Data validation for use in SEM

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Data validation for use in SEM

• Ned Kock

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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.

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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
  classic factor-based SEM (e.g., LISREL) it can
  be employed in classic variance-based SEM (e.g.,
  PLS) and factor-based PLS-SEM.

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Reflective measurement example
of a process modeling approach.

• Latent variable
• Ease of generation
• Question-statements
• easgen1 It is easy to conceptualize a process
  using this approach.
• easgen2 It is easy to create a process model
  using this approach.
• easgen3 This approach for process modeling is
  easy to use.
• easgen4 (reversed) It is difficult to use this
  process modeling approach.

Answers provided on a Likert-type scale ranging
from 1 (Very strongly disagree) to 7 (Very
strongly agree).
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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.

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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.

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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 Kock, 2015).

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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).
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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 Kock, 2015).
• An even more conservative discriminant validity
  assessment would involve comparing the average
  variances extracted (as opposed to their square
  roots) with the bivariate correlations.

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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 diagonal.
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.
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A reliability test

• Reliability assessment usually builds on the
  calculation of reliability coefficients, of which
  the most widely used is arguably Conbrachs
  alpha.
• The reliability of a latent variable-based
  measurement model is considered to be acceptable
  if the Cronbachs alpha coefficients calculated
  for each latent variable are .7 or above
  (Nunnaly, 1978 Kock, 2015).
• In SEM, the composite reliability coefficient can
  be used instead of the Cronbachs alpha (Fornell,
  Larcker, 1981 Kock, 2015), with the same .7
  rule of thumb as above.

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Good reliability

• Notes
• alpha Cronbachs alpha coefficient (calculated
  by WarpPLS).
• The coefficients of reliability (alphas) range
  from .81 to .93 (all above .7), suggesting that
  the measurement model presents acceptable
  reliability.

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Acknowledgements
Adapted text, illustrations, and ideas from the
following sources were used in the preparation of
the preceding set of slides

1. Fornell, C., Larcker, D.F. (1981). Evaluating
   structural equation models with unobservable
   variables and measurement error. Journal of
   marketing research, 18(1), 39-50.
2. Hair, J.F., Anderson, R.E., Tatham, R.L.
   (1987). Multivariate data analysis (2nd Edition).
   New York, NY Macmillan.
3. Kock, N. (2015). WarpPLS 5.0 User Manual. Laredo,
   TX ScriptWarp Systems.
4. Nunnaly, J. (1978). Psychometric theory. New
   York, NY McGraw Hill.
5. WarpPLS software.

Final slide