Variability in Parameter Estimates and Model Fit Across Repeated Allocations of Items to Parcels

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Item parceling is a common technique in structural equation modeling.
• It is generally assumed that random or purposive allocation of items to parcels does not affect parameter estimates or model fit.

Purpose of the Study:

• To investigate whether item-to-parcel allocation variability impacts parameter estimates and model fit within a sample.
• To analytically and empirically demonstrate the effects of allocation variability.

Main Methods:

• Analytical derivations showing population vs. sample differences.
• Monte Carlo simulation study with varying conditions (sample size, item communalities, items per parcel).
• Demonstration using the Neuroticism-Extroversion-Openness (NEO) Personality Inventory data.

Main Results:

• Analytical proof that population-level invariance does not hold at the sample level.
• Simulation results indicate significant variability in parameter estimates and model fit due to item-to-parcel allocation, particularly under high sampling error.
• Substantive conclusions can be altered by allocation variability.

Conclusions:

• Item-to-parcel allocation variability is a critical issue in psychometric research, affecting sample-based results.
• Researchers must consider this variability, especially in studies with low N or low item communalities.
• A software tool is provided to address and mitigate the consequences of this variability.