# Utilizing Multilevel Modeling to Measure Neighborhood Dynamics and Their Impact on House Prices
###### Abstract  
For decades, researchers have been concerned with house price modeling, and recognition has grown for the necessity of considering environmental and contextual variables in the process. This research examines the association between neighborhood characteristics and all individual house sale prices in Lucas County, Ohio, from 2012 to 2016, through a multilevel modeling (MLM) approach. Although there are various ways to define neighborhoods, census tracts and school districts are used in this study. Neighborhood characteristics include a foreclosure score, race heterogeneity, median household income, and built environment variables, such as walkability indexes. School district characteristics include student performance, tuition expenditures per pupil, and percent of expenditures spent on classroom instruction. The advantage of the multilevel model, is that it allows us to derive reliable estimates of place differences, representing a considerable improvement over the single-level model. Significant correlations were identified between house prices and foreclosure score, student performance, and tuition expenditures per pupil. The MLM results indicate that house prices not only lay in house characteristics themselves but also in neighborhood features, thus MLM offers good prediction accuracy and high explanatory power. house price; multilevel model; Lucas County; school district +
Footnote †: journal: Applied  
1
Footnote 1: School of Civil Engineering and Geomatics, Shandong University of Technology, Zibo 255000, China 1,  
model, such as family income, urban scale, transportation cost, schools, and other urban facilities, the modeling accuracy can be improved [10; 11; 12; 13; 14; 15]. Among all the determinants of house prices, structural characteristics have always been the fundamental factors, such as floor area, construction period, house age, the number of rooms and bathrooms, etc. [16; 17; 18]. In addition, the geographical location is also a major influencing factor of house prices, because it determines a family's access to various resources such as schools and parks. In addition to the individual characteristics of the house, these spatial neighborhood characteristics are also crucial to the estimation of house prices, and should be considered [19; 20; 21]. It is reasonable to assume that some unmeasured characteristics will also affect individual house prices. In addition, houses located in the same geographical area have similar location characteristics, such as infrastructure, common services, school districts, and other conditions [22]. Moreover, due to independent choice, residents living in the same area often have similar socioeconomic characteristics [23; 24]; this is called spatial effect (spatial dependence). This also has an important impact on house prices. The existence of spatial dependence indicates that observation objects in the same area will be related. Previous studies confirmed that families in the same community often have similar characteristics. Therefore, the location of houses often has different regional divisions. In the process of house price modeling, the existence of spatial correlation means spatially correlated errors. Therefore, the hedonic pricing method is based on ordinary least squares (OLS), which treats all variables as independent and assumes that the error follows an identical independent distribution [25]. This assumption is not considered in the inherent hierarchical characteristics of the house [26]. Considering that the house is nested in the community, the community is nested in the census tract, the census tract is nested in the county, and so on, houses in the same neighborhood show more similar price characteristics than houses in different neighborhoods. Moreover, the prices of the same census tract are more similar to those of other census tracts. Spatial correlation tends to occur in \"place.\" When the location of data is aggregated at a certain level, there is an inherent hierarchy of data [27; 28; 29].