Box 1.

Analysis of the contribution of socioeconomic changes to the link between union dissolution and mental health: the implementation of the KHB method

The Karlson, Holm and Breen (KHB) method (Stata command “khb”), developed to compare estimated coefficients of two nested logit models, involves 3 stages (Karlson et al. 2012, Kohler et al. 2011): • Intermediate equations are used to estimate the coefficients of union dissolution in estimating the probability of experiencing changes in income or in social support, considered possible mediators of the dissolution/MDE association (with adjustment for other control variables). This stage checks that these associations are significant, a necessary step before pursuing the investigation. The residuals of these intermediate equations correspond to the proportion of socioeconomic changes not explained by the dissolution • First, Model 1 estimates the coefficient of dissolution on the risk of MDE2010 (corresponding to the total effect of dissolution in the dissolution/MDE association), without the variables of changes, but introducing the residuals obtained using the intermediate equations (adjustment for control variables) • Second, Model 2 estimates the coefficient of dissolution on the risks of MDE2010, including the mediating variables (with adjustment for control variables) The extent of the contribution of each of the mediating variables is the product of the coefficient that relates it to dissolution (stage 1) and of the coefficient that relates it to MDE2010 (stage 3). It is expressed as a percentage of the total effect of dissolution on MDE2010 (stage 2)