Is More Ever Too Much? The Number of Indicators per Factor in Confirmatory Factor Analysis

TLDR

The study examined whether increasing the number of indicators per factor in confirmatory factor analysis ever becomes detrimental by systematically varying sample size and indicator‑to‑factor ratios in a large Monte Carlo simulation. Researchers conducted 35,000 Monte Carlo simulations varying sample sizes from 50 to 1,000 and indicator‑to‑factor ratios from 2 to 12, and also compared parceling strategies using the 12‑indicator condition. Results showed that higher indicator‑to‑factor ratios consistently improved solution quality and parameter accuracy, with large sample sizes compensating for fewer indicators and vice versa, while chi‑square goodness‑of‑fit declined with more indicators; overall, nonparceled 12‑indicator models performed best, suggesting that conventional rules limiting indicators per factor may be overly restrictive.

Abstract

Abstract We evaluated whether "more is ever too much" for the number of indicators (p) per factor (p/f) in confirmatory factor analysis by varying sample size (N = 50-1000) and p/f (2-12 items per factor) in 35,000 Monte Carlo solutions. For all N's, solution behavior steadily improved (more proper solutions, more accurate parameter estimates, greater reliability) with increasing p/f. There was a compensatory relation between N and p/f: large p/f compensated for small N and large N compensated for small p/f, but large-N and large-p/f was best. A bias in the behavior of the χ2 was also demonstrated where apparent goodness of fit declined with increasing p/f ratios even though approximating models were "true". Fit was similar for proper and improper solutions, as were parameter estimates form improper solutions not involving offending estimates. We also used the 12-p/f data to construct 2, 3, 4, or 6 parcels of items (e.g., two parcels of 6 items per factor, three parcels of 4 items per factor, etc. ), but the 12-indicator (nonparceled) solutions were somewhat better behaved. At least for conditions in our simulation study, traditional "rules" implying fewer indicators should be used for smaller N may be inappropriate and researchers should consider using more indicators per factor that is evident in current practice.