Descriptive model summary of the spatial hierarchical TL for each census (year).

n is the number of finite log(mean)-log(variance) pairs (here, the number of states) in each fitting. OLS is the ordinary least-squares linear regression and best LS is the least-squares linear regression with the smallest AICc. mod shows the name of the best LS. gls_exp and gls_rat are respectively the generalized least-squares linear regression with exponential spatial correlation and rational quadratics spatial correlation. est and std err are respectively the point estimate and standard error of the estimate. lower and upper are respectively the lower and upper bounds of the slope estimates with 95% confidence level. AICc and AICc wt are respectively the Akaike Information Criterion corrected for the number of parameters and the AICc weight of the corresponding model among all fitted models in a census. A model with the smaller AICc (or greater AICc wt) is better. cor is the correlation coefficient of the observed variance and the predicted variance from each model. ΔAICc is AICc of the best LS minus the AICc of the OLS. (XLSX)