Direction of traceplots for nominal model

[AM]

Dear Phil, dear everyone,

I am using the nominal response model on data of a knowledge test where each item has 5 possible options to choose from, one of which is correct. We do not binarize the answers into correct and incorrect, because our hypothesis is related to the response options themselves; also, we use nominal response model because our hypothesis is that the ordering of the thresholds (not just values of thresholds) of the correct option and incorrect option will change according to some item properties.

However, when using the nominal response model, there is no way to specify which option is correct. This results in the algorithm somehow automatically determining what the direction of the traceplots should be. To better illustrate what I mean, here are some examples:

This is an example of a "well-behaved" item, where the correct option, in this case P2, rises along with theta:

This is an example of a "badly behaved" item, where the probability to choose the correct option does not rise with theta. The correct option should be P4, but it does not show the appropriate behavior:


However, if you decide to recode the whole dataset so that the correct option is always labeled with 5 (and the category which was originally 5 gets assigned the number which was originally the correct option's number), then you get different traceplots. For example, for the problematic item from above:

The correct option, which is now always P5, rises with theta. 

However, this also visibly changes the shape of the other curves, whereas what I'd expect that the graph will be identical, but just the colors of the response options will change.

Therefore, I am wondering if the recoding approach I took was the correct one, or if there is something else I am not seeing. In general, do you have any advice how I should approach this modeling issue?