# Calculate L-function envelopes from a fitted model: Lest or Linhom?

I have fitted a model to a point pattern using INLA, and generated 1000 simulated pp from the posterior of this model. I want to use these samples to generate the L-function envelope for my data, and see whether the model captures the structure of my pattern. My question is:

Since my H0 would then be that my data fits my model, (i.e. the observations are independent conditional to the field), I believe I should use Lest instead of Linhom, as a function inside the envelope call, even if the original point pattern is not homogeneous.

Can someone confirm my logic is correct?

• In principle you are allowed to use any statistic you want. The Monte Carlo principle makes it a valid test in terms of significance. However, if your point pattern and model is inhomogeneous any interpretation of differences between the observed summary statistic and simulated statistics is hard to interpret. – Ege Rubak Aug 28 '18 at 9:07