![](data:image/png;base64,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wlAAAAeEsAAAC8JQAAAN4SAAAAbwkAAADeEgAAAG8JAACAtwQAAMBbAgAAgLcEAADAWwIAAOAtAQAA8JYAAADgLQEAAPCWAAAAeEsAAAC8JQAAAHhLAAAAvCUAAADeEgAAAG8JAAAA3hIAAABvCQAAgLcEAADAWwIAAIC3BAAAwFsCAADgLQEAAPCWAAAA4C0BAADwlgAAAHhLAAAAvCUAAAB4SwAAALwlAAAA3hIAAABvCQAAAN4SAAAAbwkAAIC3BAAAwFsCAACAtwQAAMBbAgAA4C0BAADwlgAAAOAtAQAA8JYAAAB4SwAAALwlAAAAeEsAAAC8JQAAAN4SAAAAbwkAAADeEgAAAG8JAACAtwQAAMBbAgAA4C0lAAAAwFsCAADgLQEAAPCWAAAAeEsAAADwlgAAAHhLAAAAvCUAAADeEgAAALwlAAAA3hIAAABvCQAAgLcEAAAAbwkAAIC3BAAAwFsCAADgLQEAAMBbAgAA4C0BAADwlgAAAHhLAAAA8JYAAAB4SwAAALwlAAAA3hIAAAC8JQAAAN4SAAAAbwkAAIC3BAAAAG8JAACAtwQAAMBbAgAA4C0BAADAWwIAAOAtAQAAWFKJAAAAwNcB48YPYFpCnZYAAAAASUVORK5CYII=)
PÉREZ, VARGAS: Uncertainty in Land Value Modeling of the San José, Costa Rica. 49
over-smoothing limitations in the kriging predictions [5]; but
even this feature could have likely been incorporated into the
kriging by a careful consideration on the number of neighboring
points determining a prediction. Previous exercises of kriging
models did nd limitations due to this over-smoothing problem
that seem to have been improved on by the sequential Gaussian
simulation method (in particular, by better modeling the local
changes at the peri-urban interface of the region); further work
on this issue seems promising.
A distinct advantage of conditional Gaussian simulation is
the spatially explicit measures of uncertainty that can be used
to explore the limitations of the prediction and to more easily
estimate exceedance probabilities [13]; this feature is especially
useful for land value maps in applied scenarios (for example, when
the map predicts land values claimed to be too large by a land
owner, this claim can be easily tested). Further work is required
on this issue (previous comparisons of models estimated from this
data and other data sources suggest systematic underestimation of
land values, particularly for taxation purposes [3]; while outdated
assessments are the simplest explanation, it is also possible that
data sources for the models reported in this paper may be also
partially skewing the results).
It is further worth noting that the literature has detected over-
smoothing problems associated with deterministic methods such as
ordinary kriging that can be overcome with simulation. The current
focus of this study was not the comparison of conditional Gaussian
simulation with other extrapolation predictions; however, this is
regarded as a potential area for further investigation.
The estimated uncertainty patterns are inversely related
to the predicted land value. A very clear and negative spatial
association was identied between the E-Type prediction of
land values per square meter and its standard deviation: in the
urban central area of the GAM, the highest land values (which
coincides both with previous analysis [1] and with theoretical
expectations from urban economics) and lowest uncertainties
were observed. This nding coincides with previous analysis
of the point pattern of real estate listings and its relation to the
determinants of suitability for urban land uses [11].
Indeed, the estimated uncertainty was found to decrease with
characteristics that identify suitability for urban land use (and thus
higher land values). The atter areas of the GAM, which are also
closer to urban centralities (the CBD, main municipal centers),
showed much less uncertainty (smaller location-wise standard
deviation) than zones further away and at higher elevations and
steeper slopes. Therefore, the data set and modeling eorts appear
to demonstrate eciency when predicting urban land values but
also present clear limitations if applied to rural land uses of the
urban periphery.
Despite its importance, hardly any previous case study
reports the use of simulation to understand uncertainty introduced
by interpolation into land or property value predictions (unlike
physical properties of soils, which are derived from similar point
data and for which such analysis seems common). Uncertainty has
been reported as variance of kriging estimates [1] or verication
through out-of-sample prediction [14], in relation to the mean
estimate from this indicator. While theoretical recognition of the
possibility to estimate errors and uncertainty in the context of
land valuation has been acknowledged [15], actual practice has
centered on the accuracy of the mean prediction rather than on
explaining its variance. Uncertainty is important for valuation,
especially when practical applications are performed (such as tax
assessments and potential challenges to these).
In conclusion, the analysis of uncertainties may be critical
for improving urban and regional studies (e.g., the impact of
new infrastructure or of land use regulations) and land value
assessments for tax policy. In this regard, the methods presented
have increased robustness (relative to very local estimates)
because predictions relatively far away from locations with known
values may still benet from their price information via the spatial
dependence encoded in the semivariogram. More importantly, the
estimates of uncertainty permit the assessment of the prediction
for properties that have not been recently sold in the market (and
thus include an inherent check of the prediction which is absent
in isolated tax assessment exercises).
ROLES
Eduardo Pérez Molina: Conceptualization, Methodology,
Software, Formal analysis, Writing - Original Draft
Darío Vargas Aguilar: Data Curation, Writing - Review
& Editing
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