# Utilizing Multilevel Modeling to Measure Neighborhood Dynamics and Their Impact on House Prices
## 2 Background
### Data Sources  
The original data used in this paper are housing sales data from 2012 to 2016, downloaded from the Lucas County Auditor's Office, and the Lucas County residential property sales. The geographical data are geo-coded according to the specific addresses of the houses. Each house has a property value, which is an associated attribute at the time of transaction. Figure 2 represents the spatial distribution of house prices for 2012-2016, and the point in Figure 2 depicts the location of houses, with the heights indicating the relative property values. Figure 2b is a continuous surface generated from those points, from which the essential spatial pattern of house values can be observed. Residences around Ottawa Hills, Sylvania, and Maumee, tend to be more expensive, while house prices are also relatively high along Lake Erie. The house characteristic data are also part of the Auditor's database. These data include all the individual explanatory variables that characterize the house, such as the year built, the year of sale, the size of the house area, the size of the building area, the number of bedrooms, the number of bathrooms, the garage area, and the quality of the house, etc.  
Therefore, when integrating data, we need to consider two variables: school district and year of house sale.  
These downloaded data were sorted to remove some missing data, and finally, a total of 30,109 effective house observations were used in this study (Table 2). The data includes individual information such as house prices; location information such as community names; the school district where the house is located; and household information such as poverty rates and employment information.  
Additionally, in previous studies, the purchase years of houses constituted the time index, which can be regarded as the remaining unexplained time heterogeneity, and indicates the portion of house price adjustment with time. We get the following table through simple analysis of data, which shows that the average house price increases gradually with the purchase years (Table 3). Another table shows that house price changes significantly with different school districts (Table 4).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name\_Year** & **Performance** & **Per Pupil** &
\begin{tabular}{c} **Percent of Expenditures on** \\ **Classroom Instruction** \\ \end{tabular} \\ \hline Ottawa Hills LSD 2012 & 91.7 & \$12,452 & 70.78 \\ Ottawa Hills LSD 2013 & 92.6 & \$13,241 & 74.71 \\ Ottawa Hills LSD 2014 & 91.6 & \$12,933 & 76.60 \\ Ottawa Hills LSD 2015 & 90.8 & \$13,998 & 76.24 \\ Ottawa Hills LSD 2016 & 90.1 & \$14,234 & 75.44 \\ \hline \hline \end{tabular}
\end{table}
Table 1: School district data in different years.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Year** & **Freq.** & **Mean (Sale Amount)** \\ \hline
2012 & 6226 & 80,852.5 \\
2013 & 6496 & 89,005.7 \\
2014 & 5535 & 99,516 \\
2015 & 5918 & 104,789 \\
2016 & 5934 & 107,887 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The average value of house prices gradually increases with the number of years away from the year of purchase.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Year** & **Freq.** & **Mean (Sale Amount)** \\ \hline
2012 & 6226 & 80,852.5 \\
2013 & 6496 & 89,005.7 \\
2014 & 5535 & 99,516 \\
2015 & 5918 & 104,789 \\
2016 & 5934 & 107,887 \\ \hline \hline \end{tabular}
\end{table}
Table 4: House price changes significantly with different school districts.