  This article is motivated by studying multisensory effects on brain
activities in intracranial electroencephalography (iEEG) experiments.
Differential brain activities to multisensory stimulus presentations are zero
in most regions and non-zero in some local regions, yielding locally sparse
functions. Such studies are essentially a function-on-scalar regression
problem, with interest being focused not only on estimating nonparametric
functions but also on recovering the function supports. We propose a weighted
group bridge approach for simultaneous function estimation and support recovery
in function-on-scalar mixed effect models, while accounting for heterogeneity
present in functional data. We use B-splines to transform sparsity of functions
to its sparse vector counterpart of increasing dimension, and propose a fast
non-convex optimization algorithm using nested alternative direction method of
multipliers (ADMM) for estimation. Large sample properties are established. In
particular, we show that the estimated coefficient functions are rate optimal
in the minimax sense under the $L_2$ norm and resemble a phase transition
phenomenon. For support estimation, we derive a convergence rate under the
$L_{\infty}$ norm that leads to a sparsistency property under
$\delta$-sparsity, and provide a simple sufficient regularity condition under
which a strict sparsistency property is established. An adjusted extended
Bayesian information criterion is proposed for parameter tuning. The developed
method is illustrated through simulation and an application to a novel iEEG
dataset to study multisensory integration. We integrate the proposed method
into RAVE, an R package that gains increasing popularity in the iEEG community.
