I made a land value analysis using a random-intercept multilevel model with 3 levels (lands nested in districts further nested in cities). The intercept is allowed to vary between each district and each city.
I transform my dependent variable (USD/sqm) with log-transformation. The whole model will look like this:
log(Price)_ijk = beta0 + beta1*X1 + beta2*X2 + v_k + u_jk + e_ijk
- beta0 = intercept
- X1 and X2 = predictors
- v_k = random effect from city k
- u_jk = random effect from district j in city k
- e_ijk = residual of land i in district j in city k
I have computed the result from v_k and u_jk respectively. Let's say, city A has district 1A and 2A, and city B has district 3B and 4B:
- beta0 = 23.50
- v_A = 0.77
- u_1A = 0.08
- u_2A = -0.10
- v_B = 0.13
- u_3B = 0.01
- u_4B = -0.05
My questions would be:
- How would I interpret these random effects, particularly random effects from city A and city B? Right now the DV is log-transformed, but I want to see how many USD/sqm is the difference of effect coming from city A and city B to the land value (not the log-transformed value).
- Can I interpret the result without considering the effects coming from the districts within their cities? Currently, I am only interested in seeing the effect coming from each city.
Thank you for your attention!