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.
Using latent regression and person covariates is common in IRT; especially in large-scale assessments such as PISA. In PISA (and all others) plausible values are drawn from individuals posterior distributions in order to calculate population statistics containing measurement error components (for starters, see Wu, 2005, The role of plausible values in large-scale surveys).
A good start for latent regression in adaptive testing can be Chapter 1 in Elements of Adaptive Testing; look out for the topic "initial empirical prior".