A multicomponent latent trait model for diagnosis.

Area of Science:

• Psychometrics
• Educational Measurement
• Cognitive Psychology

Background:

• Traditional latent trait models may not fully capture the complexity of broad achievement tests.
• Existing models can struggle with heterogeneous items common in large-scale assessments.

Purpose of the Study:

• To introduce the multicomponent latent trait model for diagnosis (MLTM-D).
• To extend the multicomponent latent trait model (MLTM) for diagnostic applications.
• To enable diagnosis at two hierarchical levels of attributes and components.

Main Methods:

• Developed a noncompensatory latent trait model (MLTM-D).
• Specified a hierarchical relationship between components and attributes.
• Described model identification conditions and presented marginal maximum likelihood estimators.
• Utilized simulation data for parameter recovery assessment.

Main Results:

• Demonstrated parameter recovery through simulation studies.
• Applied MLTM-D to a large-scale mathematics achievement test.
• Showcased the model's utility for diagnostic purposes.

Conclusions:

• MLTM-D is a generalization of MLTM applicable to broad traits with varying item component structures.
• MLTM-D offers advantages for diagnosing performance on large-scale assessments with heterogeneous items compared to latent class models.