Can Linear Discriminant Analysis be used to classify data the way that logistic regression can be used to classify an outcome of something?
This question has been answered, at least, for binary classification here: Logistic regression vs. LDA as two-class classifiers , where the significant comment is:
LDA works when all the independent/predictor variables are continuous (not categorical) and follow a Normal distribution. Whereas in Logistic Regression this is not the case and categorical variables can be used as independent variables while making predictions.
Now, per this source , 'Comparison of Logistic Regression and Linear Discriminant Analysis: A Simulation Study', to quote:
Contrary to the popular beliefs, both methods can be applied to more than two categories (Hosmer and Lemeshow, 1989, p. 216).
Hosmer and Lemeshow provide technical details in their online book, Applied logistic regression, on page 56, freely available here.
So, in the multi-categorical case, both techniques can be employed and the underlying comments in the binary case remain essentially applicable.