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Thurstonian Scaling of Compositional Questionnaire Data

Brown, Anna (2016) Thurstonian Scaling of Compositional Questionnaire Data. Multivariate Behavioral Research, 51 (2-3). pp. 345-356. ISSN 0027-3171. E-ISSN 1532-7906. (doi:10.1080/00273171.2016.1150152) (KAR id:54224)


To prevent response biases, personality questionnaires may use comparative response formats. These include forced choice, where respondents choose among a number of items, and quantitative comparisons, where respondents indicate the extent to which items are preferred to each other. The present article extends Thurstonian modeling of binary choice data (Brown & Maydeu-Olivares, 2011a) to “proportion-of-total” (compositional) formats. Following Aitchison (1982), compositional item data are transformed into log-ratios, conceptualized as differences of latent item utilities. The mean and covariance structure of the log-ratios is modelled using Confirmatory Factor Analysis (CFA), where the item utilities are first-order factors, and personal attributes measured by a questionnaire are second-order factors. A simulation study with two sample sizes, N=300 and N=1000, shows that the method provides very good recovery of true parameters and near-nominal rejection rates. The approach is illustrated with empirical data from N=317 students, comparing model parameters obtained with compositional and Likert scale versions of a Big Five measure. The results show that the proposed model successfully captures the latent structures and person scores on the measured traits.

Item Type: Article
DOI/Identification number: 10.1080/00273171.2016.1150152
Uncontrolled keywords: Thurstonian factor models, compositional data, multiplicative ipsative data
Subjects: B Philosophy. Psychology. Religion > BF Psychology
H Social Sciences > HA Statistics
Divisions: Divisions > Division of Human and Social Sciences > School of Psychology
Depositing User: Anna Brown
Date Deposited: 17 Feb 2016 09:06 UTC
Last Modified: 09 Dec 2022 02:14 UTC
Resource URI: (The current URI for this page, for reference purposes)

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