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Re: st: More mixed confusion
From
Scott Baldwin <[email protected]>
To
[email protected]
Subject
Re: st: More mixed confusion
Date
Wed, 10 Jul 2013 16:39:37 -0600
The constant is a person-specific intercept in the model described
above (that is, it is constant at the person-level). However,
--mixed-- doesn't estimate the intercept for each person, although you
can predict them. Rather it it estimates the variance of these
person-specific intercepts. When you use the || id: boy girl, nocons
you are asking for person-specific intercepts for everyone as before,
but you are asking for variance to be estimated separately for boys
and girls. When you predict the intercepts for this model, you would
use the gender specific variance to make the prediction (i.e.,
empirical bayes estimate). You have to ask for --nocons-- here so that
you don't try to get an overall variance (averaging across boys and
girls), as that overlaps with the two distinct intercepts.
If you are confused about how these things are estimated, the
--mixed-- manual provides a nice description of the mixed-model
equation and how the random effects matrices are generated.
Best,
Scott
On Wed, Jul 10, 2013 at 1:44 PM, Lucas <[email protected]> wrote:
> Thanks! But, is that constant a constant, a variance, something else
> (e.g., a mean for the context-level error term)?
>
> I guess my confusion is that when I think "equation" I think there's a
> left hand side of some outcome (which could be a variance) and a right
> hand side of one or more inputs. If we say there's an equation for
> the variance, then is the constant a variance? I think you can see my
> confusion just by juxtaposing "constant" and "variance". (Feels like
> "Who's on first?" -- I can't believe this is the clearest way for
> these statistical ideas to be expressed.)
>
> Anyway, thanks a bunch for your response. So, now my question is, is
> the constant a variance? Something else?
>
> Sam
>
> On Wed, Jul 10, 2013 at 12:33 PM, Scott Baldwin <[email protected]> wrote:
>> Suppressing the constant in the random effects will ensure that a
>> random intercept for the given id variable isn't estimated. The
>> --nocons-- option is useful in a number of scenarios. For example,
>> using the 'childweight' data from the manuals, you can fit the
>> following model:
>>
>> webuse childweight
>> mixed weight age || id:
>>
>> which provides the variance for the random intercept (person specific
>> deflections in weight)
>>
>> ------------------------------------------------------------------------------
>> Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
>> -----------------------------+------------------------------------------------
>> id: Identity |
>> var(_cons) | .6076662 .2040674 .3146395 1.173591
>> -----------------------------+------------------------------------------------
>> var(Residual) | 1.524052 .1866496 1.198819 1.937518
>> ------------------------------------------------------------------------------
>>
>> This dataset includes boys and girls.
>>
>> tabulate girl
>>
>> gender | Freq. Percent Cum.
>> ------------+-----------------------------------
>> boy | 100 50.51 50.51
>> girl | 98 49.49 100.00
>> ------------+-----------------------------------
>> Total | 198 100.00
>>
>> we may want to estimate a unique random intercept for boys and one for
>> girls because we think the person specific deflections in weight are
>> different for boys and girls. To do this you need to create a boy
>> dummy variable to go with the girl dummy variable (I don't think you
>> can use standard factor variables in --mixed--).
>>
>> gen boy=girl==0
>>
>> tabulate girl, nolabel
>> tabulate boy, nolabel
>>
>>
>> The model is specified as:
>>
>> mixed weight age || id: boy girl, nocons
>>
>> which gives you separate random intercepts variances by boy and girl.
>>
>> ------------------------------------------------------------------------------
>> Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
>> -----------------------------+------------------------------------------------
>> id: Independent |
>> var(boy) | .7620931 .3329286 .3237065 1.794174
>> var(girl) | .4330075 .2723947 .12619 1.485819
>> -----------------------------+------------------------------------------------
>> var(Residual) | 1.530808 .1887532 1.202168 1.94929
>> ------------------------------------------------------------------------------
>>
>> You need to suppress the overall intercept in the random effects
>> portion or you can't estimate this model (the dummy variables will be
>> collinear with the overall intercept). Indeed, try
>>
>> mixed weight age || id: boy girl
>>
>> you will see that Stata will automatically drop one of the variables.
>>
>> Best,
>> Scott
>>
>>
>> On Wed, Jul 10, 2013 at 1:15 PM, Scott Baldwin <[email protected]> wrote:
>>> Sorry about that -- I sent my email before I was done. Starting over...
>>>
>>> Suppressing the constant in the random effects will ensure that a random
>>> intercept for the given id variable isn't estimated. The --nocons-- option
>>> is useful in a number of scenarios. For example, using the 'childweight'
>>> data from the manuals, you can fit the following model:
>>>
>>> webuse childweight
>>> mixed weight age || id:
>>>
>>> which provides the variance for the random intercept (person specific
>>> deflections in weight)
>>>
>>> ------------------------------------------------------------------------------
>>> Random-effects Parameters | Estimate Std. Err. [95% Conf.
