Monte Carlo simulation of polychoric correlation and Pearson correlation coefficient
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摘要: 为了解对于有序分类数据，使用多分格相关系数估计数据间线性依存关系的精确性，运用蒙特卡罗仿真法考察样本量的大小、分类数的多少、相关程度的高低以及数据分布的偏度对多分格相关系数估计精确度的影响；同样条件下计算皮尔逊相关系数并与之相比较.在实验设计的条件下，多分格相关系数的表现非常稳定，绝大多数情况下给出的估计值都比皮尔逊相关系数更精确.两种相关系数受样本量的影响都很有限，且估计值的偏差会明显随着分类数的增多而变小；但数据的偏态分布对皮尔逊相关系数的精确度有很大影响.Abstract: 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.
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Key words:
- correlation theory /
- Monte Carlo methods /
- data processing /
- multivariant analysis
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