# Utilizing Multilevel Modeling to Measure Neighborhood Dynamics and Their Impact on House Prices
## 4 Discussion  
The hedonic pricing modeling theory describes housing value as a function of a bundle of attributes, which can be grouped into two main categories: structural and neighborhood factors. Structural factors encompass features such as house age, number of rooms, size, sales year, and the number of full and half bathrooms. On the other hand, neighborhood factors pertain to community characteristics, such as census district or school district characteristics, which are measured by macro social and economic indicators, and related to large units. These factors inherently possess a hierarchical structure, with the macro determinants exerting both direct and indirect impacts on the micro factors for housing premiums. Although the current study does not investigate the effects of census tract- and school district-level determinants on county-level drivers, these effects are indeed present in the housing market at the county level. For instance, in Lucas County, our study area, house prices exhibit spatial relationships. As demonstrated in Table 4, house prices are regionally clustered. In general, the house prices of Ottawa Hills surpass those of Toledo, and the average house price near the university is the highest. The OLS regression result in Table 7 shows that most variables are significant for house prices. The coefficient of determination \(R^{2}\) for house price is 0.7865, and the Variance Inflation Factor (VIF) values do not suggest any multicollinearity among the independent variables. In Table 6, Model 1 tested the effect of house characteristics. Model 2 added different years to Model 1, Model 3 added census tract variables to Model 2, Model 4 added school district variables to Model 3, and Model 5 was the final model including all significant place-based contextual variables in previous models. Based on the AIC values, Model 5 is preferred. The hierarchical linear model results reveal several key insights:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Coef. ** & **Std. Err. ** & **t** & **P \textgreater{} \textless{} \textless{} \textless{} \textgreater  
In terms of housing structure, we found that the land area, floor area, number of bedrooms, number of bathrooms, and garage size, were positively correlated with the house price;
2. House age is negatively related to house price. We can attribute this to people's preference for new houses. New houses generally have better facilities, such as lower heating costs in winter and cooling costs in summer due to good thermal insulation;
3. Traffic has a positive correlation with house price because infrastructure near road intersections can provide convenience for families, so house price will be higher;
4. The overall trend of house price is steadily increasing with the increase of years;
5. The socioeconomic variables of the census tract level are significantly related to the house prices of Lucas County, the foreclosure score is negatively correlated with house price, and average family income is positively correlated with house price. Unemployment rate, poverty rate, walkability index, and average family education level, are not statistically significant, which is not surprising because house price is susceptible to location. Thus, it is challenging to use high-level comprehensive census socioeconomic indicators to explain the difference of low-level house price;
6. At the school district level, student performance, tuition expenditures per pupil, and percent of expenditures spent on classroom instruction, are all positively related to house prices. This indicates that house prices are higher in areas with good educational resources. This paper analyzes house prices using hierarchical regression models. The proposed modeling framework is advantageous for modeling house prices because it appropriately considers the typical hierarchical structure of the data. Specifically, house selling prices with associated individual attributes (level one) are grouped in the census tract (level two), which form school districts (level three).