Re: [TMB users] Digest for tmb-users@googlegroups.com - 6 updates in 2 topics

[Cole Monnahan - NOAA Federal]

Try running the model through tmbstan and look at the posterior for the slope compared to the MLE and SE. I'd be surprised if it gives you something meaningfully different but I don't understand the theory of these models well. -Cole

On Fri, Jul 21, 2023 at 9:40 PM <tmb-...@googlegroups.com> wrote:

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• Digest for tmb-...@googlegroups.com - 1 update in 1 topic - 2 Updates
• Possible bias when fitting linear regression with errors in variables using TMB - 4 Updates

Digest for tmb-...@googlegroups.com - 1 update in 1 topic

Cole Monnahan - NOAA Federal <cole.m...@noaa.gov>: Jul 21 09:36AM -0700 I don't see any immediate bugs in the code. I also ran the code with 100 different seeds and your coverage is about 85% for the slope. It appears slightly positively biased actually. I'm not super familiar with these models. Would you expect a 95% coverage? -Cole

DM Gillis <astros...@gmail.com>: Jul 21 01:19PM -0700 That could be it... I just ran it with one seed and hoped that it would be well behaved (very naive). I will simulate more and be especially careful when applying it to real data (including examining repeated simulations with the fitted model parameters). Thanks for your exploration and all the best for the weekend!   Cheers, Darren

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Possible bias when fitting linear regression with errors in variables using TMB

Hans Skaug <hsk...@gmail.com>: Jul 21 12:20AM -0700 Hi, I think this is more a statistical theory question than a question about TMB. There are different assumptions that can be made for this model: https://en.wikipedia.org/wiki/Errors-in-variables_models#Terminology_and_assumptions   Your approach seems to add one parameter (del) per observation, which may be problematic.

DM Gillis <astros...@gmail.com>: Jul 21 05:47AM -0700 Thank you for the quick response. There may be different model assumptions that work better, but I am interested in this form:   https://en.wikipedia.org/wiki/Errors-in-variables_models#Simple_linear_model   https://wikimedia.org/api/rest_v1/media/math/render/svg/72c8882e35c59a196c8115548e47a19b0555360e   because it would be straight forward to extend it to other models besides linear regression. However, I am not sure that either 1) this form can be coded in TMB, and 2) if I have done it correctly. In this code, both have random components: Y (represented in the classic errors) and X (the del's) . If this formulation cannot be executed in TMB then I will seek other solutions (JAGS or STAN, perhaps), but I was hoping to stay in the world of likelihood (and learn some TMB at the same time). Thanks again for taking the time to review this issue.   Regards, Darren   On Friday, July 21, 2023 at 4:20:26 AM UTC-3 Hans Skaug wrote:

Mollie Brooks <mollie...@gmail.com>: Jul 21 06:23PM +0200 In response to Han’s comment, I tried running it with del as a random variable and didn’t do any better. I don’t know why, because the Wikipedia article seems to say it should be identifiable in this case.   Obj <- MakeADFun(data=Data, parameters=Params, random=c("del"), DLL=model_name, silent=FALSE)   Mollie

DM Gillis <astros...@gmail.com>: Jul 21 12:15PM -0700 Yes, when I do the same it returns the OLS slope, which makes sense to me since setting it to "random" means it will be integrated out and should not impact the estimates (just their SEs). However, I want it to have an impact and move the slope around the true value of 2 :( Perhaps TMB only works with latent random variables/effects and not variation added to predictors that are not not LRVs to be integrated out.Thanks for taking the time to check and enjoy the weekend!   Darren

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[DM Gillis]

Thanks Cole. As you probably found, the CIs are "tricky" in these models. I was originally worried about bias, but now that that is resolved I'll pay more attention to the precision. I may just have to grind through a bootstrap for specific cases (loops in loops) but that is why I have so many cores. Thanks for another suggestion - I'll also look into tmbstan ( another new one for me ). As I just got back from the coast, so my tinkering may slow a bit - but this is one rabbit hole I am enjoying. Comparing the CIs and significance tests to those described in Lengendre & Legendre's Numerical Ecology (1998, 2nd English Edition) will be insightful when I get back to it- as well as the citations they provide. Also, they suggest permutation tests, so Monte Carlo methods are probably where I will go. I would just use their R package, but I want a general method to use in novel models - the thing that got me interested in TMB initially. I'll post any further developments and thank everyone again for their interest and support.  All the best!

Cheers, Darren