Researchers often seek to estimate the effect of a continuous predictor Z on an outcome Y, but Z is frequently observed indirectly through ordered categorical indicators Z*, such as credit ratings for government default risk or binned income categories in surveys. To approximate the underlying continuous variable Z, researchers often use score imputation methods, which introduce or exacerbate measurement error bias.
This project evaluates three methods for predicting Z from observed ordered categories Z* in income survey data: the widely used Hout’s middle-point score imputation, ordinal probit, and Bayesian rank likelihood. Using a Monte Carlo experiment, I assess their performance in terms of bias and efficiency. The results show that Bayesian rank likelihood achieves the lowest prediction error, outperforming the other methods. Moreover, when estimating the marginal effect of Z on Y, Hout's imputed scores produce biased and inconsistent estimates, while Bayesian rank likelihood provides unbiased and efficient ones. This study warns public opinion researchers to avoid Hout's income score measure and instead use categorical variables directly as provided in the survey or apply Bayesian rank likelihood, which offers more efficient estimates with the lowest measurement error. The robustness of these results is tested under non-normality of Z and model misspecification. The implications are generalizable to any regression setting that uses as independent variable ordered categorical predictors as proxies for an underlying latent continuous distribution.