I am using Item Response theory (IRT) using 3 Parameter Logistic Model(3PL) for Logic test. After training the model, I use the posterior means of the item parameters 𝛼, β and γ to estimate person trait 𝜃 during the adaptive test. I want to introduce co-variates i.e. age, gender etc in the model for estimating ability of the person using Latent Regression. But I am not able to find any research for introducing co-variates in the IRT model. Any guidance would be much appreciated.
Hello Fahad,
Though you may have already considered this, it might be useful first to determine whether your proposed control variables make any difference. Tests of DIF (differential item functioning) would be one way to determine whether estimated item parameters are influenced by gender (and any other variables under consideration). If there is no evidence of DIF, then ability estimates should be consistent across subgroups; no control variables would be needed.
If you're using ability estimates for some other purpose (e.g., as a dependent variable in some subsequent analysis), and you want to add covariates, then there is nothing special about IRT ability estimates to prevent you from doing that.
Sorry if I've misunderstood your intent.
Good luck with your work.
David Morse In 3PL model I want to include age as co-variate like age is add in the equation
pij(Xij = 1|θi , αj , βj, γj , Gender) = γj + 1 − γj / 1 + e[−(αjθi+βj+ γj*Gender)]
(Picture attached) taken from " Item Response Theory With Covariates (IRT-C): Assessing Item Recovery and Differential Item Functioning for the Three-Parameter Logistic Model "
How can I add age or education variable in my 3PL model as co-variate to estimate theta?
Hello again Fahad,
The method outlined by Tay, Huang, and Vermunt (2015) seems as if it would be easily adapted to your situation. The only concerns that I would have is that their recommendations suggest: (a) substantial sample sizes are needed for accurate parameter estimation; and (b) test lengths might have to be modest (e.g., about 20 items, max).
Tay, L., Huang, Q., & Vermunt, J. K. (2015). Item response theory with covariates (IRT-C): Assessing item recovery and differential item functioning for the three parameter logistic model. Educational and Psychological Measurement, 76, 22-42. doi: 10.1177/0013164415579488
Good luck with your work.
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