Modification index

• The modification index is a lower bound estimate of the expected chi square decrease that would result when a particular parameter is left unconstrained (making it become free parameter, or adding it as an extra path). Joreskog suggested that a modification index
  should be at least five before the researcher considers modifying the hypothesized model.
• Joreskog suggested that a modification index should be at least five before the researcher
  considers modifying the hypothesized model.
• MI values lower than 5 indicate little appraciable improvement in fit.
• Correlated errors of measurement are among the most problematic types of post hoc modifications becasue they are rarely theoretically justified and are unlikely to replicate. The need for correlated measurement error is an indication that the factor model has been unable to account for all the covariation among the variables. This may occur if, for example, more factors are needed or if method variabe is present.
• http://www2.chass.ncsu.edu/garson/pa765/structur.htm#extract

LISREL

• modification index (ML)-- the estimate of the decrease in chi-square value that would result if a given parameter were to be added to the model, MI are available for all parameters that were constrained to be zero in the original model. MI are accompanied by expected parameter change (EPC)
• EPC--the value a given parameter would have if it were added to the model

EQS

• Lagrange multiplier (LM)=MI in LISREL
• Wald test--values of the Wald test represent the amount by which the overall chi-square value will increase if a parameter were to be dropped from the model