Linkage Clustering

[Fae]

I am doing Linkage Clustering with ward's method and i noticed the Pseudo F Statistic is like huge 40000-50000, I know it's bigger is better.  But is such huge number normal?

Also, i done Canonical discriminant analysis (Plot Below), my manager is questioning why some segment is so spread apart ie: segment 9, the light blue one.  I explain that it's only a 2D projection of all the factors so it's normal but he's not buying it.  How should i explain it to him.

proc cluster data=myData method=ward ccc pseudo;
var factor1-factor7.;
	copy clus0;
run;

proc tree noprint ncl=9 out=out;
	copy factor1-factor&numFactors. clus0;
run;

Number of Clusters	Clusters Joined		Freq	Semipartial R-Square	R-Square	Approximate Expected R-Square	Cubic Clustering Criterion	Pseudo F Statistic	Pseudo t-Squared
19	OB15	OB18	736	0.0035	0.708	0.572	764	4.00E+04	460
18	OB9	OB14	3861	0.0049	0.703	0.566	772	4.20E+04	1880
17	OB10	CL19	1521	0.0079	0.695	0.558	763	4.30E+04	852
16	OB1	OB16	6658	0.0087	0.687	0.551	753	4.40E+04	3047
15	OB4	OB13	11577	0.0142	0.673	0.542	712	4.40E+04	5594
14	CL16	OB5	8143	0.0143	0.658	0.533	677	4.40E+04	3017
13	CL18	CL17	5382	0.0143	0.644	0.523	648	4.50E+04	2088
12	OB12	OB20	18770	0.0167	0.627	0.512	613	4.60E+04	1.50E+04
11	OB8	OB17	67981	0.0168	0.61	0.5	586	4.70E+04	2.50E+04
10	CL12	OB19	41771	0.0195	0.591	0.486	553	4.80E+04	1.50E+04
9	OB7	OB11	15612	0.0204	0.571	0.47	529	5.00E+04	8577
8	CL11	CL10	109752	0.022	0.549	0.452	511	5.20E+04	1.70E+04
7	OB2	OB6	125900	0.0523	0.496	0.425	346	4.90E+04	1.00E+05
6	CL7	CL15	137477	0.059	0.437	0.39	212	4.60E+04	5.10E+04
5	CL14	CL8	117895	0.0746	0.362	0.345	74.2	4.30E+04	4.10E+04
4	CL6	CL9	153089	0.078	0.284	0.29	-21	4.00E+04	4.30E+04
3	CL5	CL4	270984	0.0813	0.203	0.216	-57	3.80E+04	3.40E+04
2	CL3	OB3	293984	0.1008	0.102	0.125	-118	3.40E+04	4.00E+04
1	CL2	CL13	299366	0.1023	0	0	0	.	3.40E+04

[mkeintz]

"he's not buying it?"  Tell him if you rotated the data in another dimension, all those clusters looking relatively compact in this plot may very will look quite dispersed from another angle.  And the one in question may look more compact.

[PaigeMiller · Accepted solution]

The light blue segment is spread out because:

The data in the light blue segment is spread out.

Regarding the comment by @mkeintz, yes, rotating the view would certainly cause some colors to look more spread out or less spread out, but when you have 2 dimensions and you plot the results in 2 dimensions I'm not sure why rotation is needed or meaningful. But anyway, you can't get spread out data unless the data itself is spread out; if the data was really dispersed over a TINY area, no rotation would change that.

Pseudo F statistic 40000-50000 because that's what the data is saying. Perhaps it's an outlier, perhaps the clusters really really really really are distinct and separated. How can we say without your data?

[mkeintz]

My point was to find a way to communicate to the manager that any 2-dimensional view of a 3-or-higher dimension set of colored dots can be distorted.

It may be that the 2 dimension chosen is optimized to chose the largest number of clusters as compact, possibly at the expense of apparent compactness of a particular cluster.

[PaigeMiller]

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@mkeintz wrote:



It may be that the 2 dimension chosen is optimized to chose the largest number of clusters as compact, possibly at the expense of apparent compactness of a particular cluster.

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Okay, but that's not what canonical correlation does.