Relationships Among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Classical Test Theory (CTT) assumes person and item statistics are sample-dependent.
• Item Response Theory (IRT) is often perceived as theoretically superior for parameter estimation.
• Previous comparisons often neglected CTT with an underlying normal variable (UNV) assumption.

Purpose of the Study:

• To relate CTT models with UNV assumption to IRT.
• To assess the comparability of person and item statistics between IRT and CTT-UNV.

Main Methods:

• Confirmatory factor analysis to link CTT-UNV and IRT.
• Monte Carlo simulation to compare statistics from both frameworks.

Main Results:

• CTT with UNV assumption and IRT are comparable.
• Neither framework demonstrated a significant advantage over the other in the simulation.

Conclusions:

• The theoretical superiority of IRT over CTT may be conditional on the CTT model used.
• CTT with UNV assumption offers a comparable alternative to IRT for certain applications.