## 4 Results  
In the case of census blocks, the LR values for perceptions of neighborhood social cohesion, self-perceived health status, and perceptions of neighborhood safety were 0.608, 0.865, and 0.245 respectively; all values were lower than the threshold of 3.83. These results suggest that there are not significant internal similarities of individual perceptions of place in the corresponding census blocks. Moreover, the census blocks could not significantly represent the external variability of the PSI values in relation to self-perceived health status, perceptions of neighborhood safety, or perceptions of neighborhood social cohesion. As shown in Figure 3, when we used the perceptions of neighborhood safety to validate the PSI contextual values, 35 to 80% of clustering layers in each clustering algorithm could effectively explain the internal variability of perceptions of neighborhood safety. In the case of models using the self-perceived health status, excepting the \(HAC\) clustering algorithm (96% of clustering layers with LR larger than 3.84), the proportion of clustering layers that can explain the internal variability of self-perceived health status dramatically declined from 8 to 26%. Additionally, there are practically no clustering layers in all the six clustering algorithms that can effectively demonstrate the internal variability of perceptions of neighborhood social cohesion. In conclusion, the neighborhood context in relation to the PSI index influences the variances of self-perceived health status and perceptions of neighborhood safety, but not variances of perceptions of neighborhood social cohesion. Table 1 shows the averages of the VPCs with an LR higher than 3.84. The higher the VPC, the lower the internal (neighborhood) heterogeneities and the higher the external heterogeneities. In the case of the perceptions of neighborhood safety and self-perceived health status, results show that neighborhoods constructed using the different cluster algorithms are places where citizens share similar perceptions (VPCs averages higher than 0.50). Especially in the case of self-perceived health status, citizens living in different kinds of neighborhoods share practically equivalent perceptions (VPCs closer or equal to 1). By contrast, in the case of the perceptions of neighborhood social cohesion, only the neighborhoods created with the \(SKATER\) algorithm are places where people share similar perceptions of social cohesion. In general, the SKATER-based neighborhood units which account for the spatial connectivity features demonstrate higher spatial efficacy than the other five clustering results in terms of connecting objective neighborhood context information and subjective individual perceptions of place. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & _Fuzzy_ & _HAC_ & _Kmeans_ & _Mcluster_ & _SKATER_ & _SOM_ \\ \hline Neighborhood & Avg VPCs (LR \(>\) 3.84) & 0.815 & 1 & 0.773 & 0.572 & 0.530 & 0.732 \\ \cline{2-8} safety & Variance (LR \(>\) 3.84) & 0.340 & 0.446 & 0.366 & 0.270 & 0.322 & 0.260 \\ \hline Neighborhood & Avg VPCs (LR \(>\) 3.84) & 0 & 0 & 0.078 & 0.060 & 0.65 & 0 \\ \cline{2-8} social cohesion & Variance (LR \(>\) 3.84) & 0 & 0 & 0 & 0 & 0.303 & 0 \\ \hline \multirow{2}{*}{Health status} & Avg VPCs (LR \(>\) 3.84) & 0.948 & 1 & 0.985 & 0.985 & 0.916 & 0.991 \\ \cline{2-8}  & Variance (LR \(>\) 3.84) & 0.249 & 0.143 & 0.433 & 0.433 & 0.398 & 0.272 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The average variance partition coefficients (VPCs) of the multilevel models in relation to the citizens’ perceptions and the neighborhood PSI context based on six clustering algorithms. (_Fuzzy_ = Fuzzy clustering, _HAC_ = Hierarchical clustering, _Kmeans_ = K-means clustering, _Mcluster_ = Gaussian Mixture Modelling for Model-Based Clustering, _SKATER_ = Spatial “K”luster Analysis by Tree Edge Removal, _SOM_ = Self-organization maps).