Rasch analysis with a focus on Differential Item Functioning (DIF) is increasingly used for examination of psychometric properties of health outcome measures. To take account of DIF in order to retain precision of measurement, split of DIF-items into separate sample specific items has become a frequently used technique. The purpose of the paper is to present and summarise recent advances of analysis of DIF in a unified methodology. In particular, the paper focuses on the use of analysis of variance (ANOVA) as a method to simultaneously detect uniform and non-uniform DIF, the need to distinguish between real and artificial DIF and the trade-off between reliability and validity. An illustrative example from health research is used to demonstrate how DIF, in this case between genders, can be identified, quantified and under specific circumstances accounted for using the Rasch model. Rasch analyses of DIF were conducted of a composite measure of psychosomatic problems using Swedish data from the Health Behaviour in School-aged Children study for grade 9 students collected during the 1985–2014 time periods. The procedures demonstrate how DIF can be identified efficiently by ANOVA of residuals, and how the magnitude of DIF can be quantified and potentially accounted for by resolving items according to identifiable groups and using principles of test equating on the resolved items. The results of the analysis also show that the real DIF in some items does affect person measurement estimates. Firstly, in order to distinguish between real and artificial DIF, the items showing DIF initially should not be resolved simultaneously but sequentially. Secondly, while resolving instead of deleting a DIF item may retain reliability, both options may affect the content validity negatively. Resolving items with DIF is not justified if the source of the DIF is relevant for the content of the variable; then resolving DIF may deteriorate the validity of the instrument. Generally, decisions on resolving items to deal with DIF should also rely on external information.

The literature in modern test theory on procedures for identifying items with differential item functioning (DIF) among two groups of persons includes the Mantel–Haenszel (MH) procedure. Generally, it is not recognized explicitly that if there is real DIF in some items which favor one group, then as an artifact of this procedure, artificial DIF that favors the other group is induced in the other items. Using the Rasch model for dichotomous responses as a theoretical basis, this article proves that the source of artificial DIF in the MH procedure is that estimates of the person locations are substituted for their unknown values. The article then demonstrates that the formalization of artificial DIF implies mathematically (a) a particular sequential, iterative procedure for detecting items with real DIF and for identifying a set of items that may have no DIF and (b) a resolution of the items with real DIF for quantifying the DIF on the same metric as the items showing no DIF and provides expected value curves and tests of fit for the item for each of the groups. Finally, because the source of artificial DIF in the MH procedure is the substitution of a parameter with its estimate, it is suggested that all procedures that use the substitution of an estimate for a parameter are likely to induce artificial DIF.

The purpose was to analyse the association between physical activity taking place in different contexts (sports club, gym, exercise independently and other organized physical activities) and symptoms of depression. The study was based on self-reported cross-sectional data from the Ungdata survey, conducted in 2017 by the Norwegian Social Research (NOVA) institute in cooperation with regional centres for drug rehabilitation. The target group comprised 5531 15–16 years old adolescents (Grade 10 students) and 11,655 students in grades 8 and 9 in Norway. Based on Rasch analysis, six items on depressions symptoms were used to create a composite measure of depression. Binomial logistic regression was used to analyse the association between physical activities in different contexts and symptoms of depression. In the crude model, the odds for symptoms of depression were lower for those who were physically active in a sports club (OR: 0.40, 95% CI: 0.30–0.53), in a sports club and gym (OR: 0.40, 95% CI: 0.28–0.56), in a sports club and exercise or keep fit independently (OR: 0.52, 95% CI: 0.38–0.72) and in a sports club, gym and exercise or keep fit independently (OR: 0.58, 95% CI: 0.41–0.81). After adjustment for potential confounders, the association became significant only for those who were physically active in a sports club (OR: 0.57, 95% CI: 0.40–0.81) and other organized physical activities, e.g. dance, martial arts (OR: 0.52, 95% CI: 0.31–0.86). Analysis for grade 8 and 9 showed the same patterns for the associations between sports club and symptoms of depression (grade 8: crude model, OR: 0.47, adjusted model, OR: 0.63, grade 9: crude model, OR: 0.44, adjusted model, OR: 0.49). Physical activity in a sports club was associated with significantly lower odds for symptoms of depression, suggesting a possible role for social interaction in addition to physical activity per se. It is important, therefore, to consider in which types of contexts physical activities take place, not only focusing on physical activity frequency and volume when investigating the association between adolescents’ physical activity and mental health. Additional research is needed to further explore these associations as well as measures of physical activity and mental health.