[R-lang] Re: Random slopes

[Levy, Roger]

OK, Garry, that helps a lot!  So, crucially, your model comparison is really a step in a larger effort to find which random-effects structure to use in drawing inferences about fixed effects.

In this case, my suggestion is to start by skipping the model-comparison stuff and see if you can fit the full model

  response ~ A*B + (A*B | subjects) + (A*B | items)

If you are able to fit that (i.e. lme4 doesn't complain about singular convergence and gives you sensible-looking random-effects covariance matrices) and get significant fixed effects of A, B, and/or their interaction, then the result is maximally trustworthy.

The trouble comes when you aren't able to fit that full model, which is *often*.  If this is the case, then stepwise model selection is a reasonable way to go, and Alex's advice (that is, always include the A*B fixed effect, even when testing whether to introduce just the random slope A) is sound.

Best & good luck!

Roger



On Jan 2, 2011, at 4:05 PM, Zhenguang Cai wrote:

> Hi Roger,
> 
> Thanks. I am interested in average fixed effects.
> 
> Garry
> 
> 于 2011-1-2 20:28, Levy, Roger 写道:
>> 
>> On Jan 1, 2011, at 4:56 PM, Zhenguang Cai wrote:
>> 
>>> Dear Roger and Alex,
>>> 
>>> Thanks for the replies. My goal of doing the model comparisons is to
>>> determine whether to include random slopes (besides the random subject
>>> and item intercepts) in my model.
>> 
>> Hi Garry,
>> 
>> Yes, this makes sense, but what is the ultimate goal of your modeling effort?  Are you ultimately trying to answer whether there are meaningful inter-participant differences in sensitivity to your factor A?  Are you trying to figure out whether the "average" (fixed) effect of A is non-zero?  Are you ultimately interested in whether there's an "average" (fixed-effect) interaction between A and B?  Or something else?
>> 
>> Best
>> 
>> Roger
>> 
>>> 
>>> Thanks,
>>> 
>>> Garryu
>>> 
>>> 于 2011-1-1 22:15, Levy, Roger 写道:
>>>> 
>>>> On Dec 30, 2010, at 5:59 PM, Alex Fine wrote:
>>>> 
>>>>> 
>>>>> 
>>>>> Zhenguang Cai wrote:
>>>>>> In determining whehter to include
>>>>>> the by-subject slope for the main effect of A (in a 2*2 design), shall
>>>>>> I just compare two simple models with A as the predictor only, as in
>>>>>> the following:
>>>>>> 
>>>>>> model1<- lmer (Y~A+(1|Subject)+(1|Item), data=dat, family=binomial)
>>>>>> model2<- lmer (Y~A+(A+1|Subject)+(1|Item), data=dat, family=binomial)
>>>>>> 
>>>>>> or shall I do it between two full models, as the following:
>>>>>> 
>>>>>> model1<- lmer (Y~A*B+(1|Subject)+(1|Item), data=dat, family=binomial)
>>>>>> model2<- lmer (Y~A*B+(A+1|Subject)+(1|Item), data=dat, family=binomial)
>>>>> if the model you're interested in working with is Y ~ A*B, then you'd
>>>>> want to do the latter comparison.  that way you're asking if a random
>>>>> by-subject slope for A is justified for the model you're interested in
>>>>> using to analyze your data.  if you're doing stepwise regression and
>>>>> adding one predictor at a time, then it's more complicated.  but you
>>>>> already said it's a 2x2 design, so it sounds like this isn't relevant.
>>>>> 
>>>>> right, everyone?
>>>> 
>>>> Garry:
>>>> 
>>>> I think Alex is hitting the nail on the head in the sense that you haven't made completely clear what the goal of your statistical analysis is.  Usually it's easier to determine what model comparisons to make once the modeling goals are articulated fully.
>>>> 
>>>> Best&   Happy New Year to all!
>>>> 
>>>> Roger
>>>> 
>>>> --
>>>> 
>>>> Roger Levy                      Email: rlevy@ucsd.edu
>>>> Assistant Professor             Phone: 858-534-7219
>>>> Department of Linguistics       Fax:   858-534-4789
>>>> UC San Diego                    Web:   http://idiom.ucsd.edu/~rlevy
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>> 
>>> --
>>> The University of Edinburgh is a charitable body, registered in
>>> Scotland, with registration number SC005336.
>>> 
>> 
>> --
>> 
>> Roger Levy                      Email: rlevy@ucsd.edu
>> Assistant Professor             Phone: 858-534-7219
>> Department of Linguistics       Fax:   858-534-4789
>> UC San Diego                    Web:   http://idiom.ucsd.edu/~rlevy
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
> 
> -- 
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
> 

--

Roger Levy                      Email: rlevy@ucsd.edu
Assistant Professor             Phone: 858-534-7219
Department of Linguistics       Fax:   858-534-4789
UC San Diego                    Web:   http://idiom.ucsd.edu/~rlevy