Assessing Partial Association Between Ordinal Variables: Quantification, Visualization, and Hypothesis Testing

• 成果类型: Article
• 署名作者: Liu, Dungang; Li, Shaobo; Yu, Yan; Moustaki, Irini
• 署名单位: University System of Ohio; University of Cincinnati; University of Kansas; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1796394
• 发表日期: 2021
• 页码: 955-968
• 关键词: maximum-likelihood-estimation; polychoric correlation; regression-models; binary

摘要

Partial association refers to the relationship between variableswhile adjusting for a set of covariates. To assess such an association whenY(k)'s are recorded on ordinal scales, a classical approach is to use partial correlation between the latent continuous variables. This so-called polychoric correlation is inadequate, as it requires multivariate normality and it only reflects a linear association. We propose a new framework for studying ordinal-ordinal partial association by using Liu-Zhang's surrogate residuals. We justify that conditional on,Y-k, andY(l)are independent if and only if their corresponding surrogate residual variables are independent. Based on this result, we develop a general measureto quantify association strength. As opposed to polychoric correlation,does not rely on normality or models with the probit link, but instead it broadly applies to models with any link functions. It can capture a nonlinear or even nonmonotonic association. Moreover, the measuregives rise to a general procedure for testing the hypothesis of partial independence. Our framework also permits visualization tools, such as partial regression plots and three-dimensional P-P plots, to examine the association structure, which is otherwise unfeasible for ordinal data. We stress that the whole set of tools (measures,p-values, and graphics) is developed within a single unified framework, which allows a coherent inference. The analyses of the National Election Study (K = 5) and Big Five Personality Traits (K = 50) demonstrate that our framework leads to a much fuller assessment of partial association and yields deeper insights for domain researchers.for this article are available online.