Exploring the Impact of Missing Data on Residual-Based Dimensionality Analysis for Measurement Models

Area of Science:

• Psychometrics
• Statistical modeling

Background:

• Rasch models are widely used for survey data analysis, offering accurate estimates with missing data.
• Dimensionality assessment is crucial for Rasch model interpretation, but the impact of missing data on this assessment is not fully understood.

Purpose of the Study:

• To investigate how missing data influence the accuracy of dimensionality assessment in Rasch analyses, specifically using principal components analysis (PCA) of standardized residuals.
• To evaluate the utility of an adapted modified parallel analysis in conjunction with PCA for dimensionality assessment in the presence of missing data.

Main Methods:

• A simulation study was conducted to examine the accuracy of standardized residual PCA under varying conditions of missing data proportions and multidimensionality.
• An adaptation of modified parallel analysis was explored as a supplementary method for dimensionality assessment.

Main Results:

• Missing data were found to impact the accuracy of PCA on standardized residuals.
• The adapted modified parallel analysis provided valuable supplementary information regarding dimensionality when missing data were present.

Conclusions:

• Researchers must consider the effects of missing data on dimensionality assessment in Rasch analyses.
• Modified parallel analysis can be a useful tool to supplement PCA for dimensionality assessment when dealing with missing data.