In this paper we consider the well known two-parameter logistic model from the Item Response Theory (IRT) and suppose the presence of several latent classes among the test population which classes differ each other in the item parameter...
moreIn this paper we consider the well known two-parameter logistic model from the Item Response Theory (IRT) and suppose the presence of several latent classes among the test population which classes differ each other in the item parameter structure. We give a computer implementation of this model and also empirically examine the model by means of a software test simulator. Parameters are estimated via the MMLE/EM method. i i i i b a b a b a P − θ + − θ = θ exp 1 exp , , , ( 1) and value 0 with probability () ( ) i i i i b a P b a Q , , 1 , , θ − = θ , where i a , n i , , 2 , 1 K = , is the item discrimination parameter and i b , n i , , 2 , 1 K = , is connected with the item difficulty. The value θ represents the person ability level. Assuming the local independence, the test answer joint probability distribution is given by ( ) ( ) ( ) ∏ = − θ θ = θ n i u i i u i i i i b a Q b a P f 1 1 ,
