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st: Re: comparison between a repeated ordinal measures


From   "Michael Wood" <mwood@hunter.cuny.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: comparison between a repeated ordinal measures
Date   Thu, 31 Mar 2005 16:10:31 -0500

Thanks to Joseph Coveney for an interesting illustration of Stata categorical
commands and data reshaping.

Joseph W. may want to consider dropping column 5 which has only one, unique 
observation, which will allow the use of Stata's -symmetry- command.

Using the data prior to the -reshape long- command, 

symmetry sco0 sco1, contrib 

---------------------------------------------
          |               sco1               
  sco0 |   1      2      3      4    Total
----------+----------------------------------
        1 |   28     18      6     0     52 
        2 |   21     78     44    1    144 
        3 |    7     34     96     5    142 
        4 |    0      3     18    16     37 
           | 
  Total |   56    133    164     22    375 
---------------------------------------------

                     Contribution
                     to symmetry
   Cells           chi-squared
--------------  --------------

 n1_2 & n2_1          0.2308
 n1_3 & n3_1          0.0769
 n1_4 & n4_1          0.0000
 n2_3 & n3_2          1.2821
 n2_4 & n4_2          1.0000
 n3_4 & n4_3          7.3478


                                                                   chi2         df      Prob>chi2
------------------------------------------------------------------------
Symmetry (asymptotic)                            |      9.94      5         0.0770
Marginal homogeneity (Stuart-Maxwell)  |      9.79      3         0.0205
------------------------------------------------------------------------

The symmetry model fits, albeit poorly; the marginals are different. The main source 
of difference for the symmetry chi sq is respondents (n=5) who reported 3 at time0 
and 4 at time1, versus those (n=18) who responded 4 at time0 and 3 at time1.

Michael Wood
<mwood@hunter.cuny.edu>


> --- In statalist@yahoogroups.com, Joseph Coveney <jcoveney@b...> wrote:
> > Joseph Wagner wrote
> > 
> > I need to do a comparison between two ordinal measures, one at baseline
> > (hlths) and the other, repeated at followup(f6hlths).  I have done
> > something similar in SAS using CATMOD.  I wish to know if there has been
> > a change between the two time points and in which direction.
> > 
> > 
> > The data takes this form:
> > 
> > 
> > Self Rated |    6M Self Rated Health
> >     Health |    1     2    3    4    5 | Total
> > -----------+--------------------------+-----
> >          1 |   28    18    6    0    0 |    52
> >          2 |   21    78   44    1    0 |   144
> >          3 |    7    34   96    5    1 |   143
> >          4 |    0     3   18   16    0 |    37
> > -----------+--------------------------+-----
> >      Total |   56   133  164   22    1 |   376
> > 
> > 
> > Is the command -mvrepeat- that Philip Ender wrote, appropriate?
> > 
> >
> ----------------------------------------------------------------------------
> > 
> > In this case, -mvrepeat- would give the same answer as -ttest- using the
> > paired t-test syntax.  I vaguely recall reading that under these
> > circumstances Student's t-test does surprisingly well with ordinal
> data with
> > as few as three categories, but consider using an alternative, such as a
> > nonparametric test or a modeling command intended for ordered
> categorical
> > data.  There are several of each from which to choose.  In addition
> > to -ologit- (illustrated below), Stata has user-written commands
> that don't
> > rely upon the proportional odds assumption, at least one of which
> > (-gologit-) allows the -cluster()- option.
> > 
> > To observe the direction of change and its magnitude, you can either
> > use -predict- after one of the modeling commands or plot the data
> using a
> > graphing command specifically for ordered categorical data.  (I've
> > illustrated using -ordplot-, but be aware that its author, Nick Cox, has
> > enhanced it and updated it for Stata Release 8 under the name
> > of -distplot-.)
> > 
> > Joseph Coveney
> > 
> > clear
> > set more off
> > input byte sco0 byte cou1 byte cou2 byte cou3 byte cou4 byte cou5
> > 1 28 18  6  0  0
> > 2 21 78 44  1  0
> > 3  7 34 96  5  1
> > 4  0  3 18 16  0
> > end
> > reshape long cou, i(sco0) j(sco1)
> > drop if cou == 0
> > expand cou
> > drop cou
> > signtest sco0 = sco1
> > signrank sco0 = sco1
> > generate int pid = _n
> > reshape long sco, i(pid) j(tim)
> > somersd tim sco, cluster(pid)
> > ologit sco tim, cluster(pid)
> > npt_s sco, by(tim) strata(pid) nodetail
> > version 7: ordplot sco, by(tim)
> > gllamm sco tim, i(pid) family(binomial) link(ologit)
> > estimates store A
> > gllamm sco, i(pid) family(binomial) link(ologit)
> > estimates store B
> > lrtest A B, stats
> > exit
> > 

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