Extensions of multinomial processing tree models for continuous variables: A simulation study comparing parametric...

Area of Science:

• Cognitive Psychology
• Quantitative Psychology
• Psychometric Methods

Background:

• Multinomial processing tree (MPT) models are used for analyzing discrete and continuous variables.
• Parametric and non-parametric extensions of MPT models exist but lack systematic comparison.
• The weapon identification task provides a context for evaluating these MPT model extensions.

Purpose of the Study:

• To systematically compare the statistical power and robustness of parametric and non-parametric MPT models.
• To evaluate the performance of goodness-of-fit tests for parametric MPT models.
• To assess model recovery for nested and non-nested MPT models.

Main Methods:

• Three simulation studies were conducted using the weapon identification task.
• Simulations manipulated discrepancies in latent response time (RT) distributions, sample size, and parametric assumptions.
• Evaluated calibration, statistical power, and model recovery for parametric and non-parametric MPT approaches.

Main Results:

• Parametric MPT models demonstrated higher statistical power but were sensitive to distributional assumption misspecifications.
• Non-parametric MPT models showed greater robustness but lower power, particularly with small sample sizes.
• Model recovery varied based on model complexity, sample size, and discrepancy type.

Conclusions:

• The choice between parametric and non-parametric MPT models depends on the specific research context, sample size, and data characteristics.
• Parametric models are suitable when distributional assumptions are met and high power is needed.
• Non-parametric models offer a more robust alternative when distributional assumptions are uncertain or violated.