Discriminant Analysis Structure Coefficients

[Adam Guerrero]

Hi All,

I have a question regarding how to reproduce structure coefficients given by “estat structure” after conducting a discriminant analysis. In this particular analysis, X4 is the dependent variable measured as “1” for customers located in the United States and “0” for customers located outside the United States.

The independent variables X6-X18 are “perceptions” variables scaled 1 to 10 that will hopefully distinguish customers located in the United States versus those located outside of the United States. As an example, X6 is product quality, 1 being of low quality, 10 being of high quality. For all perceptions variables, 1 is considered the worst outcome and 10 is considered the best outcome.

Again, my goal is to reproduce the canonical structure matrix that is reported in Stata when using the discriminant analysis postestimation command “estat structure.” These values are also referred to as “structure coefficients,” which according to the Stata MV manual “…measure the correlation between the discriminating variables and the discriminant functions.”

These are the commands that I have used to try to reproduce Stata results (data are also included below using “dataex”):

discrim lda X11 X13 X17 if SPLIT60==0, group(X4)
estat loadings, all
estat structure
predict dfunc, dscore
correlate X11 X13 X17 dfunc if SPLIT60==0

As you can see, the correlations between the discriminant function and the discriminating variables given by “estat structure” are different than those given by “correlate X11 X13 X17 dfunc if SPLIT60==0”.

As always, any insight would be greatly appreciated.

