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# Re: st: Non-zero covariance of orthogonal covariates with 'streg'

 From Joerg Luedicke To statalist@hsphsun2.harvard.edu Subject Re: st: Non-zero covariance of orthogonal covariates with 'streg' Date Thu, 17 Jan 2013 13:10:10 -0500

```With one treatment and one control group, you should just have one
binary indicator, not two. Your two binary indicators are carry the
exact same information and are therefore perfectly collinear. The
reason why you got Stata to output an estimated coefficient for both
variables anyhow is that, for some reason probably related to your
data/model, Stata does not recognise them as perfectly collinear.
However, if you calculate the correlation from you covariance matrix
you will see that the correlation is essentially 1:

di .06575357 / (sqrt(.06626235) * sqrt(.06613882))

Joerg

On Thu, Jan 17, 2013 at 10:04 AM, Ng, Edmond <Edmond.Ng@mhra.gsi.gov.uk> wrote:
> Dear listers,
>
> I am using 'streg' to fit a three-paramter generalized gamma model. I am fitting my model using two orthogonal dummy indicators for the control and treatment (b0 and b1) groups. I was expecting a zero covariance between b0 and b1 (i.e. covariance between [_t]b0 and [_t]b1)  in the resultant variance-covariance matrix but found a non-zero entry instead. Please see output below.
>
> I am not sure why it is  non-zero. Could anyone shed any light on this please? Many thanks in advance.
>
> BW, Edmond
>
> *************** OUTPUT EXCERPT ***************
>
> . tab b0 b1, m
>
>            |       tmt
>  control   |         0          1 |     Total
> -----------+----------------------+----------
>          0 |         0     30,798 |    30,798
>          1 |    31,711          0 |    31,711
> -----------+----------------------+----------
>      Total |    31,711     30,798 |    62,509
>
>
> . streg b0 b1 , distribution(gamma) nocons
>
>          failure _d:  case
>    analysis time _t:  dur_yr
> Fitting full model:
>
> Iteration 0:   log likelihood = -93650.975  (not concave)
> (output omitted)
>
> Iteration 38:  log likelihood = -15654.639
> Iteration 39:  log likelihood = -15654.639
>
> Gamma regression -- accelerated failure-time form
>
> No. of subjects =        62509                     Number of obs   =     62509
> No. of failures =         3456
> Time at risk    =  207216.3121
>                                                    Wald chi2(2)    =    209.00
> Log likelihood  =   -15654.639                     Prob > chi2     =    0.0000
>
> ------------------------------------------------------------------------------
>           _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           b0 |   3.683094   .2574147    14.31   0.000     3.178571    4.187618
>           b1 |   3.716548   .2571747    14.45   0.000     3.212495    4.220601
> -------------+----------------------------------------------------------------
>      /ln_sig |  -1.035381   1.714809    -0.60   0.546    -4.396346    2.325584
>       /kappa |   2.573081   4.412193     0.58   0.560    -6.074658    11.22082
> -------------+----------------------------------------------------------------
>        sigma |   .3550909   .6089133                      .0123223    10.23265
> ------------------------------------------------------------------------------
>
>
> . matrix list e(V)
>
> symmetric e(V)[4,4]
>                       _t:         _t:     ln_sig:      kappa:
>                       b0          b1       _cons       _cons
>        _t:b0   .06626235
>        _t:b1   .06575357   .06613882
> ln_sig:_cons  -.43555213  -.43556342   2.9405716
>  kappa:_cons    1.121996    1.121986  -7.5657866   19.467448
>
>
> *************** END OF OUTPUT EXCERPT ***************
>
>
>
>
>
>
>
> ***********************************************************************
> Edmond Ng
> Research Statistician
> Clinical Practice Research Datalink (CPRD), MHRA,
> 151 Buckingham Palace Road, Victoria, London, SW1W 9SZ, United Kingdom.
> Email:edmond.ng@mhra.gsi.gov.uk
>
> CPRD Knowledge Centre
> Email:kc@cprd.com; tel: +44 (0) 20 3080 6383; www.CPRD.com
> ***********************************************************************
>
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