# How do we generate the ROC curve for Linear Discriminant Analysis method

I know the method to generate the ROC curve for other methods such as naive Bayes where the tuning parameter is the threshold like also in logistic regression.

If we want to generate the ROC curve for linear discriminant analysis method used in binary classification what is the tuning parameter here?

• ROC curves generation only takes two imputes. The true binary observations and the predicted values. It sorts them based on the predicted values. And for each value of the predicted values it separates the true observation into two groups and plots the correct positives vs the false positives. No matter what method you use. If it gives real predicted values you can always generate a ROC curve. – Chamberlain Foncha Nov 14 '14 at 12:14
• @ChamberlainFoncha: but what is "predicted value" in LDA? – amoeba Nov 14 '14 at 12:24
• How will you be using the results of the analysis? What about the problem leads you to think that ROC curves are more useful that LDA's posterior probabilities? Why did you chose the more assumption-laden LDA approach over logistic regression? – Frank Harrell Nov 14 '14 at 13:11
• @amoeba: the decision boundary of the LDA is of the form $\omega.x$, where $x$ are the predictors. Normally you will say when $\omega .x>0$ predict 1 and 0 otherwise. Use the $\omega. x$ as your predicted values. So the ROC is generated from different cut-offs not just 0. – Chamberlain Foncha Nov 14 '14 at 13:40
• The ROC does not play a role here. ROC is mainly a way to avoid thinking about utilities/cost/loss functions and invites arbitrary thresholding. – Frank Harrell Nov 14 '14 at 14:25