” means?
  7. Page 7, line-13: the correlation between the predictive ariables is too high and will cause multicillinearity problems. The associated beta-hat parameters will have far too large variances. In fact, this can be noticed at the final tables where within this coorelation scenario betwen predictive variables the EOP increases substantially.
  8. It is desirable that some of the table results could be illustrated by plots
  9. At tables point more clearly which results reffer to low, medium and high infestation
  10. Page 13, line 10: what is “borda simples”and “borda dupla”
  11. Some references have problems etc etc etc
  12. There are some key references missing:
    • Baddeley and Turner (2000) Australian and New Zealand Statistical Journal, 42, 283-322
    • Biggeri et. al. (2003) A transitional non-parametric maximum pseudo-likelihood estimator for disease mapping. Computational statistics and data analysis, 41, 617-629

References cited by the referee – Denise add the PDF files below

Authors discussions/comments on the referre report
  • (PJ, 21/02/2008, 17:11 BRT) The main critics of this referre reffers to the generation fo the simulated data. I don't believe we can prove the proccess generates autologistic data – just data with some spatial correlation. Actually the mecanism is rather “non-parametric” and from this “non-parametric” data we try to capture the spatial dependence through a parametric model. It seems to me this is mainly a matter of put this in the correct, clear and convince words, saying why this still makes sense even not generating data from the autologistic model.
  • (Bryan - e-mail, 11/03/2008).
    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.
  • (Denise - e-mail to Clarice, 21/02/2008). Denise corrections
  • (Bryan - e-mail, 21/03/2008).
    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?

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