Equating the HBSC Family Affluence Scale across survey years:a method to account for item parameter drift using the Rasch model

Purpose To investigate the measurement invariance (MI) of the Family Affluence Scale (FAS) measured in the Health Behavior in School-aged Children (HBSC) survey, and to describe a method for equating the scale when MI is violated across survey years. Methods This study used a sample of 14,076 Norwegian and 17,365 Scottish adolescents from the 2002, 2006 and 2010 HBSC surveys to investigate the MI of the FAS across survey years. Violations of MI in the form of differential item functioning (DIF) due to item parameter drift (IPD) were modeled within the Rasch framework to ensure that the FAS scores from different survey years remain comparable. Results The results indicate that the FAS is upwardly biased due to IPD in the computer item across survey years in the Norwegian and Scottish samples. Ignoring IPD across survey years resulted in the conclusion that family affluence is increasing quite consistently in Norway and Scotland. However, the results show that a large part of the increase in the FAS scores can be attributed to bias in the FAS because of IPD across time. The increase in the FAS was more modest in Scotland and slightly negative in Norway once the DIF in the computer item was accounted for in this study. Conclusions When the comparison of family affluence is necessary over different HBSC survey years or when the longitudinal implications of family affluence are of interest, it is necessary to account for IPD in interpretation of changes in family affluence across time