  We performed a rigorous reverberation-mapping analysis of the broad-line
region (BLR) in a highly accreting ($L/L_{\mathrm{Edd}}=0.74-3.4$) active
galactic nucleus, Markarian 142 (Mrk 142), for the first time using concurrent
observations of the inner accretion disk and the BLR to determine a time lag
for the $H\beta$ $\mathrm{\lambda}$4861 emission relative to the ultraviolet
(UV) continuum variations. We used continuum data taken with the Niel Gehrels
Swift Observatory in the UVW2 band, and the Las Cumbres Observatory, Dan Zowada
Memorial Observatory, and Liverpool Telescope in the g band, as part of the
broader Mrk 142 multi-wavelength monitoring campaign in 2019. We obtained new
spectroscopic observations covering the $H\beta$ broad emission line in the
optical from the Gemini North Telescope and the Lijiang 2.4-meter Telescope for
a total of 102 epochs (over a period of eight months) contemporaneous to the
continuum data. Our primary result states a UV-to-$H\beta$ time lag of
$8.68_{-0.72}^{+0.75}$ days in Mrk 142 obtained from light-curve analysis with
a Python-based Running Optimal Average algorithm. We placed our new
measurements for Mrk 142 on the optical and UV radius-luminosity relations for
NGC 5548 to understand the nature of the continuum driver. The positions of Mrk
142 on the scaling relations suggest that UV is closer to the "true" driving
continuum than the optical. Furthermore, we obtain $\log(M_{\bullet}/M_{\odot})
= 6.32\pm0.29$ assuming UV as the primary driving continuum.
