What is Quality as a measure in Multiple Correspondence Analysis?

[#1]

This is a continuation of a project the result of which has been met with approval.

Context: Multiple Correspondence Analysis was done on questions from a survey in 7 countries.  We were able to extract insights on by-country responses to the grouped questions (the responses are supercategories T2B, Neutral, B2B).  There are a few questions posed:

Questions: 1) Is the Quality statistic a measure of response homogeneity, i.e., how consistent the consumers in the country responded to the question?  If so, it would lead us to make some assumptions about the country.  The JMP library does state quality is an indication of how well the point (the country in this case) is represented in the dimensions. [I am having a hard time understanding what this means in the real world].  Appreciate further explanation.

                  2) How is Quality calculated?  (I can't get to the Quality values in the table with the other givens below).

Table 1: Singular Values
Singular Value	Inertia	ChiSquare	Percent	Cumulative Percent
0.18306	0.03351	17179	59.61	59.61
0.10871	0.01182	6058	21.02	80.63
0.06633	0.0044	2255	7.83	88.45
0.04753	0.00226	1158	4.02	92.47
0.04138	0.00171	878	3.05	95.52
0.03776	0.00143	731	2.54	98.05
0.03309	0.00109	561	1.95	100
Table2: Summary Statistics
COUNTRY	Quality(dim=2)	Mass	Inertia
C	0.98951	0.12497	0.44327
F	0.72069	0.12509	0.07058
G	0.55672	0.12497	0.1194
I	0.54983	0.12509	0.06586
R	0.95129	0.12478	0.15764
S	0.31392	0.12497	0.03898
U	0.41543	0.12503	0.04796
A	0.56778	0.12509	0.05631
Table3: Partial Contributions to Inertia for Row Points
Category	Dim 1	Dim 2	Dim 3
C	0.72843	0.0211	0.01593
F	0.06995	0.04362	0.03728
G	0.10299	0.02419	0.61815
I	0.01318	0.13487	0.20306
R	0.00772	0.69153	0.03045
S	0.00639	0.04008	0.07791
U	0.0329	0.00149	0.00725
A	0.03843	0.04311	0.00998

Thank you in advance for any help!

[#2 · Accepted solution]

Hi TCM,

From towards the end of the JMP help section for MCA, there's a section that (potentially) answers your questions: 

Quality is the ratio of the squared distance of a point from the origin in the space defined by the specified number of dimensions to the distance from the origin in the space with the maximum number of dimensions. For the Chi-Square metric, a point’s quality in a given dimension can be obtained from the cosine that its vector makes with the vector that defines the dimension. Quality is also equal to the ratio of the sum of inertias in the specified dimensions to the sum of the inertias in all dimensions. Quality indicates how well the point is represented in the lower-dimensional space.

There are also similar explanations of mass, inertia, and relative inertia. Hope this helps.

[#3]

Apologies for the late response:  I was out... 

Yes, I did see that paragraph.  I tried to follow it in my attempts to calculate for myself where the quality values came from.  Still didn't get to the reported values :(.  Surprisingly, I didn't see a lot of info out there in the www.

Appreciate your help.--tm