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# Re: st: standard errors after xtmixed, predit.., fitted

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: standard errors after xtmixed, predit.., fitted Date Thu, 22 Dec 2011 00:43:12 -0500

```Correction:

I think that in your case the last three statements will be:
*************************************************************
predict se_region1 se_region2  se_country_year se_country, rses
des se*   //check above against variable labels
gen se_fitted =  ///
sqrt(se_fix^2 +se_region1^2 +  se_region2^2 + ///
+ se_country^2 + (year_cat*se_country_year)^2 +sd_res^2)
************************************************************

Steve

Jennyfer,

I misunderstood your request: my solution was for an observation chosen at random and it incorrectly omitted the residual SD term, to boot.  Try this.

*******************************************
webuse productivity, clear
xtmixed gsp private emp hwy water other unemp ///
|| region: || state: unemp

matrix list e(b)  //names of terms
scalar sd_res = exp([lnsig_e]_cons)

predict se_fix,  stdp
predict se_region se_state_u se_state, reses
des se* //check against variable labels
gen se_fitted =  ///
sqrt(se_fix^2 +se_region^2 +  se_state^2 ///
+ (unemp*se_state_u)^2 +sd_res^2)
*******************************************

I think that in your case the last three statements will be:
******************************************************************
predict se_region1 se_region2  se_country_year se_country, rses
des se*  //check against variable labels
sqrt(se_fix^2 +se_region1^2 +  se_region2^2 + ///
+ se_country^2 + (year_cat*se_country_year)^2 +sd_res^2)
******************************************************************

Note that these statements assume that there is no correlation between the country and countryXyear random effects, which is what your model implies.  If there is such correlation (and you can test for it), then a covariance term must be added to the estimated standard error.

If you happen to have sample survey data, then be sure to read the section of Survey Data in the manual entry for -xtmixed-.

Steve
sjsamuels@gmail.com

On Dec 21, 2011, at 10:01 AM, Jennyfer Wolf wrote:

Thank you very much for your answer. I've tried it in many different
variations but I guess there are problems with this approach:

1. the squared standard deviations that we are adding up are
describing variation from the fixed effects but, when I understand
right, not the error of the model

2. the CIs I need describe the uncertainty for the estimates for each
country so countries with more datapoints have a narrower CI and also
for future predictions the CI should get wider (which does not happen
with the approach you suggested.

I tried gllamm and used the "ci_marg_mu" command after "gllapred x, mu
marg fsample" but this does not fit to my individual country data and
still gives me the same CIs no matter how many survey points I have
per country.

Any more ideas on how to get confidence intervals after "xtmixed" and
"predict x, fitted" for the predicted values in multilevel modeling?
(Alternatively with gllamm)
Thank you very, very much.

Jennyfer

2011/12/17 Steve Samuels <sjsamuels@gmail.com>:
>
> Correction: I should not have included the SD for the error term, as it is not part of the fitted value.
>
>
> Here's an example more like yours, but with two levels, not three. I expect that you can take it
> from here
> *******************************************
> webuse productivity, clear
> xtmixed gsp private emp hwy water other unemp  || region: || state: unemp
>
> matrix list e(b)  //names of terms
> scalar sd_region = exp([lns1_1_1]_cons)
> scalar sd_state_u  = exp([lns2_1_1]_cons)
> scalar sd_state   = exp([lns2_1_2]_cons)
> scalar dir // check these SDs against results
>
> predict se_fix,  stdp
>
> gen se_fitted =  ///
> sqrt(se_fix^2 +sd_region^2 +  sd_state^2 + (unemp*sd_state_u)^2)
> *******************************************
>

> Steve
> sjsamuels@gmail.com
>
> On Dec 16, 2011, at 11:34 AM, Jennyfer Wolf wrote:
>
> Dear Statalist,
>
> sorry for asking the question again, but we are a bit desperate so it
> would be great if anybody has a solution for my question:
>
> Is it possible to get standard errors for the fitted values of a
> multilevel-model (three levels, random slope and intercept) after
>
> xtmixed dep_var indep_var || region1: || region2: || country :year_cat
> predict var, fitted
>
> ?
>
> We would like to present the estimated values with a confidence interval?
> If it is not possible to get the standard errors for the predicted
> values from Stata, is it possible to calculate these values from the
> Standard Errors from the individual estimates?
>
> Thank you very very much.
> With kind regards,
> Jennyfer
> *

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```