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Re: st: SE erroes for xtmixed-predict fitted


From   Ricardo Ovaldia <ovaldia@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: SE erroes for xtmixed-predict fitted
Date   Thu, 1 Mar 2012 06:55:36 -0800 (PST)

Thank you Steve.
I am sorry ti bother you again, but I do not understand how you got that the se_fixed was 17.3125 in the "no random slope model". Obviously I am doing some thing wrong whe calclating the SE_fitted for this simple model. By the way I am using Stata 12. Here is what I am doing:

clear
input id str1 sex fat1 fat2 fat3 fat4
1  M 44.5 7.3 3.4 12.4 16.900
2  M 33.0 21.0 23.1 25.4 25.625
3  M 19.1 5.0 11.8 22.0 14.475
4  F 9.4 4.6 4.6 5.8 6.100
5  F 71.3 23.3 25.6 68.2 47.100
6  F 51.2 38.0 36.0 52.6 44.450
end
 
reshape long fat ,i(id) j(pill)

xtmixed fat i.pill ||id:  , nolog
predict fitted, fitted
predict se_fix,  stdp
predict se_u*, reses
gen se_fitted=  sqrt(se_fix^2 + se_u1^2 )
drop fitted se_fix se_u*
tab pill, gen(pill)
xtmixed fat pill1 pill2 pill3 pill4, nocons || id:, nolog
predict fitted, fitted
predict se_fix,  stdp
predict se_u*, reses
gen se_fitted2=  sqrt(se_fix^2 + se_u1^2 )

. sum se_fitted se_fitted2

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
   se_fitted |        24    8.373251           0   8.373251   8.373251
  se_fitted2 |        24    8.373251           0   8.373251   8.373251



Ricardo Ovaldia, MS
Statistician 
Oklahoma City, OK


--- On Wed, 2/29/12, Steve Samuels <sjsamuels@gmail.com> wrote:

