Direct estimation of correlation as a measure of association strength using multidimensional item response models

The Pearson correlation is used to depict effect sizes in the context of item response theory. A multidimensional Rasch model is used to directly estimate the correlation between latent traits. Monte Carlo simulations were conducted to investigate whether the population correlation could be accurately estimated and whether the bootstrap method provided a good approximation of the distribution of the sample correlation. The independent variables were (a) the item response model, (b) test length, (c) sample size, and (d) the magnitude of correlation. The dependent variable was the empirical correlation coefficient. The results indicate that the population correlation can be accurately estimated and that the bootstrap method yields very a good approximation of the sampling distribution.