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Re: 'informative' missing ordinal data
Posted:
May 8, 1997 12:23 AM


Richard
I'm not sure what you mean by this statement! vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv >  NO, you cannot haphazardly include a 'missing' category as an > extra category when your variables are treated as ORDINAL, that is > 'ordered', when it is apt to be informative. (If missing is > 'noninformative' then you might justify rescoring Missing to be > the mean, or to be zero... depending.)
In case you did not receive the message below, I'm sending it again. The approach described below can be quite useful. The "missing data" can be "missing" for ANY KIND OF VARIABLE, NOMINAL, ORDINAL, ETC.
When a responder chooses NOT to "answer" a paricular item, THAT IS A RESPONSE!
 Joe *********************************************************************** * Joe Ward 167 East Arrowhead Dr. * * Health Careers High School San Antonio, TX 782282402 * * Phone: 2104336575 * * joeward@tenet.edu * ***********************************************************************
 EARLIER REPLY TO DICON  Subject: Re: 'informative' missing ordinal data
Dicon 
Not sure of your situation but consider the following situation:
Prediction of Y = performance in a highly technical school from GRADE MADE IN HIGH SCHOOL PHYSICS.
If the high school physics grades are not measured very well, it could be the case of weather or not a student CHOSE TO TAKE PHYSICS is a good predictor.
Let
Y = dependent variable (future performance in a highly technical school)
P = 1 IF THE STUDENT CHOSE TO TAKE PHYSICS, 0 OTHERWISE. G = PHYSICS COURSE GRADE IF THE STUDENT CHOSE TO TAKE PHYSICS, 0 OTHERWISE. N = 1 IF THE STUDENT DID NOT TAKE PHYSICS, 0 OTHERWISE. U = 1 for every observation
Y = a1*P + a2*G + a3*N + E1
a1 will be the Yintercept for the line relating Y to Grade a2 will be the slope of the line relating Y to Grade a3 will be the AVERAGE of the Y values for those who DID NOT TAKE PHYSICS.
If you wish to find out if GRADE (FOR THOSE WHO TAKE PHYSICS) can effectively predict Y then compare model 1 above with the restricted model
Y = b1*P + b3*N + E2
b1 will be the AVERAGE of the Y values for those who TOOK PHYSICS. b3 will be the AVERAGE of the Y values for those who DID NOT TAKE PHYSICS.
Then if GRADE may not be "significant" (PRACTICAL SIGNIFICANCE) then it may be of interest to investigate whether or not CHOOSING TO TAKE PHYSICS is a good predictor. The new restricted model wold be:
Y = c1*U + E3
c1 will be the AVERAGE of all the elements in Y (THE GRAND MEAN)
A similar example might involve predicting any Y from SELFREPORTED AGE and GENDER. Whether or not a respondent CHOOSES TO REPORT AGE may be a useful predictor, and there could be INTERACTION between SELFREPORTED AGE and GENDER.
Yes, MISSING INFORMATION MAY BE "INFORMATIVE"!
 Joe
*********************************************************************** * Joe Ward 167 East Arrowhead Dr. * * Health Careers High School San Antonio, TX 782282402 * * Phone: 2104336575 * * joeward@tenet.edu * ***********************************************************************
On Tue, 6 May 1997, SF Ng & SD Montford wrote:
> Date: Tue, 6 May 1997 07:24:16 0400 > From: SF Ng & SD Montford <daryln@pl.jaring.my> > To: Multiple recipients of list <edstatl@jse.stat.ncsu.edu> > Subject: 'informative' missing ordinal data > > I have some missing data for ordinal variables that I believe > to be 'informative'. > > Can I take the fact that the data is missing as part of the analysis > by including the missing category in the analysis as an extra category. > > I assume that no adjustments would have to be made to the df in this > case. > > Dicon Montford <s.d.montford@bham.ac.uk> > >
On Tue, 6 May 1997, Richard F Ulrich wrote:
> Date: Tue, 6 May 1997 23:57:16 0400 > From: Richard F Ulrich <wpilib+@pitt.edu> > To: Multiple recipients of list <edstatl@jse.stat.ncsu.edu> > Subject: Re: 'informative' missing ordinal data > > << Dicon Montford <s.d.montford@bham.ac.uk> >> > SF Ng & SD Montford (daryln@pl.jaring.my) wrote: > : I have some missing data for ordinal variables that I believe > : to be 'informative'. > > : Can I take the fact that the data is missing as part of the analysis > : by including the missing category in the analysis as an extra category. > >  NO, you cannot haphazardly include a 'missing' category as an > extra category when your variables are treated as ORDINAL, that is > 'ordered', when it is apt to be informative. (If missing is > 'noninformative' then you might justify rescoring Missing to be > the mean, or to be zero... depending.) > > If you are analysing as nominal/categorical, then you can just use > another category, which DOES cost a degree of freedom. > > > > Rich Ulrich, biostatistician wpilib+@pitt.edu > http://www.pitt.edu/~wpilib/index.html Univ. of Pittsburgh >



