bam model selection with 3 million data

Thanks Cesko.
I tried your suggestion (using the select argument) and got to a reasonable optimal model in which I keep all the main effects and interactions except for one main effect.
I tried, however, to do model selection using the buildbam function (buildmer library) and I get a different optimal model, where all effects are highly significant. I?m not sure why. According to the buildmer package documentation:

 ?"As bam uses PQL, only crit='deviance' is supported."
where
crit=Character string or vector determining the criterion used to test terms for elimination. Possible options are 'LRT' (likelihood-ratio test; this is the default), 'LL' (use the raw -2 log likelihood), 'AIC' (Akaike Information Criterion), 'BIC' (Bayesian Information Criterion), and 'deviance' (explained deviance ? note that this is not a formal test)

I?m not sure if you are familiar with buildmer package though.

Thanks,

David

El lun., 3 feb. 2020 a las 13:09, Voeten, C.C. (<c.c.voeten at hum.leidenuniv.nl <mailto:c.c.voeten at hum.leidenuniv.nl>>) escribi?:

    Hi David,

    Please keep the mailing list in cc.

    Yes, gam() can indeed be prohibitively slow, hence why I suggested the select=TRUE approach. I hope the below explanation helps.

    Smooth terms are composed of a null space and a range space, which respectively represent the completely smooth part of the effect and the wiggly part of the effect. In the mathematical representation, these are equivalent to fixed effects and random effects, respectively. As such, the range space is subject to penalization and can shrink to zero. In GAM terms, this would correspond to a smoothing parameter tending to infinity, resulting in a completely smooth effect: you would be left only with the null space. What select=TRUE does is add an additional penalty to all null spaces, so that these too can shrink towards zero. Effects which are shrunk to (near) zero in this way can then be removed from the model by the user.

    The degree of shrinkage can be seen by looking at the edf. Smooths that are (near) zero will also use (near) zero edf. In practice, when I do model selection using select=TRUE, I always remove terms whose edf < 1. Then I fit the model again with select=TRUE to ensure that no further reduction is necessary, and then I fit a final model with select=FALSE.

    Best,
    Cesko

    -----Oorspronkelijk bericht-----
    Van: David Villegas R?os <chirleu at gmail.com <mailto:chirleu at gmail.com>>
    Verzonden: maandag 3 februari 2020 11:28
    Aan: Voeten, C.C. <c.c.voeten at hum.leidenuniv.nl <mailto:c.c.voeten at hum.leidenuniv.nl>>
    Onderwerp: Re: [R-sig-ME] bam model selection with 3 million data

    Thanks Cesko, really appreciate your answer.
    In my particular case however, I cannot run gam models (they take forever to run) so I?m still struggling on how to perform model selection in bam. I tried select=TRUE and the summary changed a bit, but I don?t really know what this argument is doing behind?the scenes, or whether I should trust the summary from the model using select=TRUE rather than the default select=FALSE.
    Best wishes,
    David

    El s?b., 1 feb. 2020 a las 20:39, Voeten, C.C. (<mailto:c.c.voeten at hum.leidenuniv.nl <mailto:c.c.voeten at hum.leidenuniv.nl>>) escribi?:
    Hi David,

    1) You cannot perform likelihood-based model comparisons with bam models, or -- for completeness' sake -- with gam models that were fitted using performance iteration or the EFS optimizer. All of these are based on PQL (penalized quasi-likelihood), which makes the log-likelihood (and hence LRT, AIC, BIC, etc) invalid for comparison purposes. See Wood (2017:149-151). gam() with the default outer iteration should be fine, though. Have you tried fitting your full model using bam with the select=TRUE argument to turn on mgcv's automatic smooth-term selection?

    2) I am unsure if the deviance explained is or is not suitable for indicating effect size, so I can't comment on this question. I might, however, have an alternative suggestion: have you considered partial eta squared or partial omega squared? You should be able to calculate those based on the ANOVA table.

    3) I agree with you that the warning suggests complete separation, but in my experience this doesn't automatically have to be a problem. Have you checked the summary for extremely large beta values, and also have you run gam.check() to see if your fit looks reasonable? If neither indicates a problem I wouldn't be too concerned about it.

