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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Cognitive Diagnosis Models

Background:

  • Limited-information fit measures are used for dichotomous cognitive diagnosis models (CDMs).
  • Their performance in polytomous response CDMs remains unexamined.
  • Assessing model fit is crucial for accurate diagnostic classifications.

Purpose of the Study:

  • To investigate the performance of the M_ord statistic and standardized root mean square residual (SRMSR) for polytomous response CDMs.
  • To evaluate the suitability of these measures for the sequential generalized deterministic inputs, noisy "and" gate (S-DINA) model.
  • To provide guidance on using these fit statistics in practice.

Main Methods:

  • Conducted simulation studies using the S-DINA model with varying item quality, sample sizes, and number of response categories.
  • Calculated M_ord statistic and SRMSR under different simulation conditions.
  • Analyzed a real dataset to demonstrate practical application.

Main Results:

  • The M_ord statistic demonstrated well-calibrated Type I error rates.
  • Correct detection rates for M_ord were influenced by item quality, sample size, and number of response categories.
  • SRMSR was also influenced by multiple factors, suggesting pre-specified cut-off values may be inappropriate.

Conclusions:

  • The M_ord statistic shows promise for assessing fit in polytomous CDMs, but its detection accuracy requires careful consideration of study factors.
  • The SRMSR's sensitivity to various factors challenges the use of fixed cut-off values.
  • Both M_ord and SRMSR can be valuable tools when interpreted cautiously within the context of specific study parameters.