If Null 4 is checked, the Null 4 model will be fitted and used to calculate CFI4 for each model generated by the specification search.
With incomplete data, both Saturated and Null 4 must be checked in order to fit the Null 4 model and to calculate CFI4.
In the Null 4 model, the correlations among the observed variables are required to be equal. The variances of the observed variables are unconstrained. Their means are required to be zero. (See Appendix F for more about null models.)
There is little reason to fit the Null 4 model in the common situation where means and intercepts are not constrained, but are estimated for the sole purpose of allowing maximum likelihood estimation with missing data.
The Null 4 option is enabled only for models in which means and intercepts are explicit model parameters.