Maartje Boer

CHAPTER 5 138 CLPM partials out all possible confounding time-invariant traits by adding a random intercept for each measure, which captures the stability of the respective measure at the between-person level. As a result, cross-lagged relations in the RI-CLPM solely reflect within-person dynamics that are not confounded by time-invariant traits at the between-person level (Hamaker et al., 2015), such as stable individual differences in temperament. After measurement invariance was established and factor scores were generated, the RI-CLPM was fitted using Mplus 8.1 with MLR-estimation (Hamaker, 2018; L. K. Muthén & Muthén, 2017b). A two-variable RI-CLPM is illustrated in Figure 5.1. In this study, this model was extended to a five- variable RI-CLPM, including SMU intensity, SMU problems, attention deficits, impulsivity, and hyperactivity (see Appendix, Figure A5.1). The between-person part of the RI-CLPM is denoted by the random intercepts. Random intercepts are latent variables that are extracted from the computed factor scores that reflect the same construct over time with loadings fixed to one. Each random intercept represents the person-specific time-invariant stability of the measure. Correlations between all random intercepts were specified. Positive correlations between the random intercepts indicate, for example, that adolescents with high averages in attention deficits also report high averages in SMU problems. The within-person part of the RI-CLPM is denoted by within-person values, which are additional latent variables that are extracted from their respective computed factor scores, again with loadings fixed to one. Residual variances of the computed factor scores were constrained to zero. The within-person values denote the adolescent’s deviations from their expected score. The expected score at T x consists of the grand mean of the respective wave and the adolescent’s random intercept. Cross-lagged paths, auto-regressive paths, and within-wave (residual) correlations were specified between the within-person values (Figure 5.1). Positive cross-lagged paths indicate, for example, that adolescents whose attention deficits at T x increased relative to their expected score, also reported increased SMU problems relative to their expected score at T x+1 . By including auto-regressive paths, the model controls for preceding increases or decreases (e.g., SMU problems at T x on SMU problems at T x+1 ). By including within-wave (residual) correlations, the model also controls for increases or decreases that occurred simultaneously within the same year (e.g., attention deficits at T x with SMU problems at T x ). In