Best,
Adam

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte X4 double(X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18) byte SPLIT60
1 8.5 3.9 2.5 5.9 4.8 4.9   6 6.8 4.7 4.3   5 5.1 3.7 0
0 8.2 2.7 5.1 7.2 3.4 7.9 3.1 5.3 5.5   4 3.9 4.3 4.9 0
1 9.2 3.4 5.6 5.6 5.4 7.4 5.8 4.5 6.2 4.6 5.4   4 4.5 0
1 6.4 3.3   7 3.7 4.7 4.7 4.5 8.8   7 3.6 4.3 4.1   3 0
0   9 3.4 5.2 4.6 2.2   6 4.5 6.8 6.1 4.5 4.5 3.5 3.5 0
1 6.5 2.8 3.1 4.1   4 4.3 3.7 8.5 5.1 9.5 3.6 4.7 3.3 0
1 6.9 3.7   5 2.6 2.1 2.3 5.4 8.9 4.8 2.5 2.1 4.2   2 0
1 6.2 3.3 3.9 4.8 4.6 3.6 5.1 6.9 5.4 4.8 4.3 6.3 3.7 0
1 5.8 3.6 5.1 6.7 3.7 5.9 5.8 9.3 5.9 4.4 4.4 6.1 4.6 1
1 6.4 4.5 5.1 6.1 4.7 5.7 5.7 8.4 5.4 5.3 4.1 5.8 4.4 0
0 8.7 3.2 4.6 4.8 2.7 6.8 4.6 6.8 5.8 7.5 3.8 3.7   4 0
1 6.1 4.9 6.3 3.9 4.4 3.9 6.4 8.2 5.8 5.9   3 4.9 3.2 0
0 9.5 5.6 4.6 6.9   5 6.9 6.6 7.6 6.5 5.3 5.1 4.5 4.4 1
0 9.2 3.9 5.7 5.5 2.4 8.4 4.8 7.1 6.7   3 4.5 2.6 4.2 0
1 6.3 4.5 4.7 6.9 4.5 6.8 5.9 8.8   6 5.4 4.8 6.2 5.2 0
0 8.7 3.2   4 6.8 3.2 7.8 3.8 4.9 6.1   5 4.3 3.9 4.5 0
1 5.7   4 6.7   6 3.3 5.5 5.1 6.2 6.7 5.4 4.2 6.2 4.5 0
1 5.9 4.1 5.5 7.2 3.5 6.4 5.5 8.4 6.2 6.3 5.7 5.8 4.8 1
1 5.6 3.4 5.1 6.4 3.7 5.7 5.6 9.1 5.4 6.1   5   6 4.5 1
1 9.1 4.5 3.6 6.4 5.3 5.3 7.1 8.4 5.8 6.7 4.5 6.1 4.4 0
1 5.2 3.8 7.1 5.2 3.9 4.3   5 8.4 7.1 4.6 3.3 4.9 3.3 1
1 9.6 5.7 6.8 5.9 5.4 8.3 7.8 4.5 6.4 6.5 4.3   3 4.3 1
0 8.6 3.6 7.4 5.1 3.5 7.3 4.7 3.7 6.7   6 4.8 3.4   4 1
1 9.3 2.4 2.6 7.2 2.2 7.2 4.5 6.2 6.4 4.2 6.7 4.4 4.5 0
1   6 4.1 5.3 4.7 3.5 5.3 5.3   8 6.5 3.9 4.7 5.3   4 1
1 6.4 3.6 6.6 6.1   4 3.9 5.3 7.1 6.1 3.7 5.6 6.6 3.9 1
0 8.5   3 7.2 5.8 4.1 7.6 3.7 4.8 6.9 6.7 5.3 3.8 4.4 0
1   7 3.3 5.4 5.5 2.6 4.8 4.2   9 6.5 5.9 4.3 5.2 3.7 1
0 8.5   3 5.7   6 2.3 7.6 3.7 4.8 5.8   6 5.7 3.8 4.4 0
1 7.6 3.6   3   4 5.1 4.2 4.6 7.7 4.9 7.2 4.7 5.5 3.5 0
0 6.9 3.4 8.5 4.3 4.5 6.4 4.7 5.2 7.7 3.3 3.7 2.7 3.3 0
1 8.1 2.5 7.2 4.5 2.3 5.1 3.8 6.6 6.8 6.1   3 3.5   3 0
1 6.7 3.7 6.5 5.3 5.3 5.1 4.9 9.2 5.7 4.2 3.5 4.5 3.4 0
1   8 3.3 6.1 5.7 5.5 4.6 4.7 8.7 5.9 3.8 4.7 6.6 4.2 1
1 6.7   4 5.2 3.9   3 5.4 6.8 8.4 6.2   6 2.5 4.3 3.5 0
0 8.7 3.2 6.1 4.3 3.5 6.1 2.9 5.6 6.1 6.5 3.1 2.9 2.5 0
0   9 3.4 5.9 4.6 3.9   6 4.5 6.8 6.4 4.3 3.9 3.5 3.5 0
1 9.6 4.1 6.2 7.3 2.9 7.7 5.5 7.7 6.1 4.4 5.2 4.6 4.9 0
