  Large-scale matrix data has been widely discovered and continuously studied
in various fields recently. Considering the multi-level factor structure and
utilizing the matrix structure, we propose a multilevel matrix factor model
with both global and local factors. The global factors can affect all matrix
times series, whereas the local factors are only allow to affect within each
specific matrix time series. The estimation procedures can consistently
estimate the factor loadings and determine the number of factors. We establish
the asymptotic properties of the estimators. The simulation is presented to
illustrate the performance of the proposed estimation method. We utilize the
model to analyze eight indicators across 200 stocks from ten distinct
industries, demonstrating the empirical utility of our proposed approach.