>>> Interval]
>>> -----------------------------+------------------------------------------------
>>> id: Identity |
>>> var(_cons) | .6076662 .2040674 .3146395
>>> 1.173591
>>> -----------------------------+------------------------------------------------
>>> var(Residual) | 1.524052 .1866496 1.198819
>>> 1.937518
>>> ------------------------------------------------------------------------------
>>>
>>> This dataset includes boys and girls.
>>>
>>> tabulate girl
>>>
>>> gender | Freq. Percent Cum.
>>> ------------+-----------------------------------
>>> boy | 100 50.51 50.51
>>> girl | 98 49.49 100.00
>>> ------------+-----------------------------------
>>> Total | 198 100.00
>>>
>>> we may want to estimate a unique random intercept for boys and one for girls
>>> because we think the person specific deflections in weight are different for
>>> boys and girls. To do this you need to create a boy dummy variable to go
>>> with the girl dummy variable (I don't think you can use standard factor
>>> variables in --mixed--).
>>>
>>> gen boy=girl==0
>>>
>>> tabulate girl, nolabel
>>> tabulate boy, nolabel
>>>
>>>
>>> The model is specified as:
>>>
>>> mixed weight age || id: boy girl, nocons
>>>
>>> which gives you separate random intercepts variances by boy and girl.
>>>
>>> ------------------------------------------------------------------------------
>>> Random-effects Parameters | Estimate Std. Err. [95% Conf.
>>> Interval]
>>> -----------------------------+------------------------------------------------
>>> id: Independent |
>>> var(boy) | .7620931 .3329286 .3237065
>>> 1.794174
>>> var(girl) | .4330075 .2723947 .12619
>>> 1.485819
>>> -----------------------------+------------------------------------------------
>>> var(Residual) | 1.530808 .1887532 1.202168
>>> 1.94929
>>> ------------------------------------------------------------------------------
>>>
>>> You need to suppress the overall intercept in the random effects portion or
>>> you can't estimate this model (the dummy variables will be collinear with
>>> the overall intercept). Indeed, try
>>>
>>> mixed weight age || id: boy girl
>>>
>>> you will see that Stata will automatically drop one of the variables.
>>>
>>> Hope that helps and sorry for the two emails.
>>>
>>> Best,
>>> Scott
>>>
>>>
>>>
>>> On Wed, Jul 10, 2013 at 11:12 AM, Lucas <[email protected]> wrote:
>>>>
>>>> A (seemingly) simple question: What does it mean in stata to suppress
>>>> the constant from "the" random effects equation?
>>>>
>>>> (Note: Although I use the terms here, I agree with Andrew Gelman's
>>>> very clear critical observations on the terms "fixed effect" and
>>>> "random effect", which can be found by googling "Why I don't use the
>>>> term "fixed and random effects"").
>>>>
>>>> The reason I ask is that the output does not seem to provide an
>>>> equation for the "random effect". We do see a variance, and if there
>>>> are multiple random effects, we see variances and covariances. Thus,
>>>> where is the constant (if we do not use the noconstant option)? What
>>>> is the constant giving us? What does using the noconstant take away
>>>> from the output? Is the constant some parameter for the variance? If
>>>> so, where does it appear in the greek-equation specification of the
>>>> model? (And, just for clarity-sake, why aren't the other parameters
>>>> involved in the variance (e.g., the context-level Z's) in the random
>>>> effects area as opposed to being forced up into the fixed effects area
>>>> by interactions?)
>>>>
>>>> Things become a bit less clear if multiple parameters are allowed to
>>>> vary across contexts (e.g., the slope for Education and the slope for
>>>> Occupation vary across contexts). It seems one is allowed to specify
>>>> noconstant for one, both, or none of the "random effects." But,
>>>> 1)how, and, 2)what would it mean, as the random effect section of the
>>>> output doesn't seem to contain constants whether one uses the
>>>> noconstant option or not?
>>>>
>>>> I've been using the software, nut, as my work becomes more complex, I
>>>> am pushed to consider many options I had not needed before. And, upon
>>>> closer inspection, I realize I am confused as to the basic
>>>> "noconstant" option for the "re" equation, and now this de-stabilizes
>>>> my sense of what the "re" section of the output is doing (or
>>>> suppressing). Although I did not read every example, I have looked
>>>> over some of the -me- examples in the stata13 manual and so far have
>>>> not found any cases where the noconstant option is used in the random
>>>> effects equation. Perhaps I missed it, and, if so, I'd appreciate
>>>> being pointed to the example(s) that might clarify matters. At any
>>>> rate, these are emerging questions.
>>>>
>>>> Thanks a bunch.
>>>> Sam
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>>>
>>>
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