1 8.2 3.6 3.9 6.2 5.8 4.9   5   9 5.2 7.1 4.7 6.9 4.5 1
1 6.1 4.9   3 4.8 5.1 3.9 6.4 8.2 5.1 6.8 4.5 4.9 3.2 1
1 8.3 3.4 3.3 5.5 3.1 4.6 5.2 9.1 4.1 1.7 4.6 5.8 3.9 1
0 9.4 3.8 4.7 5.4 3.8 6.5 4.9 8.5 4.9 6.2 4.1 4.5 4.1 1
0 9.3 5.1 4.6 6.8 5.8 6.6 6.3 7.4 5.1 4.1 4.6 4.6 4.3 0
1 5.1 5.1 6.6 6.9 4.4 5.4 7.8 5.9 7.2 5.2 4.9 6.3 4.5 0
0   8 2.5 4.7 7.1 3.6 7.7   3 5.2 5.1 3.9 4.3 4.2 4.7 0
1 5.9 4.1 5.7 5.9 5.8 6.4 5.5 8.4 6.4 5.1 5.2 5.8 4.8 0
0  10 4.3 7.1 6.3 2.9 5.4 4.5 3.8 6.7 3.7   5   4 3.5 0
1 5.7 3.8 6.8 7.5 5.7 5.7   6 8.2 6.6 4.8 6.5 7.3 5.2 0
1 9.9 3.7 3.7 6.1 4.2   7 6.7 6.8 5.9 7.2 4.5 3.4 3.9 0
0 7.9 3.9 4.3 5.8 4.4 6.9 5.8 4.7 5.2 3.6 4.1 4.2 4.3 0
1 6.7 3.6 5.9 4.2 3.4 4.7 4.8 7.2 5.7 5.3   4 3.6 2.8 1
0 8.2 2.7 3.7 7.4 2.7 7.9 3.1 5.3 5.3   5 4.5 4.3 4.9 0
1 9.4 2.5 4.8 6.1 3.2 7.3 4.6 6.3 6.3 9.2 4.7 4.6 4.6 0
0 6.9 3.4 5.7 4.4 3.3 6.4 4.7 5.2 6.4 4.4 3.2 2.7 3.3 0
1   8 3.3 3.8 5.8 3.2 4.6 4.7 8.7 5.3 4.2 4.9 6.6 4.2 1
0 9.3 3.8 7.3 5.7 3.7 6.4 5.5 7.4 6.6 5.9 4.1 3.2 3.4 0
1 7.4 5.1 4.8 7.7 4.5 7.2 6.9 9.6 6.4 7.4 5.7 6.5 5.5 1
0 7.6 3.6 5.2 5.8 5.6 6.6 5.4 4.4 6.7 6.4 4.6 3.9   4 0
0  10 4.3 5.3 3.7 4.2 5.4 4.5 3.8 6.7 4.5 3.7   4 3.5 1
1 9.9 2.8 7.2 6.9 2.6 5.8 3.5 5.4 6.2   7 5.6 4.9   4 0
0 8.7 3.2 8.4 6.1 2.8 7.8 3.8 4.9 7.2 4.5 5.4 3.9 4.5 0
1 8.4 3.8 6.7   5 4.5 4.7 5.9 6.7 5.1 4.2 2.7   5 3.6 1
0 8.8 3.9 3.8 5.1 4.3 4.7 4.8 5.8   5 7.2 4.4 3.7 2.9 0
1 7.7 2.2 6.3 4.5 2.4 4.7 3.4 6.2   6 4.7 3.3 3.1 2.6 0
1 6.6 3.6 5.8 4.1 4.9 4.7 4.8 7.2 6.5 3.9 3.5 3.6 2.8 0
1 5.7 3.8 3.5 6.7 5.4 5.7   6 8.2 5.4   5 4.7 7.3 5.2 1
1 5.7   4 7.9 6.4 2.7 5.5 5.1 6.2 7.5 6.4   5 6.2 4.5 0
1 5.5 3.7 4.7 5.4 4.3 5.3 4.9   6 5.6 2.5 4.5 5.9 4.3 0
1 7.5 3.5 3.8 3.5 2.9 4.1 4.5 7.6 5.1 5.2   4 5.4 3.4 0
1 6.4 3.6 2.7 5.3 3.9 3.9 5.3 7.1 5.2 5.5 4.7 6.6 3.9 1
1 9.1 4.5 6.1 5.9 6.3 5.3 7.1 8.4 7.1 5.7 5.4 6.1 4.4 1
0 6.7 3.2   3 3.7 4.8 6.3 4.5   5 5.2 2.5 2.9 2.6 3.1 0
1 6.5 4.3 2.7 6.6 6.5 6.3   6 8.7 4.7 6.3 4.6 5.6 4.6 1
1 9.9 3.7 7.5 4.7 5.6   7 6.7 6.8 7.2 4.6 4.1 3.4 3.9 1
1 8.5 3.9 5.3 5.5   5 4.9   6 6.8 5.7 3.6 4.4 5.1 3.7 1
0 9.9   3 6.8   5 5.4 5.9 4.8 4.9 7.3 7.6 3.1 4.3 3.8 1
1 7.6 3.6 7.6 4.6 4.7 4.6   5 7.4 8.1 6.6 4.5 5.8 3.9 1
0 9.4 3.8   7 6.2 4.7 6.5 4.9 8.5 7.3 2.4 4.3 4.5 4.1 1
0 9.3 3.5 6.3 7.6 5.5 7.5 5.9 4.6 6.6 3.1 5.2 4.1 4.6 0
