Revisiting dispersion in count data item response theory models: The Conway-Maxwell-Poisson counts model

Area of Science:

• Psychometrics
• Cognitive Science
• Statistical Modeling

Background:

• Count data are prevalent in cognitive ability tests (e.g., processing speed, verbal fluency).
• Existing item response theory models like the Rasch Poisson Counts Model (RPCM) lack flexibility for simultaneous over- and underdispersion.
• The RPCM assumes equidispersion, which is often violated in real-world data.

Purpose of the Study:

• To introduce the Conway-Maxwell-Poisson Counts Model (CMPCM) for analyzing count data in cognitive ability testing.
• To demonstrate the CMPCM's ability to handle underdispersion, equidispersion, and overdispersion at the item level.
• To compare the CMPCM's performance against the RPCM using simulation and empirical data.

Main Methods:

• Development and application of the Conway-Maxwell-Poisson Counts Model (CMPCM).
• A simulation study to assess parameter recovery and standard error bias.
• Analysis of verbal fluency data using the proposed CMPCM and comparison with the RPCM.

Main Results:

• The CMPCM demonstrated satisfactory parameter recovery and unbiased standard errors in simulations.
• Reliability estimates from CMPCM were more accurate than RPCM, which showed bias when data deviated from equidispersion.
• The CMPCM with item-specific dispersion parameters provided the best fit for verbal fluency data, indicating underdispersion for most items.

Conclusions:

• The Conway-Maxwell-Poisson Counts Model (CMPCM) offers a flexible and feasible approach for modeling count data in cognitive ability testing.
• The CMPCM's ability to account for varying dispersion is crucial for accurate psychometric analysis.
• This flexible modeling approach is important for improving the precision and validity of cognitive ability assessments.