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Validity and Reliability in Confirmatory Factor Analysis (CFA)

Validity and Reliability in Confirmatory Factor Analysis (CFA)

It is absolutely necessary to establish convergent and discriminant validity, as well as reliability, when doing a CFA. If your factors do not demonstrate adequate validity and reliability, moving on to test a causal model will be useless – garbage in, garbage out! There are a few measures that are useful for establishing validity and reliability: Composite Reliability (CR), Average Variance Extracted (AVE), Maximum Shared Variance (MSV), and Average Shared Variance (ASV). The video tutorial will show you how to calculate these values. The thresholds for these values are as follows:

Reliability

  • CR > 0.7

Convergent Validity

  • AVE > 0.5

Discriminant Validity

  • MSV < AVE
  • Square root of AVE greater than inter-construct correlations

If you have convergent validity issues, then your variables do not correlate well with each other within their parent factor; i.e, the latent factor is not well explained by its observed variables. If you have discriminant validity issues, then your variables correlate more highly with variables outside their parent factor than with the variables within their parent factor; i.e., the latent factor is better explained by some other variables (from a different factor), than by its own observed variables.

If you need to cite these suggested thresholds, please use the following:

  • Hair, J., Black, W., Babin, B., and Anderson, R. (2010). Multivariate data analysis (7th ed.): Prentice-Hall, Inc. Upper Saddle River, NJ, USA.

AVE is a strict measure of convergent validity. Malhotra and Dash (2011) note that “AVE is a more conservative measure than CR. On the basis of CR alone, the researcher may conclude that the convergent validity of the construct is adequate, even though more than 50% of the variance is due to error.” (Malhotra and Dash, 2011, p.702).

  • Malhotra N. K., Dash S. (2011). Marketing Research an Applied Orientation. London: Pearson Publishing.

Here is an updated video that uses the most recent Stats Tools Package, which includes a more accurate measure of AVE and

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