Studying item-effect variables and their correlation patterns with multi-construct multi-state models

by Tina H. Erhardt, Timo Gnambs, Marie-Ann Sengewald

Method effects on the item level can be modeled as latent difference variables in longitudinal data. These item-effect variables represent interindividual differences associated with responses to a specific item when assessing a common construct with multi-item scales. In latent variable analyses, their inclusion substantially improves model fits in comparison to classical unidimensional measurement models. More importantly, covariations between different item-effect variables and with other constructs can provide valuable insights, for example, into the structure of the studied instrument or the response process. Therefore, we introduce a multi-construct multi-state model with item-effect variables for systematic investigations of these correlation patterns within and between constructs. The implementation of this model is demonstrated using a sample of N = 2,529 Dutch respondents that provided measures of life satisfaction and positive affect at five measurement occasions. Our results confirm non-negligible item effects in two ostensibly unidimensional scales, indicating the importance of modeling interindividual differences on the item level. The correlation pattern between constructs indicated rather specific effects for individual items and no common causes, but the correlations within a construct align with the item content and support a substantive meaning. These analyses exemplify how multi-construct multi-state models allow the systematic examination of item effects to improve substantive and psychometric research.