1 7.1 3.4 4.9 4.1   4   5 5.9 7.8 6.1 3.5 2.6 3.1 2.7 0
0 9.9   3 7.4 4.8   4 5.9 4.8 4.9 5.9 6.9 3.2 4.3 3.8 0
0 8.7 3.2 6.4 4.9 2.4 6.8 4.6 6.8 6.3 5.1 4.3 3.7   4 1
0 8.6 2.9 5.8 3.9 2.9 5.6   4 6.3 6.1   4 2.7   3   3 1
1 6.4 3.2 6.7 3.6 2.2 2.9   5 8.4 7.3 6.5   2 3.7 1.6 1
0 7.7 2.6 6.7 6.6 1.9 7.2 4.3 5.9 6.5 4.1 4.7 3.9 4.3 1
1 7.5 3.5 4.1 4.5 3.5 4.1 4.5 7.6 4.9 2.8 3.4 5.4 3.4 0
1   5 3.6 1.3   3 3.5 4.2 4.9 8.2 4.3 7.6 2.4 4.8 3.1 0
0 7.7 2.6   8 6.7 3.5 7.2 4.3 5.9 6.9 7.7 5.1 3.9 4.3 0
0 9.1 3.6 5.5 5.4 4.2 6.2 4.6 8.3 6.5 4.1 4.6 4.3 3.9 1
1 5.5 5.5 7.7   7 5.6 5.7 8.2 6.3 7.4 4.9 5.5 6.7 4.9 1
0 9.1 3.7   7 4.1 4.4 6.3 5.4 7.3 7.5 4.6 4.4   3 3.3 1
1 7.1 4.2 4.1 2.6 2.1 3.3 4.5 9.9 5.5 3.5   2   4 2.4 0
0 9.2 3.9 4.6 5.3 4.2 8.4 4.8 7.1 6.2 6.6 4.4 2.6 4.2 1
1 9.3 3.5 5.4 7.8 4.6 7.5 5.9 4.6 6.4 4.9 4.8 4.1 4.6 0
0 9.3 3.8   4 4.6 4.7 6.4 5.5 7.4 5.3 4.8 3.6 3.2 3.4 0
0 8.6 4.8 5.6 5.3 2.3   6 5.7 6.7 5.8 3.6 4.9 3.6 3.6 1
1 7.4 3.4 2.6   5 4.1 4.4 4.8 7.2 4.5 6.4 4.2 5.6 3.7 1
0 8.7 3.2 3.3 3.2 3.1 6.1 2.9 5.6   5 4.3 3.1 2.9 2.5 0
1 7.8 4.9 5.8 5.3 5.2 5.3 7.1 7.9   6 5.7 4.3 4.9 3.9 1
1 7.9   3 4.4 5.1 5.9 4.2 4.8 9.7 5.7 5.8 3.4 5.4 3.5 0
end

[Phil Bromiley]

You didn't get a quick answer. Part may reflect you asking two separate questions almost at the same time. Part may also reflect folks not being interested in the issue.

[Adam Guerrero]

Hi Phil,

I usually don't get quick answers, but I have found that in many cases it is in part due to Stata's limitations/preferences in certain areas relative to other packages used in business. Anyway, my question above has to do with using Stata results from a discriminant analysis to reproduce structure coefficients, that's it, so I apologize if I was being unclear (If you'd be willing, please help me understand what my 2 separate questions are so that I can be more clear in the future). Finally, I assumed that a lack of interest is definitely part of the reason I didn't get a reply, but thank you for kindly putting extra emphasis on that possibility, that is very helpful. I am sure that many users know the answer, but are just not interested enough in the question to share their knowledge (this possibility is clearly outlined in Stata Forum's Q&A).

Adam