Comparing log likelihood & AIC for two spatial error regression models with the same dependent but different independent variables

Question

I have two spatial lag models using the same dependent variable (average income) and different independent variables (1- living environment deprivation; 2- education deprivation) for towns in the UK.

I would like to see which model accounts for greatest variation, hence should I compare r squared or log likelihood and AIC values to determine this?

I have read on forums that the log likelihood can only be compared for models with the same data, so does this mean I cannot compare them if the independent variables are different?

Thank you.

Answer 1

What purpose does a model comparison serve if your independent variables are identical?

You can use either measure to compare your models. One limitation of $R^2$ is that you should not compare models with different numbers of independent variables. In that case you need the adjusted $R^2$.