> From: Steve Samuels <sjsamuels@gmail.com>
> Subject: Re: st: SE erroes for xtmixed-predict fitted
> To: statalist@hsphsun2.harvard.edu
> Date: Wednesday, February 29, 2012, 6:29 PM
> 
> This is exactly what I wished you'd shown us the first time,
> Ricardo.
> 
> To answer your questions:
> 
> 1. Constant SEs for no random slope model?  Yes
> 
> You have a perfectly balanced data set: four pills with six
> subjects per pill. Therefore the standard errors for the
> fitted values will be identical, because they are based on
> the same SDs and the same number of observations.  This
> is easier to see if you run:
> ***********************************************************
> tab pill, gen(pill)
> xtmixed fat pill1 pill2 pill3 pill4, nocons || id:, nolog
> ***********************************************************
> 
> This is an equivalent model and fits the four fixed pill
> means individually.
> 
> If you compute se_fitted as before, it will equal 
> 17.3125, and
> the constant standard error for the fitted pill means
> 7.068  is se_fitted/sqrt(6), which you can verify.
> 
> If, on the other hand, some subjects did not get all the
> pills, then you would expect standard errors for pill
> effects would differ, because the denominator would not
> always be sqrt(6). You can see this if you delete an
> observation.
> 
> 2. Random "slope" model? 
> 
> *************************************
> xtmixed fat i.pill ||id: pill , nolog
> *************************************
> 
> Here you are off the track. Pill is a categorical variable,
> but the "||id: pill" treats it as a continuous variable and
> fits a slope coefficient.
> 
> If "i" indicates id and "j" is the value associated with
> pill j you are fitting a model:
> 
> Y_ij = a  + a_j + u_i + b*j +
> e_ij   where the a_j's are fixed and the u
> and e terms are random
> 
> Formally, nothing prevents you from doing this, but it
> doesn't make sense. Your standard error for even this model
> was incorrect. The standard error for the fitted value
> should contain a term for b^2*j^2.  A similar term
> appeared in the post that I referred you to. For an example
> of a random slope model, see the pig weight example in the
> Manual.
> 
> 
> Steve
> sjsamuels@gmail.com
> 
> On Feb 29, 2012, at 8:32 AM, Ricardo Ovaldia wrote:
> 
> Thank you Steve for your help and patience. I am sorry that
> I was not clear with what I needed. What I was actually
> looking for was an -ado- file that would do this instead of
> what you had posted because I was not sure that I was
> changing  your code correctly to fit my model. Again I
> am sorry, I did not mean to upset you and I really
> appreciate your help very much.
> 
> That said, here is a simple example that I am not sure it is
> correct.
> There are 6 cats each treated with 4 different pills:
> 
> clear
> input id str1 sex fat1 fat2 fat3 fat4
> 1  M 44.5 7.3 3.4 12.4 16.900
> 2  M 33.0 21.0 23.1 25.4 25.625
> 3  M 19.1 5.0 11.8 22.0 14.475
> 4  F 9.4 4.6 4.6 5.8 6.100
> 5  F 71.3 23.3 25.6 68.2 47.100
> 6  F 51.2 38.0 36.0 52.6 44.450
> end
> 
> reshape long fat ,i(id) j(pill)
> <output omitted>
> 
> xtmixed fat i.pill ||id: , nolog
> 
> <output omitted>
> 
> . predict fitted, fitted
> 
> . predict se_fix,  stdp
> 
> . predict se_u*, reses
> 
> . gen se_fitted=  sqrt(se_fix^2 + se_u1^2 )
> 
> . sum se_fitted
> 
>    Variable |   
>    Obs        Mean 
>   Std. Dev.       Min 
>       Max
> -------------+--------------------------------------------------------
>   se_fitted |        24 
>   8.373251       
>    0   8.373251   8.373251
> 
> SE are the same for all observations.
> 
> Now for the random slope & intercept model:
> 
> . drop fitted se_fix se_u1 se_fitted
> 
> . xtmixed fat i.pill ||id: pill , nolog
> 
> <output omitted>
> 
> . predict fitted, fitted
> 
> . predict se_fix,  stdp
> 
> . predict se_u*, reses
> 
> . gen se_fitted=  sqrt(se_fix^2 + se_u1^2 + se_u2^2)
> 
> . sum se_fitted
> 
>    Variable |   
>    Obs        Mean 
>   Std. Dev.       Min 
>       Max
> -------------+--------------------------------------------------------
>   se_fitted |        24 
>   8.655818   
> .0559801   8.592957   8.737734
> 
> Did I modify your code correctly?
> 
> Thank you again,
> Ricardo
> 
> Ricardo Ovaldia, MS
> Statistician
> Oklahoma City, OK
> 
> --- On Tue, 2/28/12, Steve Samuels <sjsamuels@gmail.com>
> wrote:
> 
> From: Steve Samuels <sjsamuels@gmail.com>
> Subject: Re: st: SE erroes for xtmixed-predict fitted
> To: statalist@hsphsun2.harvard.edu
> Date: Tuesday, February 28, 2012, 8:06 PM
> 
> I don't know what you are looking at, but yes,I would
> expect
> the same or near identical  standard errors under many
> circumstances.
> 
> When you averaged, you are  ignoring the fact that
> Stata's linear predictors are "best". I don't see show you
> thought you could improve upon them. I suggest that you
> look
> at a book on longitudinal data. Three good ones are:
> 
> Diggle, Heagerty, Liang and Zeger, Anal of Long data 2nd Ed
> Verbeke and Molenbergs Linear mixed models for
> longitudinal analysis
> Fitzmaurice, Laird,Ware, Applied Longitudinal Data
> 
> but there are many others.
> 
> Finally, please follow the FAQ in the future and show
> exactly what you did and what Stata replied.  It is
> quite irritating to be told that you had searched and found
> no answer to your question, when, apparently you had found
> an answer, but just didn't like what it showed.
> 
> Steve
> sjsamuels@gmail.com
> 
> On Feb 28, 2012, at 7:46 PM, Ricardo Ovaldia wrote:
> 
> Thank you Steve.
> 
> I did see Steve's post, however when I tried doing this, I
> got the same SE for every patient when I leave out the
> random slope term i.e.:
> 
> xtmixed cholest i.drug month || patid
> 
> So I was not sure that it was working correctly. When I
> included the random slope term, I get slightly different
> values for each patient but still very similar to each
> other. Is that what I should expect?
> 
> Ricardo
> 
> Ricardo Ovaldia, MS
> Statistician
> Oklahoma City, OK
> 
> --- On Tue, 2/28/12, Steve Samuels <sjsamuels@gmail.com>
> wrote:
> 
> From: Steve Samuels <sjsamuels@gmail.com>
> Subject: Re: st: SE erroes for xtmixed-predict fitted
> To: statalist@hsphsun2.harvard.edu
> Cc: rgutierrez@stata.com
> Date: Tuesday, February 28, 2012, 4:37 PM
> You must have missed http://www.stata.com/statalist/archive/2011-12/msg00852.html
> 
> where I tried to answer a related questionn. I'm not
> sure
> I'm right. If I'm not, I bet that Bobby Gutierrez
> knows.
> 
> Steve
> sjsamuels@gmail.com
> 
> On Feb 28, 2012, at 3:50 PM, Ricardo Ovaldia wrote:
> 
> I searched the Statalist archives for the answer to
> the
> following query and could not find one. Can someone
> please
> help.
> 
> After using -xtmixed- to fit:
> 
> xtmixed cholest i.drug month || patid:month
> 
> I used -predict, fitted- to get predicted estimates
> that
> account for both the fixed and random effects.
> I them average these over drug and month to get mean
> predicted cholesterol values for each drug at each
> time
> point.
> Is there a way to place a CI or to calculate SE for
> these
> estimates?
> 
> Thank you,
> Ricardo.
> 
> 
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