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                                Fronto-striatal connectivity predicts patience
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 longitudinal studies, since these datasets have time points within participants and the mixed model approach can recognize this type of data dependency. In order to test for developmental effects, we followed a formal model-fitting procedure (for a similar approach, see Braams et al. (2015)). We started by using a null model that only included a fixed and a random intercept, to allow for individual differences in starting points and to account for the repeated nature of the data. We fitted three polynomial age-models with increasing complexity that tested the grand mean trajectory of age: i.e., a linear, quadratic and cubic age-trend. Akaike Information Criterion (AIC; Akaike (1974)) and Bayesian Information Criterion (BIC; Schwarz (1978)), both standardized model-fit metrics were used to compare the different models. Lower AIC and BIC values indicates a better model fit. Log likelihood ratio tests were used between nested models, to test which age-trend best described the data. Reported p-values for the mixed models are based on log likelihood ratio tests. All models were fit with full information maximum likelihood estimates.
Ultimately, linear regression models in SPSS were used to test longitudinal prediction models. In specific, we tested whether fronto-striatal white matter integrity (FA and MD) at T1 could predict delay of gratification skills at T2, while taking into account delay of gratification performance at baseline.
Results
Age effects on delay discounting
Cross sectional data showed that advanced age was related to a larger AUC (normalized), meaning less steep discounting of delayed rewards with age, at both T1 (r=.207, p=.004) and at T2 (r=.204, p=.004). Delay of gratification skills at T1 were positively correlated with delay of gratification skills at T2 (r=.543, p<.001).
The longitudinal analyses, testing for linear, quadratic, and cubic changes in delay discounting, showed that age-related change in delay of gratification skills (AUC normalized) was best described by a quadratic age-model (age1: β=.1.269, p<.001; age2: β=-0.568, p=.040) see Table 2. This model indicates a ‘peak’ in AUC, during late adolescence/early adulthood (see Figure 2a). We also performed the analyses without the relative smaller group of young adults (N=21). However, age-related change in delay of gratification skills (AUC normalized) was –conform the analysis on the total sample- best described by a quadratic age-model (age1: β=.1.274, p<.001; age2: β=-0.509, p=.033). Finally, with respect to behavioral performance, we tested potential gender differences. In the current data set, there were no significant gender or gender x age interaction effects in delay of gratification.
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