  Fueled by the call for formative assessments, diagnostic classification
models (DCMs) have recently gained popularity in psychometrics. Despite their
potential for providing diagnostic information that aids in classroom
instruction and students' learning, empirical applications of DCMs to classroom
assessments have been highly limited. This is partly because how DCMs with
different estimation methods perform in small sample contexts is not yet
well-explored. Hence, this study aims to investigate the performance of
respondent classification and item parameter estimation with a comprehensive
simulation design that resembles classroom assessments using different
estimation methods. The key findings are the following: (1) although the marked
difference in respondent classification accuracy was not observed among the
maximum likelihood (ML), Bayesian, and nonparametric methods, the Bayesian
method provided slightly more accurate respondent classification in
parsimonious DCMs than the ML method, and in complex DCMs, the ML method
yielded the slightly better result than the Bayesian method; (2) while item
parameter recovery was poor in both Bayesian and ML methods, the Bayesian
method exhibited unstable slip values owing to the multimodality of their
posteriors under complex DCMs, and the ML method produced irregular estimates
that appear to be well-estimated due to a boundary problem under parsimonious
DCMs.
