Discretized Longitudinal Data with Two Sources of Measurement Error

• Activity Number: 183
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Amy Nussbaum* and Cornelis Potgieter and Michael Chmielewski
• Companies: Southern Methodist University and Southern Methodist University and Southern Methodist University
• Keywords: Personality ; Trait Measurement ; State Error ; Latent Variables ; Monte Carlo EM Algorithm ; Correlation Reconstruction

Abstract

Personality traits are latent variables, and as such, are impossible to measure without the use of an assessment. Responses on the assessments can be influenced by both state-related error and measurement error, obscuring the true trait levels. These assessments typically utilize Likert scales, which yield only discrete data. The loss of information due to the discrete nature of the data represents an additional challenge in estimating an individual's true trait level. This paper explores a latent variable model relating personality traits, state error and measurement error. Two methods for parameter estimation are detailed: correlation reconstruction, which is based on polychoric correlations, and a Monte Carlo EM algorithm for maximum likelihood implementation. These methods are applied to a motivating dataset of 440 college students taking the Big Five Inventory twice in a two month period.