Open Conference Systems, ITC 2016 Conference

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POSTER: Bayesian Estimation of the Polychoric Correlation Coefficient with Skewed and Sparse Data
Oscar Lorenzo Olvera Astivia, Bruno Zumbo

Building: Pinnacle
Room: 2F-Harbourside Ballroom
Date: 2016-07-03 11:00 AM – 12:30 PM
Last modified: 2016-06-08

Abstract


In applied research and validation practice, it is common to find items, scales and measures exhibiting a strong degree of skewness in the participants’ responses, creating ceiling or floor effects (Ho & Yu, 2015). Although this tends to be attributed to the inability of the items to discriminate among participants, it could also naturally arise in checklists or scales designed to detect severe but infrequent anomalies in a typical sample (Catts et.al., 2009). If polychoric correlations are calculated from data exhibiting these characteristics, the sparseness of the contingency tables that occurs can yield biased estimates of the correlations and incorrect inferences (Savalei, 2011). A Bayesian solution is proposed to this problem through the use of a log-normal latent model that can naturally capture the inherent skewness and sparseness of this kind of data (Albert,1992). In order to document the extent of the problem and offer a potential solution, two computer simulations were conducted in the R programming language to explore this issue. The first one sets a value of 0 in the population for the correlation coefficient and varies the thresholds at 2, 2.3 and 3 standard deviations above the mean with sample sizes from 200 to 1000. The second one compares three effect sizes (0.1, 0.3 and 0.5) with two and three response option thresholds set at real-life estimated parameters from empirical research and compares the bias and variability of the correlation estimates. Preliminary results indicate that the maximum likelihood (ML) approach yields biased correlation estimates whereas the Bayesian alternative shows less bias and outperforms the normal theory ML method in cases with extreme skeweness of item responses and sparse contingency tables.


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