Hedonic House Price ModelingBased on Multilevel Structured Additive Regression - Computational Approaches for Urban Environments - page 108

R> plot(b, model=3, term="sx(district)", map=DistrictsBnd)
One way to inspect convergence of the MCMC chains is to look at the resulting sam-
pling paths, for example, for term c_area , the sampling paths of the coefficients
are plotted with

R> plot(b, model=1, term="sx(c_area)", which="coef-samples")
The estimated effects can also be extracted, for example, the effect of c_age_ind
of level-2, using function fitted()
R> fit <- fitted(b, model=2, term="sx(c_age_ind)")
where the object fit is a data frame containing the estimated mean as well as the
2.5, 50, and 97.5 % quantiles of the effect, among others.
For a detailed description of the package R2BayesX , including a number of
examples, see also Umlauf et al. ( 2012 ).

5.7 Results

We now present the estimation results for the mean regression, the GAMLSS regres-
sion based on the gamma distribution, and the quantile regression. The results are
based on a final MCMC run with 120,000 iterations and a burn in period of 20,000
iterations. We stored every 100th iteration resulting in a sample of 1,000 practically
independent draws from the posterior. Computing times for the MCMC sampler
were approximately 2 1/2 min (mean regression), 55 min (GAMLSS regression),
and 4 min (quantile regression) on a modern desktop computer (Intel quad-core
processor 2.7 GHz). Note that no more than 32,000 iterations are typically enough
in preliminary MCMC runs to obtain sufficiently exact estimation results. However,
we used the comparably large number of iterations in the final run to be absolutely
sure about the precision of estimates.
We first show in Sect. 5.7.1 the effects of the continuous covariates on the
expected house price per sq. m. received from the mean regression and the GAMLSS
regression based on the gamma distribution. Next, we will focus on different
quantiles of the house price per sq. m. and compare the results of these two models
with those of the quantile regression ( 5.7.2 ). The last Sect. 5.7.3 is devoted to the
spatial effects.

5.7.1 Continuous Covariate Effects

5.7.1.1 Structural Covariates

Figure 5.1 shows the effects of the structural continuous covariates. In order to
get an impression of the magnitude of effects and make the results comparable,
we hold the other structural covariates constant at mean level of attributes and the