Re: st: Recreating SAS "sums of squares" in Stata using anova and regress

[David Fisher <djfisher81@gmail.com>]

Hi Joseph,
Thanks for your reply.
Unfortunately your example has the same problem -- the F and p values
are very slightly different (as can be seen by typing "disp e(F)"
etc).  Furthermore, from reading the -contrast- documentation, I'm not
sure the operators change the overall (joint) test result, just the
values of the contrasts.
Regards,
David.





On Wed, Feb 19, 2014 at 11:15 AM, Joseph Coveney <stajc2@gmail.com> wrote:
> Try using the -gw.- contrast operator.
>
> Joseph Coveney
>
> . version 13.1
>
> .
> . clear *
>
> . set more off
>
> . set seed `=date("2014-02-19", "YMD")'
>
> . quietly set obs 30
>
> . generate byte clinic = _n
>
> . generate double clinic_u = rnormal()
>
> . quietly expand 30
>
> . bysort clinic: generate byte treatment = mod(_n, 2)
>
> . drop if runiform() < 0.10
> (79 observations deleted)
>
> .
> . generate double response = treatment / 10 + clinic_u + rnormal()
>
> .
> . anova response clinic treatment clinic#treatment, sequential
>
>                            Number of obs =     821     R-squared     =  0.4323
>                            Root MSE      = .992115     Adj R-squared =  0.3883
>
>                   Source |    Seq. SS     df       MS           F     Prob > F
>         -----------------+----------------------------------------------------
>                    Model |  570.498163    59  9.66946039       9.82     0.0000
>                          |
>                   clinic |  532.275049    29   18.354312      18.65     0.0000
>                treatment |  7.84163637     1  7.84163637       7.97     0.0049
>         clinic#treatment |  30.3814777    29  1.04763716       1.06     0.3754
>                          |
>                 Residual |  749.046921   761  .984292931
>         -----------------+----------------------------------------------------
>                    Total |  1319.54508   820  1.60920132
>
> . quietly regress response i.clinic i.treatment i.clinic#i.treatment
>
> . contrast gw.treatment, asobserved
>
> Contrasts of marginal linear predictions
>
> Margins      : asobserved
>
> ------------------------------------------------
>              |         df           F        P>F
> -------------+----------------------------------
>    treatment |
> (0 vs mean)  |          1        7.98     0.0049
> (1 vs mean)  |          1        7.98     0.0049
>       Joint  |          1        7.98     0.0049
>              |
>  Denominator |        761
> ------------------------------------------------
>
> --------------------------------------------------------------
>              |   Contrast   Std. Err.     [95% Conf. Interval]
> -------------+------------------------------------------------
>    treatment |
> (0 vs mean)  |  -.0978414   .0346361     -.1658351   -.0298477
> (1 vs mean)  |     .09808   .0347206      .0299205    .1662395
> --------------------------------------------------------------
>
> .
> . exit
>
> end of do-file
>
> On Wed, Feb 19, 2014 at 7:02 PM, David Fisher <djfisher81@gmail.com> wrote:
>> Dear all,
>>
>> As part of a larger piece of research, I am interested in recreating
>> the series of related one-stage meta-analysis models described by Senn
>> (2000)*.  These are described in terms of SAS-style ANOVA "sums of
>> squares", which I would like to recreate in terms of a regression
>> model.
>>
>> The models are as follows:
>> Model 2: Fixed trial strata, fixed treatment effect, no interaction
>> (i.e. the standard one-stage fixed-effects meta-analysis model)
>> Model 4.1: Trial + treatment interaction model using Type II SS
>> Model 4.2: Trial + treatment interaction model using Type III SS.
>>
>> Given outcome "y", treatment "trt" and trial strata "trial", where the
>> effect of interest is that of "trt" (binary), Model 2 can be fitted
>> as:
>> . anova y i.trial i.trt
>> or
>> . regress y i.trial i.trt
>>
>> Model 4.2 can be fitted as:
>> . anova y i.trial##i.trt
>> or
>> . regress y i.trial##i.trt
>> . contrast r.trt, asbalanced
>>
>> No problems -- the anova and regress F and p values for "trt" match exactly.
>>
>> Now, Model 4.1 can be fitted as:
>> . anova y i.trial##i.trt, seq
>>
>> ...and I thought that this could be recreated with regress using
>> "contrast, asobserved", that is:
>> . qui regress y i.trial##i.trt
>> . contrast r.trt, asobserved
>>
>> But the F and p values for "trt", whilst close, are not the same.
>>
>> Have I misunderstood what "contrast" is doing here (I am a
>> statistician, but don't use ANOVA in my day-to-day work, so this may
>> well be the case)?  If so, is there a way to recreate this ANOVA
>> result using "regress"?  If not, why not?
>>
>> Many thanks,
>>
>> David.
>>
>>
>> * Senn S. The many modes of meta. Drug Information Journal 2000; 34: 535-49
>>
>>
>>
>>
>> David Fisher
>> Statistician
>> MRC Clinical Trials Unit at UCL
>> Aviation House
>> 125 Kingsway
>> London  WC2B 6NH
>>
>> Direct line: +44 (0)20 7670-4646
>> Main switchboard: +44 (0)20 7670-4700
>> e-mail:  d.fisher@ucl.ac.uk
>> Website: http://www.ctu.mrc.ac.uk/
>> *
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