AUTHOR=Verdam Mathilde G. E. , Oort Frans J. 

TITLE=Measurement bias detection with Kronecker product restricted models for multivariate longitudinal data: an illustration with health-related quality of life data from thirteen measurement occasions

JOURNAL=Frontiers in Psychology

VOLUME=Volume 5 - 2014

YEAR=2014

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2014.01022

DOI=10.3389/fpsyg.2014.01022

ISSN=1664-1078

ABSTRACT=Longitudinal measurement invariance is usually investigated with a longitudinal factor model. However, with multiple measurement occasions, the number of parameters to be estimated increases with a multiple of the number of measurement occasions. 
To guard against too low ratios of numbers of subjects and numbers of parameters, we can impose Kronecker product restrictions to model the multivariate longitudinal structure of the data. These restrictions can be imposed on all parameter matrices, including measurement invariance restrictions on factor loadings and intercepts. The resulting models are parsimonious and have attractive interpretation, but require different methods for the investigation of measurement bias.
Specifically, additional parameter matrices are introduced to accommodate possible violations of measurement invariance. These additional matrices consist of measurement bias parameters that are either fixed at zero or free to be estimated. In cases of measurement bias, it is also possible to model the bias over time, e.g., with linear or non-linear curves. 
Measurement bias detection with Kronecker product restricted models will be illustrated with multivariate longitudinal data from 682 bone metastasis patients whose health-related quality of life was measured at 13 consecutive weeks.