This behaviour is actually expected in stepwiselm.
If you're running stepwiselm with the default options, the issue is because the selection criterion is not based on the p-value of the coefficient directly. Specifically, the default criterion uses the p-value of the F-stat for a comparison of the two models. Depending on your data, and the starting model, you can have individual coefficients which have non-significant coefficients (based on some level) but which pass the inclusion or exclusion criteria.
The second model they present there has a coefficient with a p-value of 0.08. In general, you wouldn't want to do data analysis using the p-value directly, because you're essentially just data mining for significant coefficients at that point, instead of considering the explanatory power of the model as a whole. A coefficient may fall below some (arbitrary) significance level but still be informative as a control in the model; this is especially true of categorical controls.
There are a couple of things you can try:
- Start from a lower-order model (like just a constant) instead of starting from a more complex model.
- Change either your tolerance on the F-stat or change the criterion to either aic or bic and play with the tolerance.
In general, though, you should try not to exclude this outcome. This model is the best fit for your data!