    Hope this helps,

    Cesko

    P.S.: please send messages in plain text only, as you can see the formatting of your message was slightly screwed up because the mailing list automatically strips HTML markup

    -----Oorspronkelijk bericht-----
    Van: R-sig-mixed-models <mailto:r-sig-mixed-models-bounces at r-project.org <mailto:r-sig-mixed-models-bounces at r-project.org>> Namens David Villegas R?os
    Verzonden: zaterdag 1 februari 2020 19:57
    Aan: r-sig-mixed-models <mailto:r-sig-mixed-models at r-project.org <mailto:r-sig-mixed-models at r-project.org>>
    Onderwerp: [R-sig-ME] bam model selection with 3 million data

    Dear list,

    I?m investigating the effect of three variables (X, Y, Z) on the probability that an animal uses a particular habitat A. I have a time series of relocations for each animal (>300 individuals), with one relocation every 30 minutes. There are only two options for the response
    variable: 1=present in habitat A, 0=not present in habitat A. The effects of the three variables are expected to be non-linear so I?m using gam models. My dataset is very large, with >3 million data points so I?m using the bam function from the mgcv library in R. In my models I include a random effect ?individual ID?, and a temporal autocorrelation term that corrects much but not all of the autocorrelation in the models.

    *Question 1.*

    When I run a model with the three main effects (X, Y, Z) and the three double interactions (X:Y, X:Z, Y:Z), I get that all terms are highly significant, except for one interaction. If I remove it, then everything is highly significant. However, I also wanted to run simpler models with only one interaction, no interactions, only two main effects and only one main effect. Then, if I compare all these models with AIC or BIC, I get that the best model (by far) is the one with only main effects.

     >

     ? ? AIC(codcoaAR2,codcoaAR2.1,codcoaAR2.2,codcoaAR2.3,codcoaAR2.4,codcoaAR2.5,codcoaAR2.6,codcoaAR2.7,codcoaAR2.8,codcoaAR2.9,codcoaAR)

     ? ? ? ? ? ? ? ? ? df? ? ? AIC

    codcoaAR2? ?306.1310 -1442543

    codcoaAR2.1 293.1608 -1440642

    codcoaAR2.2 292.9615 -1438219

    codcoaAR2.3 294.3657 -1435346

    codcoaAR2.4 284.0026 -1434286

    codcoaAR2.5 280.3472 -1396765

    codcoaAR2.6 279.6380 -1435862

    codcoaAR2.7 269.4968 -1377806

    codcoaAR2.8 269.0480 -1393897

    codcoaAR2.9 281.8584 -1214270

    codcoaAR? ? 271.7066 -2353481? # model with only main effects



    I wonder how this is possible if two of the interactions are highly significant.

    So my underlying question is: *for a model like this in which sample size is huge, should I make model selection looking at the significance of the different terms in the model, or should I rather look at AIC/BIC?*

    *Question 2.*

    Let?s assume the model with only main effects is indeed the optimal one.
    Then I?d like to get the effect size of each explanatory variable. It?s not clear to me how to do it even after reading some post on this and other forums, but I tried to figure it out by sequentially running the model without one explanatory variable at a time, and then comparing the deviance explained in the optimal model with X, Y, Z with the deviance explained with the reduced model with only Y and Z, for instance. Assuming that the difference would the variance explained by X. *Is this correct? *Looking at the results, the deviance explained by each variable X, Y, Z is quite low, but if the three main effects explain so little variance, who is explaining the rest?

    Model

    Deviance explained

    X, Z, Y

    69.3%

    Y, Z

    68.5%

    X, Z

    69.3%

    X, Y

    60.5%



    *Question 3.*

    In my models I usually get this error message:

    Warning message:

    In bgam.fitd(G, mf, gp, scale, nobs.extra = 0, rho = rho, coef = coef,? :

     ? fitted probabilities numerically 0 or 1 occurred



    which seems to indicate that there is perfect separation in my logistic regression. I?m not sure this is the case in my data, how could I check it and correct for it if needed? Should it be always corrected?



    Thanks for your help,

    David

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