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Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@fabians yes, for some species I have a lots of very small $N_{i,j}$ - like 0, 1, 2, 3, i.e. small numbers per site (low density), yet they have a very reliable data because they are present at a large number of sites. Anyway, I get your point with gradually building complexity, but how do I know if my simpler model is good enough? Comparing with the result of "perfect" bayesian approach with the simple model on several species?
Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@fabians note aside, the model I proposed is already used in the literature, look at the citation here. Unfortunatelly the transformation described there only works for simpler model without the random effect $\gamma_{j}$.
Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@fabians I get your point about the simplicity. However I don't agree on points 1, 2 - I insist my approach goes along the GLM line (see my equation in pt. 2 above) and it doesn't make sense to bring $N$ instead of $\mu$ to the equation, be it right or left side. Well, but if you say "OK, your approach is theoretically correct but don't be so strict and just go for simple solution for practical reasons", I get your point! Maybe I complicate things to much, but I simply hate "solutions" like $log(x+1)$. Why 1? Why not 0.5 or 0.01 or 0.0001? I think there's a lot of dirt in the simple solution.
Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@fabians and 2) if you rewrite the model as $log(\mu_{i,j+1}/\mu_{i,j}) = \alpha + \beta x_{i,j} + \gamma_j$, then it looks like you are modelling the population growth and it perhaps will make much more sense to you than if you wrote $log(\mu_{i,j+1}/N_{i,j}) = ...$. And finally 3) How would you do $log(N_{i,j})$ when $N_{i,j}$ is zero? This is the way GLM models work.
Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@fabians - I was thinking on this line too but I came to conclusion that this is not correct way to do it, for several reasons: 1) you wrote: "what affecs the subsequent time period is not the theoretical/latent quantity \mu but the size of the pop. that actually was present previously" - well, you could say the same about the $\mu_{i,j+1}$ on the left side too - but this is how the model values $\mu$ work, they are theoretical model coefficients bound by the population model this way and I think it's correct. This is how GLM models work in general.
Mar
28
comment How to fit log-linear poisson autoregressive mixed model?
@probabilityislogic I can write the model in JAGS or WinBUGS, but it takes too long to compute. BayesX does the same? How can something called BayesX be based on REML, I thought it is frequentist methond. PS: $\mu_{i,0}$ can be treated as a model parameter if necessary (i.e. it would get an uninformative prior in bugs).
Mar
26
revised How to fit log-linear poisson autoregressive mixed model?
added 3 characters in body; edited title
Mar
26
comment Different powers of coefficient - solvable within GLM?
+1 thanks Glen_b. I now have a similar problem, but with random effect: stats.stackexchange.com/questions/90702/… - would you know the answer? I've put 200 bounty on it.
Mar
24
comment Goodness of fit for a Poisson random effect regression model
Peter Flom, why not $\sum({P_i-Y_i})^2$? And why not use RMSE? Why not residual deviance reported by the glm function, and why not some pseudo R-squared formula?
Mar
24
revised How to fit log-linear poisson autoregressive mixed model?
deleted 6 characters in body; edited title
Mar
23
awarded  Popular Question
Mar
21
revised R2jags does not remove the burn in part sometimes?
added 232 characters in body
Mar
21
revised R2jags does not remove the burn in part sometimes?
added 368 characters in body
Mar
20
comment How to fit log-linear poisson autoregressive mixed model?
@gung, OK, I've edited the question (but, what about another 5,688 R questions?). This question definitely needs a statistician, not a pure R programmer. Only statistician would know if for example PESTS models can be used to fit this. You need to understand those models very well.
Mar
20
revised How to fit log-linear poisson autoregressive mixed model?
added 14 characters in body; edited title
Mar
20
asked How to fit log-linear poisson autoregressive mixed model?
Mar
18
comment Poisson with an autoregressive term
-1, there is no autoregression in the model you wrote. Fix the model and I will undo the downvote. The second problem is $\lambda_i$ vs $E_i$ vs $N_i$ - what is the difference between $E_i$ and $N_i$? The $Pois(\lambda_i E_i)$ looks too weird. Normally it is like $Pois(\lambda_i)$ and if there is something more at all then it is an overdispersion: $Pois(\lambda_i \sigma)$.
Mar
18
comment JAGS burn-in phase takes ZERO time?
I examined the issue in detail and got the answer! If you just change dunif to dgamma(0.01, 0.01), you will start to observe the problem :-) See stats.stackexchange.com/a/90492
Mar
18
answered R2jags does not remove the burn in part sometimes?