  Survey instruments and assessments are frequently used in many domains of
social science. When the constructs that these assessments try to measure
become multifaceted, multidimensional item response theory (MIRT) provides a
unified framework and convenient statistical tool for item analysis,
calibration, and scoring. However, the computational challenge of estimating
MIRT models prohibits its wide use because many of the extant methods can
hardly provide results in a realistic time frame when the number of dimensions,
sample size, and test length are large. Instead, variational estimation
methods, such as Gaussian Variational Expectation Maximization (GVEM)
algorithm, have been recently proposed to solve the estimation challenge by
providing a fast and accurate solution. However, results have shown that
variational estimation methods may produce some bias on discrimination
parameters during confirmatory model estimation, and this note proposes an
importance weighted version of GVEM (i.e., IW-GVEM) to correct for such bias
under MIRT models. We also use the adaptive moment estimation method to update
the learning rate for gradient descent automatically. Our simulations show that
IW-GVEM can effectively correct bias with modest increase of computation time,
compared with GVEM. The proposed method may also shed light on improving the
variational estimation for other psychometrics models.
