Alscal

**Notes**
Output Created		19-NOV-2006 10:02:15
Comments
Input	Data	pa765\mds_flight_distances.sav
	Active Dataset	DataSet2
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	10
Syntax		ALSCAL VARIABLES= Atlanta Chicago Denver Houston LosAngel Miami NewYork SanFran Seattle WashDC /SHAPE=SYMMETRIC /LEVEL=RATIO /CONDITION=MATRIX /MODEL=EUCLID /CRITERIA=CONVERGE(.001) STRESSMIN(.005) ITER(30) CUTOFF(0) DIMENS(2,2) /PLOT=DEFAULT ALL /PRINT=HEADER .
Resources	Elapsed Time	0:00:08.30

[DataSet2] pa765\mds_flight_distances.sav

Above, the Notes section simply repeats the parameters input by the researcher. In this case the file "mds_flight_distances.sav" was used, taken from the SPSS Professional Statistics manual.

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Alscal Procedure Options



Data Options-

Number of Rows (Observations/Matrix).   10
Number of Columns (Variables) .  .  .   10
Number of Matrices   .  .  .  .  .  .    1
Measurement Level .  .  .  .  .  .  .    Ratio
Data Matrix Shape .  .  .  .  .  .  .    Symmetric
Type  .  .  .  .  .  .  .  .  .  .  .    Dissimilarity
Approach to Ties  .  .  .  .  .  .  .    Leave Tied
Conditionality .  .  .  .  .  .  .  .    Matrix
Data Cutoff at .  .  .  .  .  .  .  .     .000000


Model Options-

Model .  .  .  .  .  .  .  .  .  .  .    Euclid
Maximum Dimensionality  .  .  .  .  .    2
Minimum Dimensionality  .  .  .  .  .    2
Negative Weights  .  .  .  .  .  .  .    Not Permitted


Output Options-

Job Option Header .  .  .  .  .  .  .    Printed
Data Matrices  .  .  .  .  .  .  .  .    Not Printed
Configurations and Transformations  .    Plotted
Output Dataset .  .  .  .  .  .  .  .    Not Created
Initial Stimulus Coordinates  .  .  .    Computed


Algorithmic Options-

Maximum Iterations   .  .  .  .  .  .       30
Convergence Criterion   .  .  .  .  .     .00100
Minimum S-stress  .  .  .  .  .  .  .     .00500
Missing Data Estimated by  .  .  .  .    Ulbounds
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The text output above shows all the settings, including defaults not specifically requested by the researcher, for this run of MDS.





Iteration history for the 2 dimensional solution (in squared distances)

                  Young's S-stress formula 1 is used.

                Iteration     S-stress      Improvement

                    1           .00308

                         Iterations stopped because
                         S-stress is less than   .005000

Self-explanatory: the SPSS ALSCAL algorithm above computed only one iteration and found insufficient improvement for a second one by the S-stress criterion, so it stopped.



            Stress and squared correlation (RSQ) in distances

RSQ values are the proportion of variance of the scaled data (disparities)
           in the partition (row, matrix, or entire data) which
            is accounted for by their corresponding distances.
             Stress values are Kruskal's stress formula 1.



                For  matrix
    Stress  =   .00298      RSQ =  .99996
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Above, the Kruskal's stress statistic is printed, based on distances (rather than squared distances, as with S-stress in the iteration list above. RSQ shows that nearly all the variance in distances in MDS space is accounted for by the input distance data.





           Configuration derived in 2 dimensions



                   Stimulus Coordinates

                        Dimension

Stimulus   Stimulus     1        2
 Number      Name

    1      Atlanta     .9575   -.1905
    2      Chicago     .5090    .4541
    3      Denver     -.6416    .0337
    4      Houston     .2151   -.7631
    5      LosAngel  -1.6036   -.5197
    6      Miami      1.5101   -.7752
    7      NewYork    1.4284    .6914
    8      SanFran   -1.8925   -.1500
    9      Seattle   -1.7875    .7723
   10      WashDC     1.3051    .4469

Above, SPSS prints out the coordinates of each object on each dimension. These coordinates are the ones used in constructing the plot below.

Above, this is the main MDS plot. In this case, the dimensions are easy to interpret: Dimension 1 is West-East, and Dimension 2 is South-North. Because RSQ approaches 1, locations of objects (here, cities) in MDS space are similar to that which would occur on a map. Note it is coincidental here that dimensions are oriented as would occur on a map.

Above, the scatterplot of linear fit forms a straight 45-degree line, indicating almost perfect model fit (input distance data accounts for almost all of the variance in distances in MDS space).