# Poor model fit but significant and high path coefficient values in Structural Equation Modeling

I wonder if it is possible to have a poor model fit and at the same time strong significant and high path coefficient values among the latent variables?

How would be interpret this? Also, what if we obtained strong model fit but non-significant/low path coefficients. Can someone elaborate on this?

Yes, it's easy.

Let's say that this is your population model:

+---+    0.5       +----+
| X +------------> | Y  |
+-+-+              +-+--+
|     +----+       ^
+---->+ M  +-------+
0.5 +----+   0.5


And you fit this model:

+---+              +----+
| X |              | Y  |
+-+-+              +-+--+
|     +----+       ^
+---->+ M  +-------+
+----+


You've omitted the direct path from X to Y. This omission will make the model fit, very badly.

However, the parameters from X to M and M to Y will be high - higher than they should be, and (for any reasonable sample size) highly significant.

Model fit comes first. If your model doesn't fit, you don't trust the parameter estimates.

(That doesn't mean that if your model does fit, you do trust them.)