# Interpreting Random Effects for 3-level Multilevel Model

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.