Date:         Fri, 7 Sep 2007 09:27:22 -0700
Reply-To:     Robin High <robinh@UOREGON.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Robin High <robinh@UOREGON.EDU>
Subject:      Re: HLM longitudinal data analysis question
Comments: To: Joanne Brady <Brady@NDRI.ORG>
In-Reply-To:  A<46E04046.E7AC.0009.0@ndri.org>
Content-Type: text/plain; charset="us-ascii"

I'm having a problem with proc mixed. I'm trying to predict the number
of injection drug users per 10,000 for 96 large metropolitan areas in
each year from 1992-2002.  I'm running 2 models with time specified
differently in each. In model 1, my independent variable is year3, where
the year 1992 has a value of -10 and the year 2002 has a value of 0. In
model 2, my independent variable is year3, where the year 1992 has a
value of 0 and the year 2002 has a value of 10.

By my understanding, UN (1,1) (shown below in the covariance parameter
estimates results) should be the variance of the slope. Why is UN (1,1)
modeled differently in Model 1 versus Model 2? In the solutions for
fixed effects, why do the slopes not have the same absolute value?

Thanks very much for your help!

Joanne

CODE:
Model 1:
proc mixed data = center_today_difs2 method=ml covtest /*noclprint
NOITPRINT NOINFO*/;
where year ge 1992;
        class msa year;
        model idu_avgest_out = year3 /solution alpha = 0.05 ddfm = bw
notest ;
                random year3  /subject=msa type=un  ;
                repeated year / type=toep subject=msa  ;

run ;
quit ;

Model 2:
proc mixed data = center_today_difs2 method=ml covtest /*noclprint
NOITPRINT NOINFO */;
where year ge 1992;
        class msa year;
        model idu_avgest_out = year2 /solution alpha = 0.05 ddfm = bw
notest ;
                random year2  /subject=msa type=un  ;
                repeated year / type=toep subject=msa  ;

run ;
quit ;


SAMPLE DATA FOR 1 MSA:


                         idu_avgest_
  Obs    MSA     year        out        year2    year3

    3    0080    1992       59.556         0      -10
    4    0080    1993       53.981         1       -9
    5    0080    1994       61.954         2       -8
    6    0080    1995       55.767         3       -7
    7    0080    1996       56.627         4       -6
    8    0080    1997       57.764         5       -5
    9    0080    1998       59.375         6       -4
   10    0080    1999       69.893         7       -3
   11    0080    2000       63.416         8       -2
   12    0080    2001       74.109         9       -1
   13    0080    2002       67.419        10        0



Joanne,

Try adding the 'intercept' term to both random statements, e.g.:

  random intercept year3  /subject=msa type=un  ;


Without it you are forcing all slopes for each MSA to be the one
intercept reported on the Fixed Effect Solution table. And since your
'0' point with each specification of year is different (i.e., where the
lines for each MSA must intersect) the slopes will be different
depending on which variable for year you enter. The 'intercept' option
allows the intercept for each MSA to also freely vary.

Also, the REPEATED statement with TYPE=toep seems like it could be a bit
much to handle the within MSA autocorrelation, when perhaps a type=ar(1)
or toep(n) where choices for n of 2,3,4,.. 11 might work better (i.e.,
check what AIC or BIC report for the various values).

Robin High
University of Oregon