1. Chapter 15 Confirmatory Factor Analysis
Copyright © 2005 by Lippincott Williams and Wilkins.
PowerPoint Presentation to Accompany Statistical
Methods for Health Care Research by Barbara Hazard Munro.

2. Confirmatory Factor Analysis (CFA)
A theory driven alternative to traditional (exploratory) factor analysis that allows the researcher to assign items to their respective factors and to use “fit statistics” to evaluate whether the collected data are consistent with the hypothesized factor model.

3. Terminology for CFA
Latent or unmeasured variables: also known as factors
Observed variables: The items on a scale or research measure.
Residuals: Measurement error.
Parameters: The structural links or paths in the factor model; the relationships between and among the latent variables, the observed variables, and the residuals.

4. Steps in Conducting a CFA
Specification: specifying the structural relationships among the components in the factor model.
Identification: a mathematical issue that involves making sure the number of known values exceeds the number of unknown values that are going to be estimated.

5. Steps in Conducting a CFA (cont.)
Estimation: The computer analysis, using observed or collected data, to test the factor model. Estimates of populations parameters (factor loadings, residuals, and factor correlations) are generated.
Evaluating fit: Using various fit statistics to evaluate if the results provide empirical evidence that the specified factor model fits the data well.

6. Steps in Conducting a CFA (cont.)
Model modification: Revising or respecifying a factor model IF the fit indices indicate a possible data-model misfit.

7. Self Confidence Life Purpose Self Confidence8 6 5 7 9 4 2 10 3 11 1 12
Self Confidence
Life Purpose
Self Confidence 13 29 19 30 14 26 20 28 24 15 21 27 22 16 23 25 18 17
Figure Measurement model for the IPPA

8. Commonly Used Fit Indices and Acceptable Values
C2 (Chi square)
C2/df (relative Chi square)
GFI (Goodness of Fit Index)
CFI (Comparative Fit Index)
IFI (Incremental Fit Index)
RMR (Root Mean Square Residual)
RMSEA (Root Mean Square Error of Approximation)
C2 should have a non-significant p-value
C2/df should be less than 3
Values of GFI, CFI, & IFI are between 0 and 1, with > .90 traditionally indicating good fit (currently > .95 is being recommended)
Values for the RMR & RMSEA are between 0 and 1, with values < .8 to .10 indicating an adequate fit and .05 or less indicating a good fit.