Date:  Thu, 15 Feb 1996 16:27:57 0700 
ReplyTo:  "Raymond V. Liedka" <liedka@UNM.EDU> 
Sender:  "SAS(r) Discussion" <SASL@UGA.CC.UGA.EDU> 
From:  "Raymond V. Liedka" <liedka@UNM.EDU> 
Subject:  Re: PRINQUAL in SAS? 

InReplyTo:  <DMnGvA.Lwv.0.s@hkusuc.hku.hk> 

On Thu, 15 Feb 1996, * AHIRU NO PEKKLE * wrote:
>
> I'm looking for the underlying theorem of the option UNTIE in the
> SAS procedure PRINQUAL. Is there any book or paper discussing it
> and also its applications??
>
> How does it deal with those missing data?
>
There is a SAS Technical Report R108 that can be ordered (probably <$5)
from SAS publications. This report is entitled: "Algorithms for the
PRINQUAL and TRANSREG Procedures."
On page 2, it reads:
" The PRINQUAL procedure (principal components of qualitative data) is
a data transformation procedure that is based on the work of Kruskal and
Shepard (1974); Young, Takane, and de Leeuw (1978); and Winsberg and
Ramsay (1983)."
On page 3, it reads:
" * For all transformations, missing data can be estimated without
constraint, with category constraints (that is, missing values within
the same group get the same value), and with order constraints (that is,
missing value estimates in adjacent groups can be tied to weakly
preserve a specified ordering) (Gifi, 1981; Young, 1981; Kuhfeld and de
Leeuw, in preparation)."
On page 4, it reads:
" The UNTIE transformation (Kruskal, 1964, primary approach to ties)
uses the same algorithm on the means of the nonmissing values
(1 2 3 4 6 4 5 6 7)' but with different results for this example: 1<2:OK,
2<3:OK, 3<4:OK, 4<6:OK, 6>4: average 6 and 4 and replace 6 and 4 by the
average. The new means of the nonmising values are (1 2 3 4 5 5 5 6 7)'.
The check resumes: 4<5:OK, 5=5:OD, 5=5:OK, 5<6:OK, 6<7:OK. If some of
the special missing values are ordered, the upward checking, downward
averaging method is applied to them too, independently of the other
missing and nonmissing partitions. Once the means conform to any
required category or order constraints, an optimally scaled vector is
produced from the means. The following example results from a MONOTONE
transformation:
X: (. . .A .A .B 1 1 1 2 2 3 3 3 4)'
Y: (5 6 2 4 2 1 2 3 4 6 4 5 6 7)'
result: (5 6 3 3 2 2 2 2 5 5 5 5 5 7)'
"
References:
Gifi, A. (1981) _Nonlinear Multivariate Analysis_. Department of Data
Theory, The Netherlands: The University of Leiden. (this has since been
published as a book)
Kruskal, J.B. (1964) "Multidimensional Scaling By Optimizing Goodness of
Fit to a Nonmetric Hypothesis," _Psychometrika_, 29: 127.
Kruskal, J.B., and Shepard, R.N. (1974) "A Nonmetric Variety of Linear
Factor Analysis," _Psychometrika_, 38: 123157.
Kuhfeld, W.F., and de Leeuw, J., "Optimal Scaling of Partitioned
Variables," (in preparation).
Winsberg, S., and Ramsay, J.O. (1983) "Monotone Spline Transformations for
Dimension Reduction," _Psychometrika_, 48: 575595.
Young, F.W. (1981) "Quantitative Analysis of Qualitative Data,"
_Psychometrika_, 46: 357388.
Young, F.W., Takane, Y., and de Leeuw, J. (1978) "The Principal
Components of Mixed Measurement Level Multivariate Data: An Alternating
Least Squares Method with Optimal Scaling Features," _Psychometrika_, 43:
279281.
Raymond V. Liedka
Department of Sociology
University of New Mexico
