[R-sig-ME] Science Fair data

[Christopher David Desjardins]

Douglas Bates wrote:
> On Mon, Jan 25, 2010 at 9:41 PM, Doug Adams <dougadams53 at gmail.com> wrote:
>   
>>> you want ...
>>>
>>> lmer(score ~ division + (1|district/school), data=Age6m)
>>>
>>> and not
>>>
>>> lmer(score ~ division + (1|school|district), data=Age6m)
>>>
>>>
>>> You want school nested within district correct? The first line specifies
>>> that. Or maybe you really wanted ...
>>>
>>> lmer(score ~ division + (1|school + district), data=Age6m)
>>>       
>> Thanks; I think that makes sense.
>>     
>
> Well, actually it doesn't.  If you tried that it would fail because
> there is no addition operator for factors.
>
>   
>> What's the difference between
>> listing your factors as:
>>     
>
>   
>> lmer(score ~ division + (1|district/school), data=Age6m)
>>     
>
> In this model the effects of the district and the school are modeled
> with random effects.  The model specification is equivalent to
>
>  lmer(score ~ division + (1|district) + (1|school:district), Age6m)
>
> and, if the levels of school are distinct (i.e. you don't have a
> school 1 in both district 1 and district 2 or something like that),
> then the specification is equivalent to
>
> lmer(score ~ division + (1|district) + (1|school), Age6m)
>   

Sorry I thought that

lmer(score ~ division + (1|district) + (1|school), Age6m)


Was equivalent to:

lmer(score ~ division + (1|school + district), Age6m)


>   
>> and
>> lmer(score ~ division + (1|school) + district, data=Age6m)
>>     
>
> In this model the effect of the school is modeled by random effects
> but the effect of the district is modeled by fixed-effects parameters.
>
> The choice of fixed effects or random effects depends on the structure
> of the data and the type of inferences you wish to make.  If you have
> data from only some of the school districts and you wish to form
> conclusions about a generic district then random effects are
> preferred.  If you have data from all districts and you want to reach
> conclusions only about those specific districts then fixed effects are
> preferred.  If you want to consider how the variability in the
> responses splits into student-to-student variability and
> school-to-school variability and district-to-district variability then
> random effects are preferred.
>
>   
>> since district is another level?  Sorry if that question is quite
>> 'newbie.'   : )
>>
>> Doug
>>
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>>
>>     
>
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