Date: Thu, 26 Aug 2004 14:36:54 -0700
Reply-To: Dale McLerran <stringplayer_2@YAHOO.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <stringplayer_2@YAHOO.COM>
Subject: Re: Type 3 test of fixed effects and "Solution" command don't
give same results
In-Reply-To: <20040825225421.68322.qmail@web61208.mail.yahoo.com>
Content-Type: text/plain; charset=us-ascii
Anne,
The solutions and the Type 3 test of fixed effects tables examine
different contrasts, at least for lower order terms in a model
that has interactions. The code below generates data like that
which might be seen in a factorial design. There are two factors,
A and B, each of which has two levels. We observe 25 responses
at each combination of A and B. (Note that in the simulation
below, there are no effects of either A or B on the response.
However, we can still use this little simulation to demonstrate
the different contrasts which are reported in the solutions table
and the Type 3 table.)
/* Generate data from factorial design with factors A and B */
data test;
do a=1 to 2;
do b=1 to 2;
do i=1 to 25;
y = rannor(1234579);
output;
end;
end;
end;
run;
/* Fit full factorial ANOVA model */
proc mixed data=test;
class a b;
model y = a|b / s;
contrast "Effect of A at B=1"
a 1 -1
a*b 1 0 -1 0;
contrast "Effect of A at B=2"
a 1 -1
a*b 0 1 0 -1;
contrast "Effect of A in B=1 and B=2 combined"
a 1 -1
a*b .5 .5 -.5 -.5;
run;
First of all, you will observe that the interaction effect has
the same p-value in both the solution and Type 3 table. It is
only the lower order terms (main effects of A and B) which have
different p-values.
Now, the contrast labeled "Effect of A at B=2" yields exactly the
same p-value as is reported in the solutions table. You will
further observe that the contrast labeled "Effect of A in B=1 and
B=2 combined" yields the same p-value as is reported in the Type 3
tests of fixed effects table. So, the test of the main effect of
A reported in the Type 3 table is an average effect of factor A
across all levels of B. The test of the parameter A reported in
the solutions table is the effect of A within the reference level
of factor B.
In your data, the effect of A reported in the solutions table is
the effect of A within reference levels for variables B and C.
The effect of A reported in the Type 3 table is the effect of A
over all levels of B and C.
Now, I would note that none of the interactions is significant
in your fitted model. Also, as pointed out above, all of the
interaction terms have the same p-value in both tables. There
is no ambiguity in the interpretation of the p-values for the
interaction effects. I would drop the interaction effects from
your model. Note that when you drop the interaction effects,
you can construct a likelihood ratio test for the joint effect
of all the interaction terms. If that likelihood ratio test is
nonsignificant, then a simple main effects model is better in
these data. If the likelihood ratio test is significant, the
you have more work to do to determine which interactions are
informative about the data.
HTH,
Dale
--- anne olean <annekolean@yahoo.com> wrote:
> Sorry, here they are. a, b and c are two-level dummy
> variables (0/1). week is 0-11. in the output you will
> see that in the type 3 table "b" and "week" are
> significant but not so in the "solutions for fixed
> effects" table. thanks, ako
>
>
> proc mixed data=dataUV;
> class a b c id ;
> model y=a b c week
> week*a week*b week*c
> a*b a*c b*c/ddfm=bw outpred=mypred solution;
> random int week/subject = id (a b c) type=un g;
> run;
>
>
> Type 3 Tests of Fixed Effects
>
> Num Den
> Effect DF DF F Value Pr > F
>
> a 1 88 0.00 0.9523
> b 1 88 8.85 0.0038***
> c 1 88 0.00 0.9800
> week 1 689 6.85 0.0090***
> week*a 1 689 0.22 0.6413
> week*b 1 689 1.40 0.2377
> week*c 1 689 0.03 0.8656
> a*b 1 88 2.78 0.0991
> a*c 1 88 1.87 0.1746
> b*c 1 88 0.13 0.7156
>
>
>
> Solution for Fixed Effects
>
> Standard
> Effect a c b Estimate Error
> DF t Value Pr > |t|
>
> Intercept 0.5312 0.07336
> 88 7.24 <.0001
>
> a 1 0.02076 0.09532
> 88 0.22 0.8281
>
> b 0 -0.07043 0.09907
> 88 -0.71 0.4790
>
> c 1 -0.05454 0.09797
> 88 -0.56 0.5792
>
> week -0.00592 0.006742
> 689 -0.88 0.3803
>
> week*a 1 0.003155 0.006769
> 689 0.47 0.6413
>
> week*b 0 -0.00804 0.006802
> 689 -1.18 0.2377
>
> week*c 1 -0.00115 0.006788
> 689 -0.17 0.8656
>
> a*b 1 0 -0.1875 0.1124
> 88 -1.67 0.0991
>
> a*c 1 1 0.1534 0.1121
> 88 1.37 0.1746
>
> b*c 1 0 -0.04118 0.1127
> 88 -0.37 0.7156
>
>
>
> --- Dale McLerran <stringplayer_2@YAHOO.COM> wrote:
>
> > Anne,
> >
> > Please show your code as well as the solution table
> > and Type 3
> > table. It is really difficult to provide informed
> > comment
> > without seeing your code and results.
> >
> > Dale
> >
> >
> > --- anne olean <annekolean@YAHOO.COM> wrote:
> >
> > > Hi, I fitted a model using proc mixed with fixed
> > and
> > > random effects and requested solutions for
> > regression
> > > coefficients with the "solution" command in the
> > model
> > > statement. I have found that in the "Type 3 fixed
> > > effects" some predictors come up significant but
> > not
> > > in the "solution for fixed effects" obtained via
> > > "solution" command. Is this an indication of a
> > problem
> > > in the way I specified the model? I have observed
> > this
> > > often, and sometimes it's the other way around,
> > > "solution" produces significant effects but "type
> > 3"
> > > doesn't.
> > >
> > > any advice would be greatly appreciated. thanks,
> > ako
> > >
> > >
> > >
> > >
> > >
> > > __________________________________
> > > Do you Yahoo!?
> > > New and Improved Yahoo! Mail - Send 10MB messages!
> > > http://promotions.yahoo.com/new_mail
> > >
> >
> >
> > =====
> > ---------------------------------------
> > Dale McLerran
> > Fred Hutchinson Cancer Research Center
> > mailto: dmclerra@fhcrc.org
> > Ph: (206) 667-2926
> > Fax: (206) 667-5977
> > ---------------------------------------
> >
> >
> >
> > _______________________________
> > Do you Yahoo!?
> > Win 1 of 4,000 free domain names from Yahoo! Enter
> > now.
> > http://promotions.yahoo.com/goldrush
> >
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com
>
=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------
__________________________________
Do you Yahoo!?
New and Improved Yahoo! Mail - 100MB free storage!
http://promotions.yahoo.com/new_mail
