1) In FornellLarcker Criterion table few nondiagonal elements show negative values (Specifically where the latent variables have been conceptualized to have negative effect in the proposed model). Whether the software output is supposed to exhibit these type of raw values (with negative sign) or the output should show the absolute values (also in crossloading table)? If it is normal, then should I show these raw values or absolute values while interpreting the discriminant validity result through FornellLarcker Criterion table? [discriminant validity wellestablished while considering absolute values] If it is not normal, then what might be the problem?
2) In my proposed model, while evaluating discriminant validity through HTMT, HTMT values of all pairs of construct appear to be lower than 0.85, except between attitude and intention (0.954), although they are conceptually different and very similar in nature, as well as difficult to distinguish empirically. Hence, is there any methodological issue if I go ahead with the conceptualization?
Thanks,
*Expecting comments from Dr. Becker.
Discriminant validity
Discriminant validity
Last edited by skr on Tue Feb 12, 2019 1:01 pm, edited 1 time in total.

 SmartPLS Developer
 Posts: 932
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Discriminant validity
1) Below the diagonal we show the correlations. These can also be negative. It also seems to match your expectation about the relationship of the constructs, which is good.
Whether you want to use only absolute (i.e., positive) correlations for a FornellLarcker matrix or also negative is a matter of taste. I find a FornellLarcker matrix to be more useful and less confusing if it shows the actual correlation (positive or negative) and not only absolute and therefore positive correlations even if the relation is negative. However, in evaluating the discriminant validity you of course compare the absolute correlation against the diagonal (i.e., the square root of the AVE), because that is always positive.
2) Such a high HTMT (and thereby correlation between the constructs) will likely have adverse effects on your model interpretation. First, the effect of attitude on intention (or vice versa) cannot be interpreted correctly even if you have a strong theory, because it seems that they are conceptually not distinct (and thereby a causal effect doesn't make sense). Second, it may likely lead to collinearity problems if other constructs/variables have an effect on one of these constructs while also including the other. For example, if you want to test the effect of B on intention while controlling for attitude. The effect of B is likely to be biased (probably strongly biased) because you cannot distinguish between attitude and intention and therefore controlling for attitude does not make sense and causes a strong suppression of the effect of B.
Whether you want to use only absolute (i.e., positive) correlations for a FornellLarcker matrix or also negative is a matter of taste. I find a FornellLarcker matrix to be more useful and less confusing if it shows the actual correlation (positive or negative) and not only absolute and therefore positive correlations even if the relation is negative. However, in evaluating the discriminant validity you of course compare the absolute correlation against the diagonal (i.e., the square root of the AVE), because that is always positive.
2) Such a high HTMT (and thereby correlation between the constructs) will likely have adverse effects on your model interpretation. First, the effect of attitude on intention (or vice versa) cannot be interpreted correctly even if you have a strong theory, because it seems that they are conceptually not distinct (and thereby a causal effect doesn't make sense). Second, it may likely lead to collinearity problems if other constructs/variables have an effect on one of these constructs while also including the other. For example, if you want to test the effect of B on intention while controlling for attitude. The effect of B is likely to be biased (probably strongly biased) because you cannot distinguish between attitude and intention and therefore controlling for attitude does not make sense and causes a strong suppression of the effect of B.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Re: Discriminant validity
Thank you Dr. Becker.