Those in black without asterisks may improve the fit of the model.

Step A:  Is the measurement model consistent with the data?

Yes, go to Step C.
No, go to Step B unless you have exhausted reasonable respecifications.  IF SO, THEN  STOP!

Evaluate loadings

Too small?  Drop the measure?  **
Too large, Heywood cases?  **
        possible specification error
        constrain error variance to be non-negative
Set the loadings equal?  (Measures should have the same metric and the covariance matrix analyzed.) **

Evaluate error variances

          Too small or negative, Heywood cases?  **
          Set the error variances equal?  (Measures should have the same metric and the covariance matrix
                 analyzed.) **

Need fewer factors?

Poor discriminant validity?  (Combine factors.) **
Make sure each factor has sufficient variance.  (Drop factors)  **

Need more factors?

Run a maximum likelihood exploratory factor analysis to test the number of factors (see how to do this).  (Note that this test presumes no correlated errors and so might be misleading if the true model has correlated errors.)

Evaluate measures

Check to see if a measure has large standardized residuals and modification indices (Lagrangian multipliers in EQS).  Consider dropping that measure.

Need correlated errors?

• Considerations
• Meaningfulness Rule:  Only correlate errors for which there is a theoretical rationale.
• Transitivity Rule:  If X₁ is correlated with X₂ and X₂ with X₃, then X₁ should be correlated with X₃ unless one pair is correlated for one reason and the other for a different reason.
• Generality Rule:  If there is a reason for correlating the errors between one pair of errors, then all pairs for which that reason applies should also be correlated.
• Sometimes correlated errors imply an additional factor.  For example, if X₁, X₂ and X₃ all have correlated errors, then consideration might be given to adding a factor on which the three load.
• Single indicator variables may not have correlated errors but indicators of other factors may load on the single indicator "factor."
• Which errors to correlate?
• large modification indices
• large standardized residual

Need measures to load on more than one factor?  (Read about identification difficulties.)

Step C:  If the structural model is justidentified go directly to Step D.

        Are the unspecified paths in the structural model zero?
               No, go to Step D.
               Yes, add needed paths and go to Step D.

Step D:  Are the specified paths of the structural model needed?

Yes, keep in model.
No, trim from model.  **

Even if one's model fits, there are a myriad of other models that fit as  well.  These equivalent models should be considered (see Ed Rigdon's page on this issue).  Realize that for any model, there always exist an infinite number of models that fit exactly the same.  Thus, while the fit of the structural model confirms it, it in no way proves it to be uniquely valid.

Respecification Strategies

There are two strategies to take in respecifying a model.  One can test a priori, theoretically meaningful complications and simplifications of the model.  Alternatively, one can use empirical tests (e.g., modification indices and standardized residuals) to respecify the model.  All respecifications should be theoretically meaningful and ideally a priori.  Too many empirically based respecifications likely lead to capitalization on chance and overfitting (unnecessary parameters added to the model).  Ideally, if many respecifications are made, a replication of the model should be undertaken.  Although a priori hypotheses deserve the initial focus, an examination of empirical tests of miss-specification are in order.  But if model changes are made on the basis of such tests, there still need to be some sort of theoretical rationale for them.