Monte Carlo simulation of polychoric correlation and Pearson correlation coefficient

The more accurate estimates were obtained via the polychoric correlation coefficient rather than traditional Pearson correlation coefficient in multivariate analysis for ordinal categorical data. The statistic model and estimators of the polychoric correlation were introduced. Then a Monte Carlo simulation was conducted to discuss the influence of sample size, category number, correlation degree, and data distribution on the precision of polychoric correlation estimate. The simulation results show that the polychoric correlation coefficient is more robust, and more precise than Pearson correlation coefficient in the most of the simulation setting. To both two correlation estimation approaches, sample size is not an influential factor and the bias has explicit decrease when adding the number of category. The skew distribution would distort the Pearson correlation; however it has a very limited influence on the polychoric correlation.