Modification indices inconsistency

[Maksim Rudnev]

Hi all, 

I ran a simple path analysis and got Chi-square of 5.5, then I requested modification indices and got one of the size 17.1. How's that possible? 

I've always thought that MIs represent a potential decrease in chi-square which cannot be smaller than the actual chi-square of the model. (I realize MIs are only the Lagrange estimates of chi-square difference, but shouldn't  they be trimmed by the level of a current chi-square, to avoid such confusion?)

[Yves Rosseel]

On 9/26/19 12:16 PM, Maksim Rudnev wrote:
> Hi all,
>
> I ran a simple path analysis and got Chi-square of 5.5, then I requested
> modification indices and got one of the size 17.1. How's that possible?

The modification indices are based on the score test. The model
Chi-Square test is a likelihood ratio test (LRT). Only when the sample
size becomes very large, they will converge to the same value. In
particular in small samples, they may diverge.

Modification indices only give you roughly some information about the
impact of relaxing a single parameter (one at a time).

Yves.