% ==========================================================================
\section{Robustness Checks}
\label{sec:robustness}
% ==========================================================================

This section evaluates the sensitivity of the main hedonic estimates to
alternative sample definitions, variable transformations, model
specifications, and subsample restrictions.

% ------------------------------------------------------------------
\subsection{Outlier Treatment}
\label{subsec:winsorize}
% ------------------------------------------------------------------

We assess sensitivity to alternative outlier treatments through five
specifications: (1)~raw OLS, (2)~Winsorized dependent variable at the
1st/99th percentiles, (3)~trimmed sample dropping observations outside
the 1st--99th range, (4)~semi-log specification, and (5)~median
regression (LAD). Across all five, the sign, significance, and
approximate magnitude of the key hedonic coefficients remain stable.
The adjusted $R^2$ ranges from 0.083 to 0.098, confirming that the
results are not driven by extreme prices.

% ------------------------------------------------------------------
\subsection{Subsample Analysis by Property Type}
\label{subsec:room_type}
% ------------------------------------------------------------------

We re-estimate the full model separately for each property type.
Table~\ref{tab:robustness_type} summarizes the results.

\begin{table}[!htbp]
\centering
\caption{Hedonic Model by Property Type}
\label{tab:robustness_type}
\begin{threeparttable}
\begin{tabular}{lrrr}
\toprule
Property Type & $N$ & $R^2$ & Adj.\ $R^2$ \\
\midrule
Apartment & 77 & 0.186 & 0.082 \\
Cabin/Chalet & 691 & 0.084 & 0.068 \\
Condo & 237 & 0.104 & 0.065 \\
House & 679 & 0.098 & 0.083 \\
Other & 554 & 0.130 & 0.112 \\
Rental unit & 1,174 & 0.095 & 0.085 \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item \textit{Notes:} OLS estimates with HC1 robust standard errors.
Each row reports the model estimated on the corresponding property type
subsample. Zero-variance regressors are dropped within each subsample.
\end{tablenotes}
\end{threeparttable}
\end{table}

The Apartment subsample achieves the highest $R^2$ (0.186) despite the
smallest sample size. Cabin/Chalet and House show lower $R^2$ values,
consistent with greater heterogeneity depending on unobserved
experiential characteristics.

% ------------------------------------------------------------------
\subsection{Price Segment Heterogeneity}
\label{subsec:price_segment}
% ------------------------------------------------------------------

We partition the sample into five price segments (Budget, Moderate,
Premium, Luxury, Ultra-Luxury) and re-estimate the full model within
each. In the Budget segment, structural variables carry larger
standardized coefficients. In the Luxury and Ultra-Luxury segments,
amenity indices and reputation variables gain relative importance,
consistent with the quantile regression findings.

% ------------------------------------------------------------------
\subsection{Alternative Location Controls}
\label{subsec:alt_location}
% ------------------------------------------------------------------

We test five progressively richer location specifications: (1)~no
controls, (2)~city/neighbourhood fixed effects (top 30 by count),
(3)~latitude and longitude as continuous controls, (4)~spatial cluster
fixed effects ($K = 20$), and (5)~spatial lag (5-NN mean price). City
fixed effects raise the adjusted $R^2$ from 0.094 to 0.164. Under all
specifications, the non-locational hedonic coefficients remain stable
in sign and significance.

% ------------------------------------------------------------------
\subsection{Host Type Stratification}
\label{subsec:professional}
% ------------------------------------------------------------------

We stratify by host type: all hosts (baseline), Superhosts only
($R^2 = 0.077$), and multi-listing hosts. The lower $R^2$ for
Superhosts suggests that, conditional on meeting the quality threshold,
other observables explain less of the remaining price variation.

\medskip
In summary, the main findings---the dominant role of bedrooms and
structural capacity, the significant review score premium, the concave
bedroom--price relationship, competitive density effects, and positive
local price contagion---are robust across alternative sample definitions,
outlier treatments, property type subsamples, price segments, location
controls, and host type stratifications.