[R-sig-ME] lmertest F-test anova(fullm) and anova(fullm, reducedm)

marie devaine marie.devaine at gmail.com
Fri Nov 28 10:51:59 CET 2014

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.


2014-11-27 18:52 GMT+01:00 Lionel <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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Marie Devaine
PhD Student at the Brain and Spine Institute (France)
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