#### Average Variance Extracted

The Average Variance Extracted (AVE) is commonly used to validate constructs. AVE is a measure of the amount of variance that is captured by a construct in relation to the amount of variance due to measurement error. In other words, AVE is the average amount of variance in observed variables that a latent construct is able to explain.  AVE is calculated by squaring the factor loading (correlation) of each indicator on a construct and computing the mean value.

#### Example

We have a latent variable A with four observed variables (x1, x2, x3, and x4). The value of AVE is the summation of squared factor loadings of x1, x2, x3, and x4 divided by the number of observed variables (here is 4) and the result is 0.58.

 Observed Variables λ λ^2 x1 0.73 0.53 x2 0.77 0.60 x3 0.76 0.57 x4 0.79 0.63 4 2.32

#### References

• Patricia Mendes dos Santos & Marcelo Ângelo Cirillo (2021) Construction of the average variance extracted index for construct validation in structural equation models with adaptive regressions, Communications in Statistics – Simulation and Computation, https://doi.org/10.1080/03610918.2021.1888122
• Farrell, A. M. (2009). Insufficient discriminant validity: A comment on Bove, Pervan, Beatty, and Shiu (2009). Journal of Business Research, 63(3),324-327, https://doi.org/10.1016/j.jbusres.2009.05.003.