# Having a fit: impact of number of items and distribution of data on traditional criteria for assessing IRT’s unidimensionality assumption

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## Abstract

### Purpose

Confirmatory factor analysis fit criteria typically are used to evaluate the unidimensionality of item banks. This study explored the degree to which the values of these statistics are affected by two characteristics of item banks developed to measure health outcomes: large numbers of items and nonnormal data.

### Methods

Analyses were conducted on simulated and observed data. Observed data were responses to the Patient-Reported Outcome Measurement Information System (PROMIS) Pain Impact Item Bank. Simulated data fit the graded response model and conformed to a normal distribution or mirrored the distribution of the observed data. Confirmatory factor analyses (CFA), parallel analysis, and bifactor analysis were conducted.

### Results

CFA fit values were found to be sensitive to data distribution and number of items. In some instances impact of distribution and item number was quite large.

### Conclusions

We concluded that using traditional cutoffs and standards for CFA fit statistics is not recommended for establishing unidimensionality of item banks. An investigative approach is favored over reliance on published criteria. We found bifactor analysis to be appealing in this regard because it allows evaluation of the relative impact of secondary dimensions. In addition to these methodological conclusions, we judged the items of the PROMIS Pain Impact bank to be sufficiently unidimensional for item response theory (IRT) modeling.

## Keywords

Psychometrics Item response theory Outcome measures Pain measurement Factor analysis Methodology## Abbreviations

- CAT
Computer adaptive testing

- CFA
Confirmatory factor analyses

- CFI
Comparative Fit Index

- EAP
Expected a priori

- EFA
Exploratory factor analyses

- GED
General Educational Development

- GRM
Graded response model

- IRT
Item response theory

- NIH
National Institutes of Health

- NNFI
Nonnormed Fit Index

- PROMIS
Patient-Reported Outcomes Measurement Information System

- PROs
Patient-reported outcomes

- RMSEA
Root-mean-square error of approximation

- SD
Standard deviation

- SRMR
Standardized root-mean-square error

- TLI
Tucker–Lewis index

- WLSMV
Weighted least squares with mean and variance adjustment

- WRMR
Weighted root-mean-square residual

## Notes

### Acknowledgements

The Patient-Reported Outcomes Measurement Information System (PROMIS) is a National Institutes of Health (NIH) roadmap initiative to develop a computerized system measuring patient-reported outcomes in respondents with a wide range of chronic diseases and demographic characteristics. PROMIS was funded by cooperative agreements to a Statistical Coordinating Center (Evanston Northwestern Healthcare, PI: David Cella, PhD, U01AR52177) and six Primary Research Sites (Duke University, PI: Kevin Weinfurt, PhD, U01AR52186; University of North Carolina, PI: Darren DeWalt, MD, MPH, U01AR52181; University of Pittsburgh, PI: Paul A. Pilkonis, PhD, U01AR52155; Stanford University, PI: James Fries, MD, U01AR52158; Stony Brook University, PI: Arthur Stone, PhD, U01AR52170; and University of Washington, PI: Dagmar Amtmann, PhD, U01AR52171). NIH Science Officers on this project are Deborah Ader, PhD, Susan Czajkowski, PhD, Lawrence Fine, MD, DrPH, Louis Quatrano, PhD, Bryce Reeve, PhD, William Riley, PhD, and Susana Serrate-Sztein, PhD. This manuscript was reviewed by the PROMIS Publications Subcommittee prior to external peer review. See the web site at www.nihpromis.org for additional information on the PROMIS cooperative group.

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