Maximum Likelihood Estimates
| Variable | OLS | GAMa | Model Ib | Model IIc | Model IIId | Model IVe |
|---|---|---|---|---|---|---|
| AGE | –0.014*** (–13.93) | –0.013*** (–12.86) | –0.012*** (-12.34) | –0.012*** (-12.37) | –0.012*** (-12.31) | –0.012*** (-11.97) |
| AGE·AGE | 0.001*** (9.56) | 0.001*** (8.47) | 0.001*** (8.18) | 0.001*** (8.32) | 0.001*** (8.16) | 0.001*** (7.89) |
| STORIES | –0.108*** (–5.84) | –0.102*** (-5.53) | –0.094*** (-5.22) | –0.095*** (-5.28) | –0.093*** (-5.15) | –0.095*** (-5.23) |
| RMTOT | –0.006 (–0.97) | –0.003 (-0.44) | –0.004 (-0.73) | –0.005 (-0.94) | –0.005 (-0.83) | –0.005 (-0.80) |
| FPf | 0.083*** (6.81) | 0.08*** (6.65) | 0.072*** (6.09) | 0.074*** (6.23) | 0.073*** (6.12) | 0.073*** (6.09) |
| FIXTOT | 0.023*** (6.82) | 0.022*** (6.46) | 0.021*** (6.38) | 0.021*** (6.45) | 0.021*** (6.34) | 0.021*** (6.31) |
| log(SFLA) | 0.700*** (22.19) | 0.673*** (21.26) | 0.603*** (19.37) | 0.606*** (19.43) | 0.603*** (19.35) | 0.605*** (19.44) |
| log(ACRES) | 0.255*** (8.72) | 0.271*** (9.03) | 0.23*** (8.04) | 0.23*** (8.08) | 0.238*** (8.34) | 0.216*** (7.71) |
| GASFUELf | –0.008 (–0.48) | –0.004 (–0.28) | –0.001 (–0.03) | 0.001 (0.04) | –0.001 (–0.01) | –0.001 (–0.03) |
| ELECTRICFUELf | 0.152** (2.53) | 0.140** (2.19) | 0.136** (2.31) | 0.154*** (2.63) | 0.145*** (2.49) | 0.125** (2.12) |
| CENTRALHEATf | 0.161*** (7.67) | 0.140*** (6.68) | 0.146*** (7.09) | 0.150*** (7.29) | 0.149*** (7.28) | 0.148*** (7.19) |
| POORCONDITIONf | –0.257*** (–3.12) | –0.248*** (–3.03) | –0.262*** (–3.26) | –0.272*** (–3.38) | –0.266*** (–3.30) | –0.261*** (–3.24) |
| GOODCONDITIONf | 0.148*** (4.28) | 0.157*** (4.57) | 0.129*** (3.84) | 0.127*** (3.77) | 0.129*** (3.81) | 0.130*** (3.85) |
| BRICKf | 0.073*** (4.93) | 0.067*** (4.56) | 0.061*** (4.26) | 0.060*** (4.17) | 0.062*** (4.29) | 0.062*** (4.31) |
| FRAMEf | 0.038* (1.94) | 0.034* (1.72) | 0.03 (1.56) | 0.03 (1.54) | 0.029 (1.52) | 0.031 (1.59) |
| TOWNHOUSEf | –0.277*** (–4.06) | –0.288*** (–4.25) | –0.237*** (–3.54) | –0.232*** (–3.47) | –0.235*** (–3.52) | –0.235*** (–3.52) |
| PBH | –0.006*** (–10.88) | –0.005*** (–9.27) | –0.005*** (–9.25) | –0.005*** (–9.69) | –0.005*** (–9.77) | –0.005*** (–9.73) |
| PHH | –0.009*** (–9.24) | –0.010*** (–7.95) | –0.007*** (–7.34) | –0.007*** (–7.54) | –0.007*** (–7.55) | –0.007*** (–7.53) |
| URATE | –0.006*** (–3.29) | –0.008*** (–4.28) | –0.005*** (–2.90) | –0.006*** (–3.26) | –0.005*** (–3.04) | –0.004*** (–2.39) |
| Log(MEDHHINC) | 0.191*** (6.62) | 0.128*** (4.17) | 0.119*** (4.20) | 0.123*** (4.34) | 0.114*** (4.03) | 0.101*** (3.55) |
| τ2012f | –0.048*** (–2.78) | –0.048*** (–2.8) | –0.05*** (–2.91) | –0.049*** (–2.88) | –0.049*** (–2.89) | –0.050*** (–2.94) |
| τ2013f | –0.045*** (–2.59) | –0.046*** (–2.66) | –0.046*** (–2.70) | –0.045*** (–2.67) | –0.046*** (–2.72) | –0.046*** (–2.71) |
| τ2014f | 0.036** (2.02) | 0.035* (1.95) | 0.034* (1.92) | 0.034** (1.97) | 0.034* (1.95) | 0.032* (1.82) |
| τ2015f | 0.042** (2.44) | 0.042** (2.44) | 0.04** (2.35) | 0.04** (2.37) | 0.039** (2.32) | 0.039** (2.29) |
| τ2016f | –0.081*** (–2.82) | –0.081*** (–2.84) | –0.083*** (–2.96) | –0.080*** (–2.85) | –0.083*** (–2.95) | –0.084*** (–2.98) |
| comtime | –0.008*** (–2.84) | –0.004 (–1.37) | –0.006** (–2.08) | –0.008*** (–2.75) | –0.006** (–2.27) | –0.007*** (–2.43) |
