Trying to understand FA for IRT

[sidney-tio]

I'm trying to apply confirmatory_factor_analyzer for a dataset where subjects are playing a game. The objective is similar to Item Response Theory: I would like to estimate the difficulty of each game and the ability of the participants.

Note that:

1. Each subject will attempt the same game multiple times. Game is referred to as an env in the table below.
2. We collect the score of each subject of each play through. As opposed to IRT, the response will be a continuous value, rather than a binary value.

The table looks like this:

For a simple 2 game example, my code looks as such below:

model_dict = {'diff_1: ['env1_0','env1_1','env1_2'],
                         'diff_2: ['env2_0','env2_1','env2_2'],
                         'ability': #diff1 + #diff2
                         }
 
model_spec = ModelSpecificationParser.parse_model_specification_from_dict(fa_df, model_dict)
cfa = ConfirmatoryFactorAnalyzer(model_spec, disp = False)

When I do a transform, each row, representing the subject, will have an output of 3 factors estimated, which is technically wrong since the "difficulty" parameters should be assigned to the item, rather than the subject. I attempt to estimate difficulty by averaging the difficulty across each subject.

Could I have advice as to whether this is the correct approach?