[R-sig-ME] Comparing models with different random effects

[Gang Chen]

Thanks a lot for the clarifications, Dr. Bolker!

Could you comment a little more about the following?

> I was going to write more about how one would interpret the
> relationship between Task and Subj in terms of 'effects', but I think it
> really doesn't make sense when Task is a fixed effect.

In my case Task has only 3 levels, and that's why I didn't consider
(1|Task/Subj) or (1|Task)+(1|Subj). Do you think (1|Task) should be
included in the model?

Thanks,
Gang


On Fri, Dec 10, 2010 at 4:41 PM, Ben Bolker <bbolker at gmail.com> wrote:
> On 10-12-10 10:35 AM, Yuan-Ye Zhang wrote:
>> test the sig. of random slope, if you compare these two
>> (1 | Subj): random intercept
>> (Task | Subj): random intercept and random slope
>>
>> but can you do (Task | Subj)? I thought some levels of Subj is present in
>> given levels of Task, so is nested.
>>
>
>  (Task|Subj) means that the effect of Task varies among subjects --
> perfectly sensible to try to estimate this if each subject answered
> Items representing in more than one Task category.  And because
> (Task|Subj) implicitly includes an intercept term [(Task|Subj) is
> equivalent to (1+Task|Subj)], (1|Subj) is nested (in the sense of
> models) within (Task|Subj).
>
>  I was going to write more about how one would interpret the
> relationship between Task and Subj in terms of 'effects', but I think it
> really doesn't make sense when Task is a fixed effect. The model
> specification about (Task|Subj) sets up *none* of the following models:
>
> a. there is variation among Task:Subj combinations within a Subj ["Task
> nested within Subj", (1|Task/Subj)], or
> b. there is variation among Task:Subj combinations within a Task ["Subj
> nested within Task", (1|Subj/Task)] [I may have the order of the a/b
> notation backwards: I have yet to discover a good mnemonic], or
> c. samples from each Task have random deviations from the overall mean
> that are consistent across all Subj's, or vice versa ["crossed random
> effects Subj and Task", (1|Task)+(1|Subj)]
>
>  instead, this sets up a model where (as stated above) the *effect* of
> Task varies randomly (around its overall mean) across Subj's.
>
>  Hope that helps and that I didn't screw anything up.
>
>  Anyone know of a really good clear primer for this stuff (printed or
> on the web) that includes (1) mathematical notation and (2) graphical
> representations/example data plots for the descriptions above?
>
>> 2010/12/10 Gang Chen <gangchen6 at gmail.com>
>>
>>> Thanks for the quick help, Dr. Bates!
>>>
>>>>> My second question is still open: I tend to believe that (1 | Subj) is
>>>>> nested within (Task | Subj) since the first model has one parameter
>>>>> (variance) which can be viewed as multiple variances in the second
>>>>> model being constrained as equal, but I would still appreciate it if
>>>>> somebody could confirm this.
>>>>
>>>> If you are using "is nested within" to mean "is a submodel of" then
>>>> the answer is yes.
>>>
>>> The reason I'm asking about the relationship between the two models is
>>> whether I could use anova() to compare the two models. So, under this
>>> context is likelihood ratio test meaningful?
>>>
>>> Thanks,
>>> Gang
>>>
>>>
>>>>>> 2010/12/9 Gang Chen <gangchen6 at gmail.com>
>>>>>>>
>>>>>>> Suppose that there are multiple task types (Task) and each task type
>>>>>>> is represented with a few questions (Item). And all subjects (Subj)
>>>>>>> answer the same questions (Item).
>>>>>>>
>>>>>>> How do I compare a model with (1 | Subj) + (1 | Item) versus one with
>>>>>>> (1 | Subj) + (1 | Subj:Item) in lmer()? Through AIC/BIC (assuming the
>>>>>>> fixed effect remain the same)? Would it make more sense to consider (1
>>>>>>> | Subj) + (1 | Subj:Item) + (1 | Item)?
>>>>>>>
>>>>>>> Is (1 | Subj) considered as nested within (Task | Subj)?
>>>>>>>
>>>>>>> Thanks,
>>>>>>> Gang