Latent class analysis

Latent Class Analysis (LCA) was used to identify classes of MHC for maternal and teacher reports separately. Two sets of parameters were estimated for each latent class measure: ‘class membership probabilities’ (the prevalence of each class) and ‘item response probabilities’ (the combined probability of individuals in a given class displaying each of the MHC item responses) [23]. Models ranging from two to seven classes were considered (Supplementary Materials: Tables S6 and S7), with the following factors taken into account when selecting the final model: Akaike information criterion (AIC), Bayesian information criterion (BIC), class posterior probabilities (likelihood of members of an assigned class belonging to that class), and entropy (the precision of membership assignment across all individuals) [23]. The selection of the final classes was based on these measures of model fit and interpretability of the classes (that is, the extent to which each class was distinct, in terms of its MHC profile, from the others). Children were assigned to the class they had the highest probability of belonging to. 3% (n = 388) of children did not have information on all eight maternal-report items and 9% (n = 691) did not have information on all ten teacher-report items. Missing items were automatically imputed during the LCA procedure under a “missing at random” (MAR) assumption [24].