Models and Parameters

In IRTpp: Estimating IRT Parameters using the IRT Methodology

In item response theory models , tests can be modelled through different models, in IRTpp each test calibrated parameters are in a simple data structure that is passed around the IRTpp functions.

UIRT models

In UIRT models, typically Rasch , 2PL and 3PL, in IRTpp the item parameters are usually these :

• $a$ Discrimination parameter (Also the slope of the ICC)
• $b$ Difficulty parameter
• $c$ Guessing parameter
• $d$ A transformation of the b parameter , this is $-a * b$
• $c'$. The logistic transform of the c parameter , codename : cp.

IRTpp functions must accept these parameters and transform them accordingly in the functions.

The UIRT model types accepted by IRTpp are :

• 1PL (Logistic model with b parameter only , a = 1, and c = 0)
• 2PL (Logistic model where parameters a and b are estimated, c = 0)
• 3PL (Logistic model with parameters a, b and c)

Functions

Therefore functions are required to :

• Simulate random parameters for all kinds of models and dimensions.
• Simulate tests based on a model and parameters.
• Transform between parameter types when is appropiate
• Display item parameters for the end user.
• Allow the end user to enter restrictions in the parameters.

Simulation functions :

sim.test
sim.itempars

Model checking and transformation functions :

model.transform // Transform a model parameters ?
model.check // Check if a model is valid or not.
model.extract // Extract a named parameter from a parameter list.
as.model // Makes a irtpp model from whatever you try to throw at it.

Model and parameter list examples :

$a $b $c $model $dims

Generic Probability functions :

In spite of generalism , the probability function is completely flexible for all models. To calculate a probability we need the model, the parameters and the abilities.

Functions for estimation

irtpp : estimate item parameters
latent.traits : estimate individual parameters

IRTpp documentation built on May 29, 2017, 9:58 a.m.