The One-Step vs Two-Step Approach: Notes on Anderson and Gerbing (1988)

1
The One-Step vs Two-Step Approach Notes on
Anderson and Gerbing (1988)
MKT 8543 Quantitative Marketing Seminar
March 27, 2007
Mississippi State University
Nicole Ponder
2
EFA versus CFA

• All factor analysis is confirmatory in a sense,
  if you have an idea of the number of factors you
  expect to see
• Confirmatory analysis may be thought of as
  restricted analysis because of the constraints
  you have imposed on the model

3
Theory testing and development vs. Application
and prediction

• Generalized least squares (GLS) approach is used
  for theory testing and development. It follows
  the common factor model, in which observed
  measures have random error variance and
  measure-specific variance
• Partial least squares (PLS) estimation approach
  may be used for predictive application. It
  follows the principal components model, in which
  no unique variance is assumed

4
The Need for Unidimensionality

• Unidimensionality each set of indicators has
  only one underlying trait or construct in common
  (Hattie 1985)
• Multi-item measurement models are preferred
  because they allow the most unambiguous
  assignment of meaning to the estimated constructs
• Other justifications for multiple items to
  measure a construct?

5
The SEM Process

• Model specification
• Need to set the scale
• Sample size typically 150 or more is needed
• Some problems with smaller samples
  non-convergence or improper solutions
• Model identification
• We want an overidentified model
• A just-identified model will run
• An underidentified model means we are asking for
  more information that we are supplying

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The SEM Process

• 3. Model estimation
• 4. Assessment of model fit
• Reliability construct, convergent, discriminant
  validity
• 5. Respecification of model
• Not based on statistical information alone, but
  in conjunction with theory

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Four Basic Ways to Respecify the Model

• Relate the indicator to a different factor
• Delete the indicator from the model
• Relate the indicator to multiple factors
• Use correlated measurement errors
• Only justified when they are specified a priori
• Consequence loss of interpretability and
  theoretical meaningfulness
• See Gerbing and Anderson (1984) JCR

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One-Step Versus Two-Step Approach

• Separate measurement submodels exist for x and
  for y
• y ?y? ?
• x ?x? ?
• These measurement submodels are then
  simultaneously estimated with the structural
  submodel
• ? ?? ?? ?

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One-Step Versus Two-Step Approach

• What happens if you only estimate the structural
  model and a parameter is misspecified (meaning
  the Mis are large)?
• Interpretational confounding occurs as the
  assignment of empirical meaning to an unobserved
  variable which is other than the meaning assigned
  to it by an individual a priori to estimating
  unknown parameters

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One-Step Versus Two-Step Approach

• To avoid interpretation confounding, AG suggest
  to estimate the measurement model first and
  assess model fit
• If problems exist with validity (Mis greater than
  5, crossloadings throughout), you may not want to
  run the structural model until you clean up the
  problems
• If discriminant validity holds, then ?model will
  fit ?data

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One-Step Versus Two-Step Approach

• AG suggest to test model with everything
  constrained versus one with nothing constrained
• Five models that should be tested (on the
  measurement model side)
• Your desired model
• Your desired model, but with phi constrained to
  zero
• The model with everything unconstrained
• And 5. Two other possible plausible explanations

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One-Step Versus Two-Step Approach

• AG suggest to test model with everything
  constrained versus one with nothing constrained
  (every item is allowed to load on every
  construct)

x1
?1
x1
?1
?1
?1
x2
?2
x2
?2
x3
?3
x3
?3
x4
?4
x4
?4
x5
?2
?2
?5
x5
?5
x6
?6
x6
?6
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One-Step Versus Two-Step Approach

• What is the value of fitting a model with nothing
  constrained?
• There are an infinite number of models that could
  fit the data equally well
• You should test other plausible models that would
  fit the data
• Very constrained versus very unconstrained are
  the two extreme models that could be tested

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One-Step Versus Two-Step Approach

• By running the measurement model first, can
  address any problems with validity before moving
  to the structural model
• SEM is simultaneous like a set of inter-related
  springs so first look at model without the
  structural paths present
• Any problems may be addressed before examining
  the structural model