Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up through 2018 Q1. The test period is a forecast for 2018 Q2 and includes comparison to the observed median rent estimates for data collected in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-07-31




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 291.6833 211.3911 209.5947 199.5333 209.1796
Training 313.7865 157.2392 157.6580 159.6021 115.5344



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 233.4635 149.9597 146.3652 140.7309 146.1343
Training 248.2925 113.4145 114.5124 116.3895 85.1286



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -260.144 -784.3604 -782.4603 -786.1483 -863.8185



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -259.6945 -754.3957 -752.9819 -757.8366 -839.8244

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 82.5727 5.6207 71.9463 82.4295 94.0710 82.2077
Precision for idtract 35.4127 5.0834 26.3831 35.0857 46.3626 34.4733
Precision for idqtr 14346.4716 20566.3012 1825.4842 8322.2495 64752.6397 4029.5564
Rho for idqtr 0.1936 0.4574 -0.7067 0.2341 0.9034 0.5935
Precision for idqtr1 14806.5557 13712.7443 1295.5432 10900.8209 52125.0922 3746.6649



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 82.0304 5.6064 71.4041 81.9004 93.4630 81.7216
Precision for idtract (iid component) 105.8964 26.6367 63.0859 102.7013 167.1935 96.6357
Precision for idtract (spatial component) 107.9466 34.7431 55.9446 102.5742 190.7109 92.6978
Precision for idqtr 13236.7999 17861.9989 1882.7162 7954.0833 57682.0908 4019.5064
Rho for idqtr 0.1939 0.4522 -0.6975 0.2334 0.8987 0.5669
Precision for idqtr1 13875.1194 12545.0376 1278.0759 10350.1208 48305.3611 3766.5558



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 110.1049 16.6639 77.3283 110.5023 142.1666 112.9045
Precision for idtract (iid component) 110.0769 28.5853 63.9770 106.7319 175.6843 100.3995
Precision for idtract (spatial component) 106.3903 34.1960 55.3653 101.0139 187.9655 91.1630
Precision for idqtr 10594.2446 8659.6995 2490.6160 8114.5192 34261.0821 5328.2696
Rho for idqtr 0.1895 0.4803 -0.7497 0.2379 0.9174 0.6913
Precision for idqtr1 13437.2127 9091.5232 2546.1776 11293.0513 38967.0116 7179.0518
Precision for idtractqtr 316.5158 135.5469 156.1860 282.3407 670.7305 227.1030

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)