[Do we measure the same in all persons? On measurement invariance and response shift in rehabilitation research - part 1].

Subjective constructs like health-related quality of life are often investigated in scientific surveys in rehabilitation science, usually assuming that such constructs would be equally defined between different groups in case of cross-sectional control group designs or across time in longitudinal study designs with or without control-groups. Differences between measurements of these constructs were expected to occur only regarding quantity but not regarding quality. However, this assumption cannot be expected to apply in every case and it is discussed from a theoretical angle under the terms of invariance or equivalence of measurements. Confirmatory factor analysis-based approaches are suitable to investigate measurement invariance empirically and will be described in this article. These statistical methods are applicable to test whether qualitative differences in constructs exist between several groups or time points (response shift) and what these differences mean. If measurement invariance cannot be held, comparisons of sum scores, which are often used in rehabilitation science, have to be considered to be questionable. On the basis of a measurement model specific parameters (regression weights, intercepts, measurement errors) can be analyzed both between comparison groups and over time. Different kinds of measurement invariance exist, depending on the statistical definition of parameters which are proven to be equal, and the extent of differences between models. The application of confirmatory factor analysis to test measurement invariance in a cross-sectional design will be described in this article on the example of quality of life data from inpatient rehabilitation. Methodological and substantive aspects which arise if measurement invariance is disproved will be discussed. In a companion article (Jelitte & Schuler, in press) the method will be described for a longitudinal study design and results will be discussed in the context of response shift research.