  Two networks are available to monitor PM$_{2.5}$ in Taiwan, including the
Taiwan Air Quality Monitoring Network (TAQMN) and the AirBox network. The
TAQMN, managed by Taiwan's Environmental Protection Administration (EPA),
provides high-quality PM$_{2.5}$ measurements at $77$ monitoring stations. More
recently, the AirBox network was launched, consisting of low-cost, small
internet-of-things (IoT) microsensors (i.e., AirBoxes) at thousands of
locations. While the AirBox network provides broad spatial coverage, its
measurements are not reliable and require calibrations. However, applying a
universal calibration procedure to all AirBoxes does not work well because the
calibration curves vary with several factors, including the chemical
compositions of PM$_{2.5}$, which are not homogeneous in space. Therefore,
different calibrations are needed at different locations with different local
environments. Unfortunately, most AirBoxes are not close to EPA stations,
making the calibration task challenging. In this article, we propose a spatial
model with spatially varying coefficients to account for heteroscedasticity in
the data. Our method gives adaptive calibrations of AirBoxes according to their
local conditions and provides accurate PM$_{2.5}$ concentrations at any
location in Taiwan, incorporating two types of measurements. In addition, the
proposed method automatically calibrates measurements from a new AirBox once it
is added to the network. We illustrate our approach using hourly PM$_{2.5}$
data in the year 2020. After the calibration, the results show that the
PM$_{2.5}$ prediction improves about 37% to 67% in root mean-squared prediction
error for matching EPA data. In particular, once the calibration curves are
established, we can obtain reliable PM$_{2.5}$ values at any location in
Taiwan, even if we ignore EPA data.
