Discriminant analysis, Loadings or variable importance, interpretation

[#1]

Hi, 

I'm trying to get a interpretable information about variables from the Discriminant analysis. Any way to export variable importance (something like VIP in PLS) or variable loadings? 

Thanks

Kamil

[#2]

Kamil, you may need to provide more details.  In Discriminant Analysis, you can obtain the Canonical Scores: at the red triangle, select Canonical Options > Save Canonical Scores.  Are you trying to obtain something other than these scores?

[#3]

Hi Marie, 

Thank you for your reply. Yes, I'm trying to obtain something different than scores. Score basically are coordinates for "samples" or "subjects" position in the discriminant space. But I would like to be able to say something about variables that cause this discrimination. For example, I have 100 measured metabolites and 2 group of subjects. After discriminant analysis, I see a clear separation between 2 groups but I would like to say which metabolites are causing it. In PCA or PLS you have scores (position of your samples in multivariate space) and loadings, which describe position of your variables. Additionally, in PLS, you have variable importance in projection (VIP) scores for each variable. 

Bottom line is that I would like to get some more interpretable outcome out of the discriminant analysis. How are my groups different? What causes the discrimination?

Thank you in advance for your answer. 

Best. Kamil Borkowski

[#4 · Accepted solution]

Hi Kamil,

Thank you for explaining that your interest is in assessing the influence of your independent variables on classification into the two groups. 

One way to approach the issue is the following.  From the Discriminant analysis red triangle, select Canonical Options > Show Canonical Details.  At the very bottom of the report that is generated, there is an outline for "Standardized Scoring Coefficients".  Open this outline to see the canonical weights.  These can help determine which variables influence the classification.  You can right-click in the report, select Make into Data Table, transpose the resulting table, and then sort to see which variables have the largest weights.

Or, you could use Predictor Screening (Analyze > Screening > Predictor Screening).  I think this is available in JMP Basic as well as JMP Pro.  This platform uses a bootstrap forest model to determine predictor importance. 

Another thought might be to treat your analysis as a regression problem.  If you have JMP Pro, you could use Fit Model with the Generalized Regression personality and the Binomial distribution to fit a classification model. Gen Reg will select predictors from correlated groups, so you need to be aware that the predictors in the resulting model may be surrogates for other (correlated) predictors that are influential.  (You may want to do some analysis of your predictors in the Multivariate platform.)  In the Gen Reg report, once you have obtained the Binomial Lasso report, select Profilers from its red triangle menu.  In the Prediction Profiler, you can run Assess Variable Importance. (If you don't have JMP Pro, maybe you could code your two groups with a continuous indicator variable and use Stepwise.  The caution relative to correlated predictors applies here as well.)

Anyway, just some thoughts.  Hopefully there is something useful among them!

[#5]

Thank you Marie, 

Exactly what I was looking for.

Best

Kamil

[#6]

You are very welcome, Kamil!  I'm happy that you found something useful there.

Marie

[#7]

Any idea why the ranking using predictor screening could be significantly different than ranking in the  Standardized Scoring Coefficients?