To investigate possible lack of measurement invariance in these data we followed the steps recommended in Topic 4 of Mplus’ online course [26]. Following the estimation of single-indicator growth models utilising each of the three indicators in turn as well as their sum (i.e. the sum of all 12 items), evidence for a lack of measurement invariance was sought through a series of confirmatory factory analysis models in which loadings and/or intercepts were permitted to vary across time. Whilst traditional fit-statistics (CFI/TLI/RMSEA) indicated that the fully invariant model was acceptable, some residuals were high under this degree of constraint. An approach in which loadings and intercepts were constrained/freed consecutively resulted in partially invariant models with improved residuals in comparison to their fully-invariant counterparts (Supplementary Table X1). Whilst these refined models were slightly better fitting to the data, this additional complexity had a negligible impact on the models results hence we focus here on the fully-invariant results, with more complete results available as supplementary material.
