A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times

Area of Science:

• Psychometrics
• Cognitive Psychology
• Statistical Modeling

Background:

• Generalized linear models (GLMs) commonly use transformed response time (RT) data to achieve normality.
• Normality is crucial for validating linearity and homoscedasticity assumptions in RT models.
• Existing research indicates transformed RTs often violate normality assumptions, necessitating alternative modeling approaches.

Purpose of the Study:

• To propose and evaluate a novel modeling approach for analyzing responses and response times (RTs).
• To specifically test and model non-normality in transformed RT data.
• To differentiate non-normality arising from heteroscedastic residual variances versus a skewed speed factor.

Main Methods:

• Developed a new statistical model for analyzing response and RT data.
• Employed a simulation study to assess parameter recovery and the model's power to separate sources of non-normality.
• Applied the proposed model to a real-world dataset.

Main Results:

• The simulation study demonstrated successful parameter recovery.
• The model effectively distinguished between non-normality due to heteroscedasticity and skewed speed factors.
• The model's utility was confirmed through application to empirical data.

Conclusions:

• The proposed modeling approach effectively addresses non-normality in transformed RTs.
• The distinction between heteroscedasticity and skewed speed factors provides a more nuanced understanding of RT data.
• This method offers a valuable tool for researchers analyzing RT data in generalized linear models.