A Latent Space Graded Response Model for Likert-Scale Psychological Assessments

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• Traditional psychometric models often assume conditional independence, which may not hold for ordinal response data.
• Existing models may not fully capture complex interactions between respondents and items.
• Analyzing Likert-scale data requires methods that respect its ordinal nature.

Purpose of the Study:

• To introduce a novel latent space graded response model (LSGRM) for ordinal response data.
• To extend the capabilities of the one-parameter graded response model by incorporating unobserved interactions.
• To provide a visualization tool for exploring conditional dependence in psychological assessments.

Main Methods:

• Developed a latent space graded response model (LSGRM) using a two-dimensional Euclidean space for respondent-item interactions.
• Utilized simulation studies to evaluate the LSGRM's performance.
• Conducted empirical studies on Likert-scale psychological assessment data.
• Compared LSGRM with other models, including those analyzing dichotomized or continuous ordinal data.

Main Results:

• The proposed LSGRM effectively models ordinal response data by accounting for unobserved respondent-item interactions.
• LSGRM addresses violations of the conditional independence assumption inherent in traditional models.
• The interaction map provides a novel visualization for understanding conditional dependence.
• Analysis revealed the impact of data dichotomization and continuous treatment on conditional dependence.

Conclusions:

• The latent space graded response model (LSGRM) offers a significant advancement for analyzing ordinal psychological data.
• LSGRM enhances psychometric modeling by capturing complex interactions and improving the handling of conditional dependence.
• The model's visualization capabilities aid in the interpretation of response patterns and item characteristics.