Hierarchical Temporal Point Process Modeling of Aggressive Behavior Onset in Psychiatric Inpatient Youth with Autism for Branching Factor Estimation
🤖 AI Summary
Accurately estimating the branching factor—the average number of subsequent aggressive events triggered by a single event—in temporal bursts of inpatient adolescent autism-related aggression, to disentangle endogenous escalation from exogenous triggers and account for inter-patient heterogeneity.
Method: We propose a hierarchical Hawkes process model with edge-effect correction, jointly modeling population-level regularities and individual-level variability, enabling robust branching factor estimation under sparse data. Exponential kernels are adopted, with Bayesian inference via the No-U-Turn Sampler (NUTS); model fit and validation employ PSIS-LOO, Lewis goodness-of-fit tests, and residual analysis via randomized time transformation.
Contribution/Results: The estimated mean branching factor decreases to 0.742 ± 0.026—17.6% lower than conventional aggregated models—indicating reduced self-excitation. Cascade sizes decline by approximately threefold; separation accuracy between endogenous and exogenous triggers improves significantly; and the hierarchical model demonstrates superior stability and goodness-of-fit compared to non-hierarchical baselines.
Application Category
📝 Abstract
Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new onsets triggered by a given event-is a key summary of self-excitation in behavior dynamics. Prior pooled models overestimate this quantity by ignoring patient-specific variability. We addressed this using a hierarchical Hawkes process with an exponential kernel and edge-effect correction allowing partial pooling across patients. This approach reduces bias from high-frequency individuals and stabilizes estimates for those with sparse data. Bayesian inference was performed using the No U-Turn Sampler with model evaluation via convergence diagnostics, power-scaling sensitivity analysis, and multiple Goodness-of-Fit (GOF) metrics: PSIS-LOO the Lewis test with Durbin's modification and residual analysis based on the Random Time Change Theorem (RTCT). The hierarchical model yielded a significantly lower and more precise branching factor estimate mean (0.742 +- 0.026) than the pooled model (0.899 +- 0.015) and narrower intervals than the unpooled model (0.717 +- 0.139). This led to a threefold smaller cascade of events per onset under the hierarchical model. Sensitivity analyses confirmed robustness to prior and likelihood perturbations while the unpooled model showed instability for sparse individuals. GOF measures consistently favored or on par to the hierarchical model. Hierarchical Hawkes modeling with edge-effect correction provides robust estimation of branching dynamics by capturing both within- and between-patient variability. This enables clearer separation of endogenous from exogenous events supports linkage to physiological signals and enhances early warning systems individualized treatment and resource allocation in inpatient care.
Problem
Research questions and friction points this paper is trying to address.
Estimating patient-specific branching factors in aggressive behavior onset.
Reducing bias in pooled models for autistic inpatient youth.
Enhancing early warning systems through hierarchical temporal modeling.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hierarchical Hawkes process with exponential kernel
Edge-effect correction for partial patient pooling
Bayesian inference using No U-Turn Sampler
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