Bayesian Inference for Correlations in the Presence of Measurement Error and Estimation Uncertainty

Collabra: Psychology

Wouter D. Weeda¹  Eric-Jan Wagenmakers²  Dora Matzke²  Ravi Selker²  Alexander Ly²  Benjamin Scheibehenne³  Michael D. Lee⁴ 

[1] Leiden University;University of Amsterdam;University of Geneva;Unversity of California, Irvine

关键词: Attenuation of the correlation;    Bayesian inference;    cumulative prospect theory;    diffusion model;    estimation uncertainty;    measurement error;   

DOI  :  10.1525/collabra.78

学科分类：社会科学、人文和艺术（综合）

来源: University of California Press

【 摘 要 】

Whenever parameter estimates are uncertain or observations are contaminated by measurement error, the Pearson correlation coefficient can severely underestimate the true strength of an association. Various approaches exist for inferring the correlation in the presence of estimation uncertainty and measurement error, but none are routinely applied in psychological research. Here we focus on a Bayesian hierarchical model proposed by Behseta, Berdyyeva, Olson, and Kass (2009) that allows researchers to infer the underlying correlation between error-contaminated observations. We show that this approach may be also applied to obtain the underlying correlation between uncertain parameter estimates as well as the correlation between uncertain parameter estimates and noisy observations. We illustrate the Bayesian modeling of correlations with two empirical data sets; in each data set, we first infer the posterior distribution of the underlying correlation and then compute Bayes factors to quantify the evidence that the data provide for the presence of an association.

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【 授权许可】

CC BY