This study proposed efficient Gibbs sampling algorithms for variable selection in a latent regression model under a unidimensional two-parameter logistic item response theory model. Three types of shrinkage priors were employed to obtain shrinkage estimates: double-exponential (i.e., Laplace), horseshoe, and horseshoe+ priors. These shrinkage priors were compared to a uniform prior case in both simulation and real data analysis. The simulation study revealed that two types of horseshoe priors had a smaller root mean square errors and shorter 95% credible interval lengths than double-exponential or uniform priors. In addition, the horseshoe prior+ was slightly more stable than the horseshoe prior. The real data example successfully proved the utility of horseshoe and horseshoe+ priors in selecting effective predictive covariates for math achievement. In the final section, we discuss the benefits and limitations of the three types of Bayesian variable selection methods.