Re: st: SE erroes for xtmixed-predict fitted

[Steve Samuels <sjsamuels@gmail.com>]

Two corrections:

The second  model you fit was:

Y_ij = a  + a_j + u_i + b_i*j + e_ij   where the a_j's are fixed and the u, b, and e terms are random. i indexes subjects and  j= 1,2,3,4 indexes the pills

Steve



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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