lmertest F-test anova(fullm) and anova(fullm, reducedm)

Dear Lionel,

Thanks a lot for your input.

1) I am still not sure to get how to write things down, and I am sorry 
that my description of data and model was not clear enough.
I place me in the first of the two cases that you describe, i.e. the 
Order effect is a parametrical effect, Subject specific but 
independent of levels. In fact, the Order variable is just a count of 
the number of time the task has been performed, irrespectively of 
which Condition has been performed. This is not a categorical variable 
and is just suppose to capture how well the primate is learning 
general features about the task (independent of Condition).
As it is, Scores~Condition*Specie+(1|Subject/Order) gives me an error 
since Order values are interpreted as level, but there are as many 
levels as observations by subjects.

In fact, in your example, I don't really see the difference between 
(weight|subject) and (1|subject) since in both cases, the model 
evaluate one coefficient by subject.


2)3) This is very clear, thank you again.

Marie


2014-11-27 18:52 GMT+01:00 Lionel <hughes.dupond at gmx.de 
<mailto:hughes.dupond at gmx.de>>:

    Dear Marie Devaine,

    1) The way you account for the order effects is not the way I
    would go, I can see various options:
     - The effect of Order on Scores is not changing the relationships
    between your fixed effects part and the Scores, and each
    individuals is "learning" the task differently I would then use a
    nested random part: Scores~Condition*Specie+(1|Subject/Order), you
    would then get an estimation of much variation there is in the
    Scores between subject and also how much variation there is within
    subject between Order levels.
    - Order is changing the relationship between your fixed effect
    part and the Score, ie the Condition effect on the Scores is
    different whether a primate is in its first trials or in its
    fourth one. You would then need random slopes, and then one way to
    go would be: Scores~Condition*Species+(1+Condition|Subject/Order),
    you would then get the same estimate as in the previous options
    plus how much the Condition slope vary between the Subject and
    within the Subject, between the Order. Seeing your number of
    levels I guess that the estimation will be rather tricky ...
    You can see the wiki for more infomation on this:
    http://glmm.wikidot.com/faq#modelspec
    I guess that your are misinterpreting the random slope part, you
    can see it as an interaction term between one fixed effect term
    and one random term, for example if you were to measure the
    weights of your primates and made the hypothesis that the weights
    affect the scores but that this effect (direction+strength ie
    slope) might vary between your subject then you would have a
    random slope of weight depending on the subject (weight|subject).

    2-3) The first method identify if the interaction term explain a
    big enough portion of the total sum of square, it is a measure of
    how important is this term at explaining the variation in your
    data. The second method compare the likelihood (ie the probability
    to find this dataset with this particular set of parameter)
    between the model with and the model without the interaction term,
    if the removal of the interaction term leads to a big decline in
    the likelihood of the model then the p-value should score
    significant and you should keep the full model, in the other case
    the parcimony approach would lead you to choose the reduced model.
    So the difference come from the fact that the two methods are
    computing a different thing. As to which one is better this is a
    tricky question, the way I would go would be to compute confidence
    intervals around the main effect plus interaction term using
    bootMer for example and then interpreting them. You may have a
    look at ?pvalues for more options/suggestions.

    As I am not familiar with lmerTest package I will not comment on
    your last question.

    Hoping that I clarified some points,
    Lionel



    On 27/11/2014 16:03, marie devaine wrote:

        Dear mixed-model list,

        I am sorry if my questions sound trivial: I am all new to R
        and mixed model.

        My data set is the following : I try to model scores of
        primates from
        different species in different conditions of a task. Each
        individual
        repeats each condition a certain number of time ( most of the
        time 4 times
        but with some exceptions).
        I have only few individuals by specie (from 4 to 7), 3
        conditions and 7
        species

        As dependent variables, I am mostly interested in the
        condition and the
        Specie, but I want to correct for learning effect at the
        individual level
        (parametric effect on repetition -'Order').

        I wrote the following model (letting Subject be a random
        effect and 'Order'
        a random slope) :
        fullm = lmer(Scores ~ Condition*Specie+(1+Order|Subject))
        1) Is it a sensible way to model my data?

        Then, I want to test for the interaction between Species and
        condition. I
        found two ways to do so with the lmerTest :
        *computing the p-value of the F-test corresponding to
        Specie:Condition as
        given by anova(fullm).
        *constructing the reduced model without the interaction
        reducedm= lmer(Scores ~ Condition+Specie+(1+Order|Subject))
        and performing the Likelihood ratio test : anova(reducedm,fullm).

        2) What is the conceptual difference between the two methods?

        3) The numerical results are different in my case (pvalues
        around .05,
        below in the reduced model manner, above in the F-test
        manner), why is it
        the case? Is one better than the other one?

        4) This point is not directly related to my title, but on the
        same data and
        still on the lmerTest pasckage : the Species for now are
        categorical, but I
        could instead take a numerical value such as the
        encephalization quotient
        for each specie. In this case how could I evaluate the
        significance of the
        parametric effect? lsmeans seems to care only about
        categorical factors.

        It is very likely that I miss here very simple points, and
        would be very
        thankful if you could help me with it.

        Thank you in advance,

        Marie Devaine

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