| dist2CBD | –0.175*** (–7.02) | –0.092*** (–2.64) | –0.14*** (–5.71) | –0.081*** (–4.22) | –0.104*** (–5.1) | –0.144*** (–5.91) |
| dist2roads | –0.002 (–0.2) | 0.011 (1.25) | –0.002 (–0.30) | –0.005 (–0.66) | 0.001 (0.07) | 0.004 (0.48) |
| dist2opensp | 0.014*** (2.59) | –0.006 (–0.64) | 0.011** (2.03) | 0.010** (1.97) | 0.015*** (3.05) | 0.010* (1.83) |
| dist2river | 0.182*** (6.28) | 0.105*** (2.71) | 0.147*** (5.17) | 0.070*** (4.08) | 0.087*** (4.90) | 0.148*** (5.33) |
| L50(μ) | –0.146*** (–3.32) | –0.101** (–2.09) | –0.111*** (–2.58) | –0.059** (–2.24) | –0.133*** (–3.29) | –0.111*** (–4.28) |
| log(1/dist2airport)(log(r–1)) | –0.008 (–0.08) | 0.055 (0.43) | 0.019 (0.19) | NA | 0.02 (0.22) | 0.083 (0.86) |
| log(POPDENSITY) | 0.019 (0.74) | 0.056* (1.92) | 0.030 (1.20) | 0.026 (1.11) | 0.012 (0.49) | NA |
| μ·log(r–1) | –0.027** (–2.41) | –0.025** (–1.96) | –0.025** (–2.22) | NA | –0.026*** (–2.54) | –0.032*** (–3.04) |
| μ·log(POPDENSITY) | 0.005 (1.18) | 0.001 (0.06) | 0.002 (0.59) | 0.004 (0.96) | 0.005 (1.35) | NA |
| r·cos(ϑ) | –0.026*** (–3.02) | 0.064 (1.49) | –0.022*** (–2.60) | NA | NA | –0.019*** (–2.34) |
| r·sin(ϑ) | 0.01** (2.33) | 0.04 (1.09) | 0.009** (2.09) | NA | NA | 0.011*** (2.49) |
| Intercept | 4.961*** (9.39) | 4.237*** (4.59) | 3.998*** (7.69) | 4.181*** (9.79) | 4.445*** (9.08) | 4.531*** (10.34) |
| ρ | NA | NA | 0.193*** (17.16) | 0.197*** (17.60) | 0.194*** (17.25) | 0.194*** (17.25) |
| <sub>σ </sub>2 | 0.507 (NA) | 0.250 (NA) | 0.245*** (69.04) | 0.245*** (69.03) | 0.245*** (69.04) | 0.245*** (69.04) |
| Log-likelihood | –7,063 | –6,918 | –6,919 | –6,935 | –6,923 | –6,928 |
| Akaiki information criterion | 14,272 | 14,066 | 13,986 | 14,010 | 13,990 | 14,000 |
| Λ (likelihood ratio test) | NA | NA | NA | 31.5***g (0.000)h | 7.67**i (0.022)h | 18.01**j (0.000)h |
| Number of parameter estimates | 72 | 150 | 74 | 70 | 72 | 72 |
| Sample size (N) | 9,606 | 9,606 | 9,606 | 9,606 | 9,606 | 9,606 |
Note: The numbers in parentheses are z-values. NA, missing values.
↵a Generalized additive model with integrated smoothness estimation: number of basis (k) = 40; penalty parameter computed through generalized cross-validation; smooth terms: s(LON) and s(LAT).
↵b Model I assumes the acoustic inverse law relationship between distance to airport and housing price with interaction to background noise.
↵c Model II imposes four restrictions to Model I: no aircraft/airport noise.
↵d Model III imposes two restrictions to Model I: no directional effects.
↵e Model IV imposes two restrictions to Model I: no propensity to noise annoyance.
↵f Binary variables (0/1).
↵g Log-likelihood ratio statistics ~χ2 with four degrees of freedom; rejected H0: log(1/r), μ·log(1/r), r·cos(θ), and r·sin(θ) are simultaneously equal to zero.
↵h The p-values of the log-likelihood ratio test. Lastly, estimates for 34 zip codes dummy variables are not reported, to save space, but are available upon request.
↵i Log-likelihood ratio statistics ~χ2 with two degrees of freedom; rejected H0: log(POPDENSITY), μ·log(POPDENSITY) are simultaneously equal to zero.
↵j Log-likelihood ratio statistics ~χ2 with two degrees of freedom; rejected H0: r·cos(ϑ) and r·sin(ϑ) are simultaneously equal to zero.
↵*, **, *** Significance at the 90%, 95%, and 99% level of confidence, respectively.