  Latent class models are powerful statistical modeling tools widely used in
psychological, behavioral, and social sciences. In the modern era of data
science, researchers often have access to response data collected from
large-scale surveys or assessments, featuring many items (large J) and many
subjects (large N). This is in contrary to the traditional regime with fixed J
and large N. To analyze such large-scale data, it is important to develop
methods that are both computationally efficient and theoretically valid. In
terms of computation, the conventional EM algorithm for latent class models
tends to have a slow algorithmic convergence rate for large-scale data and may
converge to some local optima instead of the maximum likelihood estimator(MLE).
Motivated by this, we introduce the tensor decomposition perspective into
latent class analysis with binary responses. Methodologically, we propose to
use a moment-based tensor power method in the first step, and then use the
obtained estimates as initialization for the EM algorithm in the second step.
Theoretically, we establish the clustering consistency of the MLE in assigning
subjects into latent classes when N and J both go to infinity. Simulation
studies suggest that the proposed tensor-EM pipeline enjoys both good accuracy
and computational efficiency for large-scale data with binary responses. We
also apply the proposed method to an educational assessment dataset as an
illustration.
