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Symmetric pattern models: a latent variable approach to item non‐response in attitude scales
Author(s) -
O'Muircheartaigh C.,
Moustaki I.
Publication year - 1999
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/1467-985x.00129
Subject(s) - latent variable , latent variable model , metric (unit) , item response theory , latent class model , variable (mathematics) , binary number , structural equation modeling , missing data , local independence , sample (material) , computer science , statistics , mathematics , artificial intelligence , machine learning , psychometrics , engineering , mathematical analysis , operations management , chemistry , arithmetic , chromatography
This paper proposes a new approach to the treatment of item non‐response in attitude scales. It combines the ideas of latent variable identification with the issues of non‐response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non‐response. We present a symmetric pattern methodology for handling item non‐response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a ‘dependent’ variable) and is pattern based in that the pattern of responses and non‐responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.