When researchers accepted a model based on fit criteria presented in
Table 4, they terminated estimation and selected that model as the final
model for TDS at that particular level of analysis. Analyses proceeded by
developing a model at the next hierarchical level. When fit indices suggested
that improvements could be achieved, researchers used modification indices
provided by AMOS to guide model respecification. According to Byrne
(2001), modification indices (MI) “reflect the extent to which the hypothesized
model is appropriately described” (p. 90) and to what extent the
estimate model may be improved if specific parameters are specified. AMOS
provides an MI for each fixed parameter, which represents the expected χ²
drop if the parameter were estimated. The researchers repeated this process
of modifying a model and examining fit indices until they obtained an adequately
fitting single-level model at each level.