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The structure of self‐reported emotional experiences: A mixed‐effects Poisson factor model
Author(s) -
Böckenholt Ulf,
Kamakura Wagner A.,
Wedel Michel
Publication year - 2003
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711003770480011
Subject(s) - poisson distribution , poisson regression , random effects model , covariate , goodness of fit , statistics , mathematics , count data , multivariate statistics , factor analysis , econometrics , set (abstract data type) , mixed model , computer science , medicine , population , meta analysis , demography , sociology , programming language
Multivariate count data are commonly analysed by using Poisson distributions with varying intensity parameters, resulting in a random‐effects model. In the analysis of a data set on the frequency of different emotion experiences we find that a Poisson model with a single random effect does not yield an adequate fit. An alternative model that requires as many random effects as emotion categories requires high‐dimensional integration and the estimation of a large number of parameters. As a solution to these computational problems, we propose a factor‐analytic Poisson model and show that a two‐dimensional factor model fits the reported data very well. Moreover, it yields a substantively satisfactory solution: one factor describing the degree of pleasantness and unpleasantness of emotions and the other factor describing the activation levels of the emotions. We discuss the incorporation of covariates to facilitate rigorous tests of the random‐effects structure. Marginal maximum likelihood methods lead to straight‐forward estimation of the model, for which goodness‐of‐fit tests are also presented.