Fig. 1: Cross-lagged panel structural equation models simultaneously examining peer influence and selection homophily effects, with cross-lagged and auto-regressive effects between focal participant scores and the average scores of their nominated friends between baseline and follow-up.

X_{i, t=base}: Focal participant (i) scores on the outcome at baseline. X_{i, t=fu}: Focal participant (i) scores on the outcome at follow-up. Ave(X)_{−i, t=base}: Average of nominated friends’ (−i) scores on the outcome at baseline. Ave(X)_{−i, t=fu}: Average of nominated friends’ (-i) scores on the outcome at follow-up. Cov_{i, t=base}: Focal participant (i) baseline covariates (gender, age, ethnicity, and socio-economic status). Cross1: Cross-lagged path from Ave(X)_{−i, t=base} to X_{i, t=fu}. This path represents the peer influence effect. Cross2: Cross-lagged path from X_{i, t=base} to Ave(X)_{−i, t=fu}. This path represents the selection homophily effect. Auto1: Auto-regressive path from X_{i, t=base} to X_{i, t=fu}. Auto2: Auto-regressive path from Ave(X)_{−i, t=base} to Ave(X)_{−i, t=fu}. Corr1: Correlation path between X_{i, t=base} and Ave(X)_{−i, t=base}. Corr2: Correlation path between X_{i, t=fu} and Ave(X)_{−i, t=fu}.