Discriminant validity

Data validation for use in
Ned Kock
Validity and reliability
• Whenever perception-based variables are used in
inferential studies, measurement errors can bias
the results.
• One effective technique employed to minimize
the impact of such measurement errors on results
is to measure each latent variable based on
multiple indicators.
• This technique also allows for validity and
reliability tests in connection with the
measurement model used.
Indicators in reflective models
• Each set of related indicators is designed, often in
the form of related question-statements, to “load
on” (or correlate with) what is referred to as a
latent variable.
• The above rule refers to reflective measurement
models, and does not apply to models in which
latent variables are measured in a formative way.
• Formative measurement is not widely discussed in
SEM texts because it cannot be employed in
covariance-based SEM (e.g., LISREL); it can only
be employed in variance-based SEM (e.g., PLS).
Reflective measurement example
• Latent variable
– Ease of generation
• Question-statements
… of a process modeling approach.
Answers provided on a Likert-type
scale ranging from 1 (Very strongly
disagree) to 7 (Very strongly agree).
– easgen1: It is easy to conceptualize a process using
this approach.
– easgen2: It is easy to create a process model using this
– easgen3: This approach for process modeling is easy
to use.
– easgen4 (reversed): It is difficult to use this process
modeling approach.
Validity assessment
• Among the most common validity tests are those
in connection with the assessment of the
convergent and discriminant validity of a
measurement model.
• Convergent validity tests are aimed at verifying
whether answers from different individuals to
question-statements are sufficiently correlated
with the respective latent variables.
• Discriminant validity tests are aimed at checking
whether answers from different individuals to
question-statements are either lightly correlated or
not correlated at all with other latent variables.
Reliability assessment
• Reliability tests have a similar but somewhat
different purpose than validity tests.
• They are aimed at verifying whether answers from
different individuals to question-statements
associated with each latent variable are
sufficiently correlated.
• Validity and reliability tests allow for the
assessment of whether the individuals responding
to question-statements understood and answered
the question-statements reasonably carefully; as
opposed to answering them in a hurry, or in a
mindless way.
A convergent validity test
• Loadings obtained from a confirmatory factor
analysis are obtained with WarpPLS – combined
or pattern loadings can be used.
• The loadings above are rotated, using an oblique
rotation method similar to Promax.
• Whenever factor loadings associated with
indicators for all respective latent variables are .5
or above the convergent validity of a
measurement model is generally considered to be
acceptable (Hair et al., 1987).
Good convergent validity
Loadings obtained from a confirmatory factor analysis. Shown in shaded cells are the loadings
expected to be conceptually associated with the respective latent variables (all above .5).
A discriminant validity test
• A measurement model containing latent variables
is generally considered to have acceptable
discriminant validity if the square root of the
average variance extracted for each latent variable
is higher than any of the bivariate correlations
involving the latent variables in question (Fornell
& Larcker, 1981).
• An even more conservative discriminant validity
assessment would involve comparing the average
variances extracted (as opposed to their square
roots) with the bivariate correlations.
Good discriminant validity
Notes on table:
Correlation coefficients shown are Pearson bivariate
correlations (calculated by WarpPLS):
* = correlation significant at the .05 level.
** = correlation significant at the .01 level.
Average variances extracted (AVEs) are shown on
Good discriminant validity because:
-All average variances extracted (AVEs)
are higher than the correlations shown
below them or to their left.
-The above is a conservative criterion;
square roots of the AVEs are usually
used in this type of test.
A reliability test
• Reliability assessment usually builds on the
calculation of reliability coefficients, of which the
most widely used is arguably Conbrach’s alpha.
• The reliability of a latent variable-based
measurement model is considered to be acceptable if
the Cronbach’s alpha coefficients calculated for
each latent variable are .7 or above (Nunnaly, 1978).
• In SEM, the composite reliability coefficient can be
used instead of the Cronbach’s alpha (Fornell, &
Larcker, 1981), with the same .7 rule of thumb as
Good reliability
•alpha = Cronbach’s alpha coefficient (calculated by WarpPLS).
•The coefficients of reliability (alpha’s) range from .81 to .93 (all above .7),
suggesting that the measurement model presents acceptable reliability.
Adapted text, illustrations, and ideas from the
following sources were used in the preparation of the
preceding set of slides:
Fornell, C., & Larcker, D.F. (1981). Evaluating structural
equation models with unobservable variables and
measurement error. Journal of marketing research, 18(1),
Hair, J.F., Anderson, R.E., & Tatham, R.L. (1987).
Multivariate data analysis (2nd Edition). New York, NY:
Nunnaly, J. (1978). Psychometric Theory. New York, NY:
McGraw Hill.
WarpPLS software.
Final slide
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