Proximities

**Notes**
Output Created		20-NOV-2006 12:35:06
Comments
Input	Data	C:\Program Files\SPSS\Cars.sav
	Active Dataset	DataSet1
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	406
Missing Value Handling	Definition of Missing	User-defined missing values are treated as missing.
Missing Value Handling	Cases Used	Statistics are based on cases with no missing values for any variable used.
Syntax		PROXIMITIES mpg engine horse weight accel cylinder /PRINT NONE /MATRIX OUT ('C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\spss2588\spssalsc.tmp') /MEASURE=EUCLID /STANDARDIZE=VARIABLE Z /VIEW=VARIABLE .
Resources	Elapsed Time	0:00:00.14
Resources	Workspace Bytes	344
Files Saved	Matrix File	C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\spss2588\spssalsc.tmp

[DataSet1] C:\Program Files\SPSS\Cars.sav

Above, the cars.sav data file is used, which is a sample file supplied by SPSS. In the dialogs, SPSS was asked to "Create distances from data" in the main MDS dialog. The metric variables mpg. engine, horse, weight , accel, and cylinder were entered. In the Measure button dialog, SPSS was also asked to transform to standardized Z scores.

**Case Processing Summary(a)**
Cases
Valid		Missing		Total
N	Percent	N	Percent	N	Percent
391	96.3%	15	3.7%	406	100.0%
a Euclidean Distance used

The input data had data on 406 automobiles, of which there were 393 valid cases with non-missing data for all variables.

Alscal

**Notes**
Output Created		20-NOV-2006 12:35:06
Comments
Input	Data	C:\Program Files\SPSS\Cars.sav
	Active Dataset	DataSet1
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	406
Syntax		ALSCAL /MATRIX= IN('C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\spss2588\spssalsc.tmp') /LEVEL=INTERVAL /CONDITION=MATRIX /MODEL=EUCLID /CRITERIA=CONVERGE(.001) STRESSMIN(.005) ITER(30) CUTOFF(0) DIMENS(2,2) /PLOT=DEFAULT ALL /PRINT=DATA HEADER .
Resources	Elapsed Time	0:00:01.20

[DataSet1] C:\Program Files\SPSS\Cars.sav

Above, the syntax equivalent of the menu choices is listed.

C




Alscal Procedure Options



Data Options-

Number of Rows (Observations/Matrix).    6
Number of Columns (Variables) .  .  .    6
Number of Matrices   .  .  .  .  .  .    1
Measurement Level .  .  .  .  .  .  .    Interval
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  .  .  .  .  .  .  .  .    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

Above, SPSS prints out all the default as well as menu-chosen parameters for this run.




                  Raw (unscaled) Data for Subject 1

                      1          2          3          4          5        6

              1       .000
              2     37.520       .000
              3     37.221      8.900       .000
              4     37.787      7.182     10.340       .000
              5     21.068     34.751     36.428     33.345       .000
              6     37.221      6.191     11.090      8.958     34.330     .000

Above, SPSS has converted the data on 393 automobiles, transforming it into standardized data on six objects, which are the variables in the order entered: mpg. engine, horse, weight , accel, and cylinder.



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

                  Young's S-stress formula 1 is used.

                Iteration     S-stress      Improvement

                    1           .01241
                    2           .01074         .00167
                    3           .01056         .00019

                         Iterations stopped because
                 S-stress improvement is less than   .001000

By default, a two-dimensional solution is sought. After starting with arbitrary point locations, MDS goes through three iterations of placing points better to minimize stress.




            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  =   .03212      RSQ =  .99702

Stress is Kruskal's stress, based on distances, in contrast to squared distances used in S-stress in the iteration list. The high RSQ indicates almost all of the variance in interpoint MDS p-space distance is accounted for by interpoint distances in the original input.

Configuration derived in 2 dimensions

Stimulus Coordinates

Dimension

Stimulus Stimulus 1 2
Number Name

1 mpg 2.0309 .7032
2 engine -.9553 .0079
3 horse -.9899 .3724
4 weight -.8979 -.2587
5 accel 1.7326 -.7914
6 cylinder -.9205 -.0333 Above, MDS prints out the object (point, stimulus) coordinates which will be used below to create the MDS perceptual map.

Optimally scaled data (disparities) for subject 1

1 2 3 4 5 6

1 .000
2 3.066 .000
3 3.037 .368 .000
4 3.091 .206 .504 .000
5 1.515 2.805 2.963 2.672 .000
6 3.037 .113 .574 .374 2.765 .000

Above, MDS prints out the inter-point distances in p-space.

Above, this is the MDS perceptual map. Engine/cylinder/weight form one cluster. Of the remaining objects, horsepower is most closely related to this cluster. Interpreting the axes diagonally, one axis is horsepower/acceleration, while the other is mpg/engine cluster.

Above, since the points form roughly a straight line, this is a well-fitting model (though less so than the inter-city distances example).

Above, appended to this output, is the MDS plot for the situation where the researcher has used Data/Select Cases to ask for a random sample of 25 of the 406 automobiles, and in the MDS dialog has asked to "Create distances from data" and in the Measure dialog has asked that it be "By cases" rather than the default "By Variables" of the earlier analysis. This clusters automobiles, here shown as "Var1", etc., rather than clustering variables.

Above, appended to this output, is the MDS plot for the 1-dimensional solution. (In order to have sufficient parameters for the 3D solution below, one additional variable (year) has been added).

Above, appended to this output, is the MDS plot for the 2-dimensional solution. (In order to have sufficient parameters for the 3D solution below, one additional variable (year) has been added). Note how respecifying the model to include an additional variable substantially affects the MDS plot compared to the previous 2-dimensional solution further above.

Above, appended to this output, is the MDS plot for the 3-dimensional solution. (In order to have sufficient parameters for the 3D solution, one additional variable (year) has been added).