A Factor-Analytic Model for Assessing Individual Differences in Response Scale Usage.

Area of Science:

• Psychometrics
• Personality Psychology
• Quantitative Psychology

Background:

• Traditional factor analysis (FA) models may not fully capture individual response nuances in personality and attitude assessments.
• Existing item response theory (IRT) models offer frameworks but can be extended for richer person-specific modeling.

Purpose of the Study:

• To propose a novel factor-analytic model incorporating a multiplicative person parameter for graded or continuous response items.
• To extend Spearman's (1904) factor analysis model by integrating a person-specific response mapping component.
• To provide a fully developed model for practical applications in personality and attitude measurement.

Main Methods:

• Modification of the Spearman factor analysis (FA) model.
• Parameterization as both an FA and an item response theory (IRT) model.
• Development of procedures for item calibration, data fit assessment, person parameter estimation, measurement precision determination, and differential predictability assessment.
• Validation through a simulation study and three empirical examples in the personality domain.

Main Results:

• The proposed model effectively incorporates an additional multiplicative person parameter.
• Procedures for calibration, estimation, precision, and predictability were developed and discussed.
• The model's functioning was assessed and demonstrated through simulation and empirical data.
• The enhanced model shows potential advantages in modeling individual response processes.

Conclusions:

• The proposed factor-analytic model with a multiplicative person parameter offers a significant advancement for personality and attitude measurement.
• The model provides a flexible framework that can be applied in various psychometric contexts.
• Further research and application of this model can enhance the understanding of individual differences in response patterns.