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I have a query regarding acceptance of AVE below .5. Gaskin in his video on 2nd and 3rd order factor analysis using PLS SEM has mentioned that AVE is too stringent a criteria. Generally speaking if AVE is below .5, the indicators are dropped to bring it to meet this minimum criteria (threshold). However, at times dropping indicators do not bring much change in AVE but severely affect the Composite Reliability. In that case the construct with AVE below .5 may be retained and the values of Composite reliability can be used as the justification. As per Gaskin, this is mentioned in some scholarly works.He further mentioned that the Composite Reliability establishes that the constuct can be retained even when AVE is less that .5.

I am running PLS SEM and has come across this situation. Dropping indicators further is not possible.

Kindly give your expert opinion.

You probabaly look into a situation of reflective-reflective or formative-reflective higher order constructs (HOCs). In that case, you want to assess the quality of the HOC based on the relationships with its lower order constructs (LOCs). For these relationships, you would like to see an AVE of 0.5 and higher (see Hair et al. 2018; https://goo.gl/b5oeuE).

Best
CR

Dear Prof Ringle,

The constructs in my model are lower order and reflective.

I have found one refrence advocating for the use of AVE <.5 . Below I am quoting the same:


"AVE varies from 0 to 1, and it represents the ratio of the total variance that is due to the latent
variable. Using the logic presented earlier, an AVE of 0.5 or more indicates satisfactory convergent
validity, as it means that the latent construct accounts for 50 percent or more of the variance in the
observed variables, on the average.
If AVE is less than 0.5, the variance due to measurement error
is larger than the variance captured by the construct, and the validity of the individual indicators, as
well as the construct, is questionable.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 percent of the variance is due to error.One should also interpret
the standardized parameter estimates to ensure that they are meaningful and in accordance
with theory."
[Marketing research : an applied orientation / Naresh K. Malhotra—6th ed, Pg 702]

Best Regards
Sarita

The mention of considering AVE below .5 is proposed in Fornell & Larcker's (1981) paper too. It is suggestive of relying on composite reliability alone for concluding the validity of the construct to be adequate.

Refer to Page no. 42 of:
"Evaluating Structural Equation Models with Unobservable Variables and Measurement Error"
Claes Fornell and David F. Larcker
Journal of Marketing Research
Vol. 18, No. 1 (Feb., 1981), pp. 39-50