How does education affect religion?

[h]igher levels of education lead to lower levels of religious participation later in life. Source.

The regressions model:

gpyc none = β edgpyc +γ Xgpyc +φp +ϕy +θc +ϑa +Tpy +τ pa +ε gpyc .

The variable gpyc none in the equation denotes the fraction of all individuals in a cell who report no religious affiliation. The variable edgpyc represents average years of educational attainment, and Xgpyc represents a set of controls including a dummy for gender, the fraction of a province’s population that is rural at the time a respondent was 12 years old, and the fraction of a province’s workers in manufacturingat age 12.

I wonder how much is due to education itself and how much to the indirect effect of education on income. The paper is here.