A generalized linear factor model approach to the hierarchical framework for responses and response times

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Hierarchical models for responses and response times are established in psychometric research.
• Existing models, such as those by van der Linden et al., offer sophisticated frameworks for data analysis.
• Simplification of these models can enhance their accessibility and applicability.

Purpose of the Study:

• To simplify the hierarchical model for responses and response times.
• To demonstrate that this simplification can be achieved by transforming it into a generalized linear factor model.
• To validate the practical utility and parameter recovery of the simplified model.

Main Methods:

• The study proposes a simplification of the hierarchical model for responses and response times.
• The simplified model is shown to be equivalent to a generalized linear factor model.
• A key restriction is imposed on the item side of the hierarchical model.

Main Results:

• The hierarchical model can be simplified to a generalized linear factor model with a mild restriction.
• This simplification allows the use of well-developed modeling tools and extensions.
• Parameter recovery is not significantly influenced by the imposed restriction under realistic conditions.

Conclusions:

• The generalized linear factor model offers a more accessible approach to analyzing response time data.
• The simplification retains the analytical power of the original hierarchical model.
• Real data analyses confirm the practical benefits of the proposed simplified model.