Combining Dynamic Mode Decomposition and Difference-in-Differences in an Analysis of At-Risk Youth

Marc Andrew Choi, Siyu Huang, Hengyuan Qi, Marco Scialanga, Emerson McMullen, Axel Sanchez Moreno, Yifei Lou, Andrea L. Bertozzi, P. Jeffrey Brantingham

Abstract:

We analyze the impact of the Los Angeles Mayor’s
Office of Gang Reduction Youth Development (GRYD) prevention programming using quasi-experimental data. We model
the evolution of questionnaire scores and apply Dynamic Mode
Decomposition (DMD) to describe the asymptotic behavior of
the dynamical system. The analysis indicates that risk decreased
for youth who enrolled in GRYD prevention services, while it
increased or remained the same for those who were in the control
group. We augment these observations using a difference-indifferences (DID) model, showing that the decrease in risk can
be attributed to enrolment in prevention services. We draw a
connection between DMD and DID using both mathematical
analysis and empirical evidence from the questionnaire data.
Combining DMD and DID with factor analysis, we investigate
the effectiveness of prevention services with respect to different
attitudinal domains. We conclude that gang prevention is most
effective in impacting attitudes towards negative peer obedience
and least effective in impacting attitudes towards violence for self
defense. Our analytical approach can be extended to other types
of repeated questionnaires.