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Understanding Confirmatory Factor Analysis: Key Concepts and Fit Indices

This overview of Confirmatory Factor Analysis (CFA) by Professor Ulf H. Olsson focuses on the relationships between observed variables and latent factors. It delves into the key principles of CFA, including the significance of factor loadings, assumptions regarding multivariate normality, and the challenges associated with chi-square tests. Additionally, it addresses RMSEA as a vital fit index, illustrating how to interpret its values for assessing model fit, alongside other fit indices like CN, RMR, GFI, and AGFI. This work is essential for those studying multivariate statistics.

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Understanding Confirmatory Factor Analysis: Key Concepts and Fit Indices

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  1. GRA 6020Multivariate StatisticsFactor Analysis Ulf H. Olsson Professor of Statistics

  2. The CFA model • In a confirmatory factor analysis, the investigator has such a knowledge about the factorial nature of the variables that he/she is able to specify that each xi depends only on a few of the factors. If xi does not depend on faktor j, the factor loading lambdaij is zero Ulf H. Olsson

  3. CFA • If does not depend on then • In many applications, the latent factor represents a theoretical construct and the observed measures are designed to be indicators of this construct. In this case there is only (?) one non-zero loading in each equation Ulf H. Olsson

  4. CFA Ulf H. Olsson

  5. CFA Ulf H. Olsson

  6. CFA • The covariance matrices: Ulf H. Olsson

  7. CFA and ML k is the number of manifest variables. If the observed variables comes from a multivariate normal distribution, then Ulf H. Olsson

  8. Testing Fit Ulf H. Olsson

  9. Problems with the chi-square test • The chi-square tends to be large in large samples if the model does not hold • It is based on the assumption that the model holds in the population • It is assumed that the observed variables comes from a multivariate normal distribution • => The chi-square test might be to strict, since it is based on unreasonable assumptions?! Ulf H. Olsson

  10. Alternative test- Testing Close fit Ulf H. Olsson

  11. How to Use RMSEA • Use the 90% Confidence interval for EA • Use The P-value for EA • RMSEA as a descriptive Measure • RMSEA< 0.05 Good Fit • 0.05 < RMSEA < 0.08 Acceptable Fit • RMSEA > 0.10 Not Acceptable Fit Ulf H. Olsson

  12. Other Fit Indices • CN • RMR • GFI • AGFI • Evaluation of Reliability • MI: Modification Indices Ulf H. Olsson

  13. Nine Psychological Tests Ulf H. Olsson

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