I am not aware of any such standards, so I suggest you do what others have typically done, since that appears to meet the standards of peer review.

I strongly suggest you do something unique, and different from what has usually been done by the majority of researchers, of course, in the situations where such an action is possible. In regard to Rules of Thumb when appraising validity data, discussions can be focused on the effect size, statistical power, standard error, confidence Interval, shared variance, factor loading, correlation coefficient, & item-total correlation...

** convergent and discriminant validity are both assessed using correlations (which comes from another older idea known as predictive validity).

While it is true that all forms of validity are “extent to which…” issues and not all-or-none, there are certain rules that we use as minimum or maximum cut-offs. To be clear: a given measure must produce certain correlations before you can safely proceed. The cutoffs that psychology uses are +.70 and ±.20 for convergent and discriminant validity, respectively. The measure must have +.70 or better correlations with all existing measures of the same theoretical construct, and cannot have a correlation above +.20 or below –.20 with any existing measure of a different theoretical construct. (Note: if you’ve already gotten into the habit of squaring correlations so that you’re dealing with the real strength of the relationship, then the +.70 and ±.20 correspond roughly to about 50% and 5%, respectively, which might be easier to remember.) If the measure fails a test for convergent validity, something will probably have to be added, because it is not measuring all of the construct. If the measure fails a test for discriminant validity, something will probably have to be removed, because it’s measuring something that isn’t part of the construct.

-Hair et al., (2013)

-Siamak Sabour (2012)

**Reporting convergent & discriminant validity using SEM

Incorporating the Fornell-Larcker AVE criterion for convergent validity along with construct reliability, Hair et al. (2009) suggested that there is evidence for convergent validity when all three of the following conditions are fulfilled: (a) CR values are 0.7 or greater, (b) all standardized factor loadings λ are 0.5 or greater, and (c) AVE values are 0.5 or greater.

Building on Bagozzi’s (1981) and Fornell and Larcker’s (1981) defnitions of discriminant validity, we recommend examining discriminant validity using multiple criteria with sampling errors considered. The four criteria include: (i) evidence of convergent validity is established; (ii) no indicator cross-loads on other constructs; (iii) the level of indicator variance explained by each construct is greater than the shared variance between two constructs (i.e., AVE-SV; both AVEX and AVEY are greater than r2 xy); and (iv) the correlation between the two constructs is assessed at three levels: 0.85, 0.8, and 0.7.

-Cheung et al. (2023); https://doi.org/10.1007/s10490-023-09871-y

-Rönkkö & Cho (2022); https://doi.org/10.1177/1094428120968614

1) Convergent validity

To examine convergent validity using SEM, one should first conduct a CFA by estimating a measurement model in which all indicators are related to the constructs they are meant to measure and are not related directly to constructs they are not intended to measure... When the hypothesized measurement model fits the data adequately, this establishes the fundamental requirement for convergent validity: all indicators converge well on their own construct; however, many consider adequate model fit as insufficient to support convergent validity because it does not guarantee measurement quality... hence, additional criteria have been proposed

-Standardized factor loadings greater than 0.4, 0.5 or 0.7

many have suggested evaluating convergent validity by examining the statistical significance of standardized factor loadings. Nevertheless, as CFA may involve using relatively large samples... to ensure convergence and reliable results, even a small standardized factor loading may be statistically significant. Hence, simply assessing the significance of a factor loading may not suffice... “A weak condition for convergent validity is that the factor regression coefficient on a particular item is statistically significant. A stronger condition is that the factor regression coefficient is substantial...Stevens (2002) suggested that the value of a factor loading should be greater than 0.4 for interpretation purposes, whereas Hair et al. (2009) argued that all standardized factor loadings should be at least 0.5 and, ideally, at least 0.7. In other words, the construct explains at least 25% or, ideally, at least 49% of the variance of each indicator (Cheung et al., 2023).

-Average variance extracted (AVE) value greater than 0.5

many studies have employed the Fornell & Larcker (1981) criterion for assessing convergent validity...they suggested that convergent validity is established when a latent construct accounts for no less than half of the variance in its associated indicators... They proposed using the average variance extracted (AVE) to represent the average amount of variance that a construct explains in its indicators relative to the overall variance of its indicators.

2) Discriminant validity

The frst condition for discriminant validity is establishing convergent validity (Bagozzi & Phillips, 1982). Stated alternatively, unless a construct is well-represented by its indicators, it is pointless to examine whether the construct can be distinguished from others (Cheung et al., 2023).

-No cross‑loaded indicators (Unidimensionality) In addition to establishing convergent validity, discriminant validity requires that each indicator loads uniquely on only one construct. If the same indicator is used to measure two constructs, it is difficult to argue that the constructs are distinct. Unidimensionality requires no cross-loaded indicator, a condition for assigning meaning to a latent construct (Anderson & Gerbing, 1988)

-Correlations between two constructs are significantly less than unity

Statistical tests have been developed that assess discriminant validity by evaluating whether a correlation between two constructs is statistically significantly less than unity.this is the most widely-used approach to evaluate discriminant validity. The procedure involves conducting a chi-square difference test between an unconstrained CFA model and a constrained CFA model in which the correlation between the targeted pair of constructs is constrained to 1.0. A statistically significant chi-square difference between the two models (with one degree of freedom) implies the unconstrained model fits the data better; that is, the correlation is statistically significantly less than 1.0. Therefore, discriminant validity is supported between the targeted pair of constructs.

-Correlation between two constructs less than 0.9, 0.85, 0.8, or 0.75

-Average variance extracted is greater than the shared variance (AVE‑SV approach) ....

-Heterotrait‑monotrait (HTMT) ratio of correlations less than 0.85

.....

-Cheung et al. (2023); https://doi.org/10.1007/s10490-023-09871-y

-Rönkkö & Cho (2022); https://doi.org/10.1177/1094428120968614