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

 From Joseph Coveney To statalist@hsphsun2.harvard.edu Subject Re: st: Recreating SAS "sums of squares" in Stata using anova and regress Date Wed, 19 Feb 2014 20:15:36 +0900

```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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```