Comparison with the ALSCAL Procedure

The MDS Procedure

Comparison with the ALSCAL Procedure

The MDS procedure generally produces results similar to those from the ALSCAL procedure (Young, Lewyckyj, and Takane 1986; Young 1982) if you use the following options in PROC MDS:

FIT=SQUARED
FORMULA=1 except for unfolding data, which require FORMULA=2
PFINAL to get output similar to that from PROC ALSCAL

Unlike PROC ALSCAL, PROC MDS produces no plots, so you must use output data sets and PROC PLOT or PROC GPLOT.

The MDS and ALSCAL procedures may sometimes produce different results for the following reasons:

With the LEVEL=INTERVAL option, PROC MDS fits a regression model while PROC ALSCAL fits a measurement model. These models are not equivalent if there is more than one partition, although the differences in the parameter estimates are usually minor.
PROC MDS and PROC ALSCAL use different algorithms for initialization and optimization. Hence, different local optima may be found by PROC MDS and PROC ALSCAL for some data sets with poor fit. Using the INAV=SSCP option causes the initial estimates from PROC MDS to be more like those from PROC ALSCAL.
The default convergence criteria in PROC MDS are more strict than those in PROC ALSCAL. The convergence measure in PROC ALSCAL may cause PROC ALSCAL to stop iterating because progress is slow rather than because a local optimum has been reached. Even if you run PROC ALSCAL with a very small convergence criterion and a very large iteration limit, PROC ALSCAL may never achieve the same degree of precision as PROC MDS. For most applications, this problem is of no practical consequence since two- or three-digit precision is sufficient. If the model does not fit well, obtaining higher precision may require hundreds of iterations.

PROC MDS accepts some PROC ALSCAL options as synonyms for the preceding options, as displayed in Table 40.1.

Table 40.1: PROC MDS Options Compared to PROC ALSCAL Options

	Accepted by	Related PROC MDS Option
PROC ALSCAL Option	PROC MDS?	or Comments
CONDITION=	Yes
CONVERGE=	Yes	Convergence measures are
		not comparable
CUTOFF=	Yes
DATA=	Yes
DEGREE=	No
DIMENS=	Yes
DIRECTIONS=	No
HEADER	Yes	Default in PROC MDS
IN=	Yes
ITER=	Yes	MAXITER=
LEVEL=	Yes	LEVEL=NOMINAL is not
		supported
MAXDIM=m	Yes	DIMENSION=n TO m
MINDIM=n	Yes	DIMENSION=n TO m
MINSTRESS=	Yes	MINCRIT=
MODEL=EUCLID	Yes	COEF=IDENTITY
MODEL=INDSCAL	Yes	COEF=DIAGONAL
MODEL=GEMSCAL	No
MODEL=ASYMSCAL	No
MODEL=ASYMINDS	No
NEGATIVE	(Yes)	In PROC MDS, the NEGATIVE
		option affects slopes and powers,
		not subject weights.
NOULB	Yes
OUT=	Yes	Some differences in contents
PLOT	No
PLOTALL	No
PRINT	No
READV, etc.	No	Use WHERE data set option
READFIXV, etc.	No
ROWS=	No
SHAPE=SYMMETRI	Yes	SHAPE=TRIANGLE
SHAPE=ASYMMETR	Yes	SHAPE=SQUARE
SHAPE=RECTANGU	No	Use SHAPE=TRIANGLE with
		extra missing values to
		fill out the matrix.
SIMILAR	Yes
TIESTORE=	Yes	Ignored by PROC MDS
UNTIE	Yes

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