# Utilizing Multilevel Modeling to Measure Neighborhood Dynamics and Their Impact on House Prices
## 3 Methods and Results
### Variables  
A detailed explanation of each level and all variables that will be used are as follows:  
Level one is the property characteristics in an individual house, such as the age of the house at the time when it was sold (houseage); the total land area of the house (tla); the area of the basement (baseBsmt); garage size (GarageSqft); the number of bedrooms (BedRms); the number of full bathrooms (FullBath); the number of half bathrooms (HalfBath); the total number of rooms (Rooms); the floor area of the house (Lotsize); a dummy index for the quality of the house (cond); a dummy index for the traffic situation (traffic); and a time index for the year the house was sold. Note that in actual processing, we reclassify the number of bedrooms (BedRms) into two categories. Either BedRms \(\leq\) 1 or BedRms \(\geq\) 5 is the reference category, while the others are defined as a different group. Reclassification is necessary because many old houses have many bedrooms, but the house prices are not high. Level two is neighborhood characteristics at the census tract, such as percent below the poverty line (poverty), race heterogeneity (raceheter), education level (bachelor), employment status (unemployme), foreclosure score (fcscore), walk score, street connectivity, and urbanity. Some noteworthy variables are explained as follows:  
_Street connectivity:_ the number of intersections per square mile. _Race heterogeneity (racheter)_: the Herfindadahl Index _1-\(\Sigma\!p_{i}^{,2}\)_[35] is used to measure racial heterogeneity, where pi is the fraction of the racial-ethnic i population in the census tracts. Racial groups are used to calculate a census tract index, that is Whites, Blacks or African Americans, Asians or Pacific Islanders, Hispanics, American Indians, and others. The heterogeneity index ranges between zero and one, where zero means that there is only one racial group in the unit, and a value approaching one indicates maximum racial heterogeneity. _Education level (bachelor)_: the rate of bachelor's degree or higher in the population aged 25 to 64 in a census tract is adopted, because it represents the average level of education in the region. There are four types of educational attainment: less than high school graduate, high school graduate (includes equivalency), some college or associate's degree, and bachelor's degree or higher. _Foreclosure score (fcscore)_: foreclosures as a percentage of all residential property sales in the census tract throughout the time period, see Figure 3.  
_Walkscore_: the walk score is measured by the walkscore ([[http://www.walkscore.com/](http://www.walkscore.com/)]([http://www.walkscore.com/](http://www.walkscore.com/)) accessed on 5 April 2022), based on the algorithm developed by the Front Seat Management ([[http://www.frontseat.org/](http://www.frontseat.org/)]([http://www.frontseat.org/](http://www.frontseat.org/)) accessed on 5 April 2022). It calculates the Euclidean distances from the point of interest to nearby amenities such as food, retail, education, parks, restaurants, recreation, and entertainment, and then integrates them by alinear combination of these distances, with weights that account for facility type priority, and a distance decay function (FrontSeat, 2013) ranging from 0 (car-dependent) to 100 (walker's paradise). In this research, we classify the walkscore into a categorical variable. We choose walkscore \(\geq\) 0 and walkscore \(\leq\) 24 as the reference category and define it as walkscore1; define walkscore \(\geq\) 25 and walkscore \(\leq\) 49 as walkscore2; define walkscore \(\geq\) 50 and walkscore \(\leq\) 69 as walkscore3; define walkscore \(\geq\) 70 and walkscore \(\leq\) 89 as walkscore4; and define walkscore \(\geq\) 90 and walkscore \(\leq\) 100 as walkscore5.