I am doing classification on a fairly imbalanced dataset (about 1:2 ratio). I have so far so far tried lasso and logistic regression. I didn't downsample the dataset because the sample size is low (about 1,300). You can find the PR curve here and the ROC curve here. As you can see, they look weird. I was under the impression that by increasing/decreasing the threshold, the measures Precision and recall go in the opposite direction which is clearly not the case here. AUC value is about 0.43 for lasso and 0.54 for logistic regression. For some thresholds, I am getting decent Recall and Specificity. Would downsampling help?
I am not sure if this is correct or if these models are even useful. Any feedback/suggestion is greatly appreciated.