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

[Ben Bolker]

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
>>>>>>
>>>>>> _______________________________________________
>>>>>> R-sig-mixed-models at r-project.org mailing list
>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>>
>>>>>
>>>>
>>>> _______________________________________________
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>>>>
>>>
>>
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