3-way interaction in random structure using gam

Dear Rudi,

Please keep the mailing list in cc.

Yes. I'd use the model with only the 3-way interaction smoother. It 
can handle all patterns of the lower interactions.

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE 
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be <http://www.inbo.be>

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more than asking him to perform a post-mortem examination: he may be 
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does 
not ensure that a reasonable answer can be extracted from a given body 
of data. ~ John Tukey
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Op di 25 mei 2021 om 13:30 schreef Rudi Reiner <rudi.reiner at boku.ac.at 
<mailto:rudi.reiner at boku.ac.at>>:

    Dear Thierry,

    thank you for your reply. I am afraid, there was a typing error in
    my initial message. Age and b.mass do have a non-linear (not lon
    or log linear) relationship. Simplified, it may be a quadratic one
    (see me model using lmer) but I think a gam would fit better. So
    would you still suggest this model?:

    gam(b.mass ~ te(age, area.forest, by = period), data = data,
    random = list(pop=~1, year=~1))

    Best regards,
    Rudi

    Am 25.05.2021 um 13:04 schrieb Thierry Onkelinx:

    Dear Rudi,

    If age has a log-linear relationship, then use logAge as
    predictor rather than age.

    I'm wondering why you insist on adding the 2-way interactions
    smoothers. You can't directly interpret 2-way interactions (or
    main effects) when you have a 3-way interaction that contains the
    same variables.

    I'd simplify the model to gam(b.mass ~ te(log.age, area.forest,
    by = period), data = data, random = list(pop=~1, year=~1)).

    Best regards,

    ir. Thierry Onkelinx
    Statisticus / Statistician

    Vlaamse Overheid / Government of Flanders
    INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR
    NATURE AND FOREST
    Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality
    Assurance
    thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>
    Havenlaan 88 bus 73, 1000 Brussel
    www.inbo.be <http://www.inbo.be>

    ///////////////////////////////////////////////////////////////////////////////////////////
    To call in the statistician after the experiment is done may be
    no more than asking him to perform a post-mortem examination: he
    may be able to say what the experiment died of. ~ Sir Ronald
    Aylmer Fisher
    The plural of anecdote is not data. ~ Roger Brinner
    The combination of some data and an aching desire for an answer
    does not ensure that a reasonable answer can be extracted from a
    given body of data. ~ John Tukey
    ///////////////////////////////////////////////////////////////////////////////////////////

    <https://www.inbo.be>


    Op di 25 mei 2021 om 09:14 schreef Rudi Reiner
    <rudi.reiner at boku.ac.at <mailto:rudi.reiner at boku.ac.at>>:


        Hi there,

        my actually trying to fit a non-linear mixed model (with a
        random
        structure) and am not sure how to do this correct using "gam"
        or "bam"
        from the mgcv package. My supervisor suggested me to ask R-sig.

        My Data:

        b.mass = body mass (continuous) - dependent variable
        _
        __predictor variables_
        age = continuous; lon-linear relationship with b.mass
        area.forest = continuous
        period =? factor; 2 levels

        _random variables
        _year = continuous (1993-2019)
        pop = factor (28 different populations)
        --------------------------------------------------

        First I fitted a linear model with quadratic age which seems
        to give me
        the "correct" results (biologically the results make sense).
        Especially
        I am interested in the 3-way interaction age x area.forest x
        period but
        also want/have to add all 2-way interactions:

        */LM <- lmer(b.mass ~ ns(age,2)*area.forest*period + (1|pop)+
        (1|year),
        data = data)/*

        Now I want to have the corresponding model using gam (or
        bam). I tried:

        */gam <- gam(b.mass ~ period+s(age)+area.forest+s(age, by =
        area.forest)+s(age, by=period)+te(area.forest,
        by=period)+te(age,
        area.forest, by = period), data = data, random = list(pop=~1,
        year=~1))/*

        The results (plot age~b.mass for different area.forest) look
        different
        to the lmer approach. Do have an idea, if my model (gam) is
        fitted
        correct, i.e., is it the "same" like the model I fitted using
        /`lmer`?/

        Thank you,
        Rudi


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