A zero- and K-inflated mixture model for health questionnaire data.

Area of Science:

• Psychometrics
• Psychiatric Assessment
• Statistical Modeling

Background:

• Item Response Theory (IRT) is widely used in psychiatric assessment to link disorder severity with questionnaire responses.
• A common IRT assumption of normally distributed severities is often violated in psychiatric populations.
• This violation occurs due to a significant number of respondents exhibiting extreme trait scores.

Purpose of the Study:

• To develop a zero- and K-inflated mixture model to address violations of the normality assumption in IRT.
• To accurately estimate the proportion of respondents at the extreme ends of the latent trait spectrum.
• To analyze the remaining 'graded component' using IRT and introduce a factor analysis method for this component.

Main Methods:

• A novel zero- and K-inflated mixture model was developed.
• The expectation-maximization (E-M) algorithm was employed for model fitting.
• Factor analysis was adapted for the graded component of the data.

Main Results:

• The proposed zero- and K-inflated model demonstrated a superior fit compared to the standard IRT model.
• This improved fit was observed in assessments of oppositional defiant disorder and conduct disorder.
• The model effectively estimated population percentages at the extreme ends of the trait spectrum.

Conclusions:

• The zero- and K-inflated mixture model provides a more accurate approach for psychiatric assessments where extreme scores are prevalent.
• This method enhances the application of IRT in clinical psychology and psychiatry.
• The model offers improved diagnostic accuracy for disorders like oppositional defiant disorder and conduct disorder.