*2.4. Statistical Analyses*

After computing descriptive statistics for all variables of interest, we attempted to test our two hypotheses by a series of inferential analyses. As these hypotheses were all based on mean comparisons, we initially conducted repeated measures analyzes of variance (rANOVA). Yet, ANOVA deals with missing data through pairwise or listwise deletion, which increases the likelihood to lose information on participants notably in a longitudinal design. For this reason, we ran additional analyses with structural equation modelling (SEM), a statistical method o ffering better options with regard to missing data. Three nested models were built for model comparison, namely; a level model assuming no change between before and after DBS (i.e., T0 = T1 = T2 = T3); a step model assuming a change between before and after DBS (i.e., T0 - T1 = T2 = T3), and; a model allowing a free slope estimation so that possible changes within post-DBS measurement times can be taken into consideration. This procedure was repeated to address each research hypothesis.

In the present study, the initial sample size (*n* = 45) increases to a potential *n* = 180 because of its longitudinal design comprising four measurement times. Although SEM is generally used with larger sample sizes, it can be applied to smaller samples starting from 30 depending on the model tested [44]. Notably, Bayesian estimation has been found adapted to small samples [45,46]. Thus, we conducted SEM analyses by comparing models estimated; first, with the traditionally used full information maximum likelihood (FIML) and; second, with Bayesian estimation of probability. In order to assess the latter, we examined the following attributes: convergence statistic (acceptable if < 1.002), trace plots stability, convergence in the comparison of first and last third of each parameter's posterior distribution, stability of autocorrelation plots, and comparison of value estimates with those obtained from FIML analyses. In addition, we provided the deviance information criterion (DIC) and the e ffective number of parameters (enp) in tables.

All statistical analyses were conducted with IBM SPSS Statistics version 25.0 (IBM Corp., Armonk, NY, USA) and IBM SPSS Amos version 25.0 (IBM SPSS, Chicago, IL, USA). A significance threshold of 0.05 was adopted for inferential statistics. All the data were normally distributed.
