# st: Re: strange? result: 95%CI and lincom

 From "Michael Blasnik" <[email protected]> To <[email protected]> Subject st: Re: strange? result: 95%CI and lincom Date Thu, 3 Jun 2004 10:03:58 -0400

```This result is not at all surprising -- the standard error for a combination
of coefficients has uncertainty that reflects uncertainty in each of the
coefficients, adjusting for their correlations.  When you perform an
exercise as below, the test for the combination of the two coefficients is
the one that tests whether the sum of those two coefficients differs from
zero.  The test for all 3 coefficients has a standard error that is
increased due to the uncertainty in _IA_1, so comparisons of confidence
intervals between that estimate and the single coefficient test estimate
will overstate the uncertainty from the added coefficents compared to a
direct test of the two coefficients (hope that's clear).

Michael Blasnik
[email protected]

----- Original Message -----
From: "n p" <[email protected]>
To: <[email protected]>
Sent: Thursday, June 03, 2004 4:30 AM
Subject: st: strange? result: 95%CI and lincom

> Dear statalisters,
> consider the following output
> .  xi:poisson count i.A i.B i.C i.A*i.C   ,cluster(id)
>
>
>
> Poisson regression
> Number of obs   =         32
>                                                   Wald
> chi2(2)    =          .
> Log pseudo-likelihood = -105.04905                Prob
> > chi2     =          .
>
>                                (standard errors
> adjusted for clustering on id)
> --------------------------------------------------------------------------
----
>              |               Robust
>        count |      Coef.   Std. Err.      z    P>|z|
>    [95% Conf. Interval]
> -------------+------------------------------------------------------------
----
>        _IA_1 |   1.572489   .0286677    54.85   0.000
>    1.516302    1.628677
>        _IB_1 |   .0204089   .0449014     0.45   0.649
>   -.0675963     .108414
>        _IC_1 |   1.254163   .0339171    36.98   0.000
>    1.187686    1.320639
>    _IAXC_1_1 |  -1.199721    .014818   -80.96   0.000
>   -1.228763   -1.170678
>        _cons |   3.228422   .0355479    90.82   0.000
>    3.158749    3.298095
> --------------------------------------------------------------------------
----
>
> . lincom _IA_1
>
>  ( 1)  [count]_IA_1 = 0
>
> --------------------------------------------------------------------------
----
>        count |      Coef.   Std. Err.      z    P>|z|
>    [95% Conf. Interval]
> -------------+------------------------------------------------------------
----
>          (1) |   1.572489   .0286677    54.85   0.000
>    1.516302    1.628677
> --------------------------------------------------------------------------
----
>
> . lincom _IA_1+_IC_1+ _IAXC_1_1
>
>  ( 1)  [count]_IA_1 + [count]_IC_1 + [count]_IAXC_1_1
> = 0
>
> --------------------------------------------------------------------------
----
>        count |      Coef.   Std. Err.      z    P>|z|
>    [95% Conf. Interval]
> -------------+------------------------------------------------------------
----
>          (1) |   1.626931   .0482076    33.75   0.000
>    1.532446    1.721416
> --------------------------------------------------------------------------
----
>
> . lincom _IC_1+ _IAXC_1_1
>
>  ( 1)  [count]_IC_1 + [count]_IAXC_1_1 = 0
>
> --------------------------------------------------------------------------
----
>        count |      Coef.   Std. Err.      z    P>|z|
>    [95% Conf. Interval]
> -------------+------------------------------------------------------------
----
>          (1) |   .0544419   .0226218     2.41   0.016
>     .010104    .0987798
> --------------------------------------------------------------------------
----
>
> A, B, C are binary covariates. As you see the upper
> limit of the 95%CI in the first "lincom" is greater
> than the beta estimate in the second "lincom" and the
> lower limit of the 95% CI in the  second "lincom" is
> lower than the beta estimate in the first "lincom".
> Given this overlap I was expecting a non-significant
> (at the 5% level) difference between the first two
> estimates. However the third "lincom" gives a p=0.016
> for the difference of the first two estimates. Is
> there something wrong with this and if not how can one
> justify the overlaping in the CIs when the difference
> is significant. Maybe I am missing something obvious
> but I can't find a good explanation.
>
>
> Nikos Pantazis
> Biostatistician

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