Discriminant validity

[Mahmood]

How can we see the result for discriminant validity in this software?

thanks

[vonbergh]

Hi Mahmood,

For the methodology you may check Fornell & Larcker (1981) Evaluating structural equation models with unobservable variables and measurement error, journal of marketing research, 18, p39-50.

You will find the correlations and AVE in the standard report.

Good luck,
Dennis

[Mahmood]

Hi,
Thanks.
But it dosenot show what level of AVE is adequate to this test.

[Hengkov]

Hi,
Discriminant Validy:
- The AVE of each latent construct should higher than the construct's highest squared correlation with any other latent construct (Fornell and Larcker 1981 criterion)
- An indicator's loadings should be higher than all of its cross loadings
- Cross loadings > 0.7.

Regards
Hengky

[vonbergh]

Discriminant validity is measured by comparing the square root average variance extracted with the inter factor correlations among factors. The sqr AVE of each factor should be larger than any of its correlations with the other factors (Fornell & Larcker, 1981).

Regards
Dennis

[vonbergh]

Hi Hengky,
you beat me to it by four minutes ;-)
I'm interested in Hair's paper; do you have a reference for me?
Thanks,
Dennis

[Mahmood]

Many thanks.
If AVE is:
AVE
0.625610
0.503450
0.808417
0.695381
0.642918
0.533284

and Factors loading these as follow, do we have this validity?

0.777453 0.357318 0.218930 0.685604 0.617724 0.277282
0.745523 0.367856 0.276503 0.502221 0.505456 0.331674
0.868737 0.254413 0.256140 0.717294 0.719557 0.308857
0.766484 0.304341 0.216186 0.619831 0.724306 0.324827
0.162779 0.535121 0.305098 0.161082 0.184032 0.251126
0.263352 0.562006 0.171481 0.183732 0.186449 0.217292
0.324577 0.826267 0.438191 0.256210 0.274848 0.398920
0.375362 0.853743 0.549221 0.325008 0.357667 0.395678
0.260240 0.522126 0.878864 0.273092 0.268025 0.445855
0.239656 0.473645 0.917013 0.275178 0.258715 0.482515
0.326298 0.512527 0.901076 0.406544 0.387334 0.526695
0.605247 0.261141 0.295945 0.840370 0.598718 0.285619
0.613124 0.300964 0.232508 0.840390 0.635611 0.283503
0.686004 0.368572 0.380314 0.867213 0.770467 0.363310
0.648825 0.117680 0.204416 0.638071 0.618167 0.248148
0.567784 0.375516 0.272579 0.661001 0.801502 0.256269
0.609617 0.314438 0.282947 0.665217 0.822111 0.226258
0.745387 0.280373 0.304525 0.756238 0.890414 0.316080
0.742955 0.282227 0.278184 0.663001 0.818788 0.357053
0.370845 0.481089 0.429945 0.235182 0.217794 0.794952
0.218833 0.330828 0.449811 0.177167 0.198196 0.746591
0.360975 0.316004 0.402342 0.385134 0.404671 0.714908
0.149101 0.326308 0.297165 0.152082 0.150948 0.704394
0.197820 0.229500 0.330616 0.276804 0.205061 0.660125
0.371545 0.297763 0.429263 0.399640 0.363915 0.753210

[Mahmood]

Hi,
Discriminant Validy:
- The AVE of each latent construct should higher than the construct's highest squared correlation with any other latent construct (Fornell and Larcker 1981 criterion)
- An indicator's loadings should be higher than all of its cross loadings
- Cross loadings > 0.7.

Regards
Hengky

Thanks.
Should be all of these three or one of them?

all cross loadings must be 0.7 or one of them?

[Mahmood]

And I used this for my paper:
According to Gefen and Straub (2005)
‘‘if one of the measurement items loads with a .70 coefficient on its latent construct, then the loadings of all the measurement items on any latent construct but their own should be below .60’’.

[Hengkov]

Hi Mahmood,
You enough use one of three method for test discriminant validy.
Please see article Hair et al (2011). "PLS-SEM:INDEED A SILVER BULLET" Journal of Marketing Theory and Practice (19:2), pp.139-151.

Hi, Dennis
Hehehe... ;-)
Hair's paper above?

[vonbergh]

Hi Hengky,

Thanks, that looks like an excellent paper I can use in my research. I will study it in more detail later :-)

Hi Mahmood,

You'll need to create a correlation table (correlations can be found in the standard report) that leads to a triangle. In the correlation table replace the diagonal correlations with the same factors (all correlation = 1) with the square root of the AVE that you'll also find in the standard report. If all values on the horizontal and vertical are < SQRT AVE for all factors (i.e. all SQRT AVE), then you have discriminant validity.

An example of such a table can be found here: http://www.swagpic.com/image/1171 . This is taken from:

Zhengzhong Shi, (2010) "The role of IS architecture planning in enhancing IS outsourcing's impact on IS performance: Its antecedents and an empirical test", Journal of Enterprise Information Management, Vol. 23 Iss: 4, pp.439 - 465

The author clearly notes how they support the conclusion for discriminant validity. In their example, the values on the horizontal line (.66) and on the vertical line (.77, ,27, .11, .23, .20 , .24, .25) are all < SQRT AVE (.78). Since this is the case for all factors F1 through F9, discriminant validity is concluded correctly

Good luck,
Dennis

[Mahmood]

thanks all.

[vonbergh]

You're welcome and good luck on your work.
Dennis

[Hengkov]

Your welcome and good luck all.

Regards
Hengky

[Mahmood]

Hi again,
If one of the AVE of my model be lower than 50, which is .46 now and also other construct has Cronbachs Alpha 0.27, Shall we conculde that this research is not valid?
How can we report it in a paper?