pacman::p_load(
olsrr,
ggstatsplot,
corrplot,
ggpubr,
sfdep,
sf,
spdep,
GWmodel,
tmap,
tidyverse,
performance,
see
)In Class exercise 11
Analysis
R
sf
tidyverse
cluster
ClustGeo
NbClust
GGally
Note
Explanatory vs Predictive modeling
Explanatory model => aims to identify factors/independent variable that are causally related to an outcome.
- Hedonic Pricing Model using GWmodel
Predictive model => aims to find the combination of factors that best predicts the dependent variable.
- Calibrating Random Forest Model
R-square VS Adj R-Square => Adj R-Square account for the number of predictors in the model, providing a more accurate measure of fit.
Regression Diagnostics
Multicollinearity
VIF
Below than 5: lower multicollinearity
More than 5 and Below 10: Moderate multicolinearity
More than 10: Strong multicolinearity
Make use of the correlation matrix to determine the pairs and drop one of them if their VIF is high.
Linearity Assumption
- The relationship between X and the mean of Y is linear or not.
Normality Assumption
- Check if the residual is normally distributed
Spatial Autocorrelation
- Use Moran’s I test to check the residual spatial autocorrelation
Loading the R packages
Importing the Data
mpsz = st_read(dsn = "data/MasterPlan2014SubzoneBoundaryWebSHP", layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`C:\Users\blzll\OneDrive\Desktop\Y3S1\IS415\Quarto\IS415\In-class_Ex\data\MasterPlan2014SubzoneBoundaryWebSHP'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21mpsz_svy21 <- st_transform(mpsz, 3414)
condo_resale = read_csv("data/In-class_Ex11/aspatial/Condo_resale_2015.csv")
condo_resale_sf <- st_as_sf(condo_resale,
coords = c("LONGITUDE", "LATITUDE"),
crs=4326) %>%
st_transform(crs=3414)Correlation Analysis - ggstatsplot methods
ggcorrmat(condo_resale[,5:23])
Building a Hedonic Pricing Model by using Multiple Linear Regression Method
condo_mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf)
summary(condo_mlr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET +
PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale_sf)
Residuals:
Min 1Q Median 3Q Max
-3475964 -293923 -23069 241043 12260381
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 481728.40 121441.01 3.967 7.65e-05 ***
AREA_SQM 12708.32 369.59 34.385 < 2e-16 ***
AGE -24440.82 2763.16 -8.845 < 2e-16 ***
PROX_CBD -78669.78 6768.97 -11.622 < 2e-16 ***
PROX_CHILDCARE -351617.91 109467.25 -3.212 0.00135 **
PROX_ELDERLYCARE 171029.42 42110.51 4.061 5.14e-05 ***
PROX_URA_GROWTH_AREA 38474.53 12523.57 3.072 0.00217 **
PROX_HAWKER_MARKET 23746.10 29299.76 0.810 0.41782
PROX_KINDERGARTEN 147468.99 82668.87 1.784 0.07466 .
PROX_MRT -314599.68 57947.44 -5.429 6.66e-08 ***
PROX_PARK 563280.50 66551.68 8.464 < 2e-16 ***
PROX_PRIMARY_SCH 180186.08 65237.95 2.762 0.00582 **
PROX_TOP_PRIMARY_SCH 2280.04 20410.43 0.112 0.91107
PROX_SHOPPING_MALL -206604.06 42840.60 -4.823 1.57e-06 ***
PROX_SUPERMARKET -44991.80 77082.64 -0.584 0.55953
PROX_BUS_STOP 683121.35 138353.28 4.938 8.85e-07 ***
NO_Of_UNITS -231.18 89.03 -2.597 0.00951 **
FAMILY_FRIENDLY 140340.77 47020.55 2.985 0.00289 **
FREEHOLD 359913.01 49220.22 7.312 4.38e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 755800 on 1417 degrees of freedom
Multiple R-squared: 0.6518, Adjusted R-squared: 0.6474
F-statistic: 147.4 on 18 and 1417 DF, p-value: < 2.2e-16Generating Tidy Linear Regression Report
ols_regress(condo_mlr) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 750799.558
R-Squared 0.652 MSE 571258408962.149
Adj. R-Squared 0.647 Coef. Var 43.160
Pred R-Squared 0.637 AIC 42970.175
MAE 413425.809 SBC 43075.567
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.515174e+15 18 8.417631e+13 147.352 0.0000
Residual 8.094732e+14 1417 571258408962.149
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 481728.405 121441.014 3.967 0.000 243504.909 719951.900
AREA_SQM 12708.324 369.590 0.580 34.385 0.000 11983.322 13433.326
AGE -24440.816 2763.164 -0.165 -8.845 0.000 -29861.148 -19020.484
PROX_CBD -78669.779 6768.972 -0.268 -11.622 0.000 -91948.061 -65391.496
PROX_CHILDCARE -351617.910 109467.252 -0.092 -3.212 0.001 -566353.201 -136882.619
PROX_ELDERLYCARE 171029.418 42110.506 0.083 4.061 0.000 88423.783 253635.053
PROX_URA_GROWTH_AREA 38474.534 12523.567 0.059 3.072 0.002 13907.809 63041.258
PROX_HAWKER_MARKET 23746.098 29299.755 0.019 0.810 0.418 -33729.461 81221.657
PROX_KINDERGARTEN 147468.986 82668.868 0.031 1.784 0.075 -14697.534 309635.506
PROX_MRT -314599.679 57947.441 -0.120 -5.429 0.000 -428271.672 -200927.687
PROX_PARK 563280.499 66551.675 0.148 8.464 0.000 432730.102 693830.897
PROX_PRIMARY_SCH 180186.083 65237.948 0.070 2.762 0.006 52212.744 308159.421
PROX_TOP_PRIMARY_SCH 2280.036 20410.435 0.002 0.112 0.911 -37757.880 42317.951
PROX_SHOPPING_MALL -206604.057 42840.595 -0.108 -4.823 0.000 -290641.863 -122566.252
PROX_SUPERMARKET -44991.803 77082.635 -0.012 -0.584 0.560 -196200.149 106216.542
PROX_BUS_STOP 683121.347 138353.278 0.134 4.938 0.000 411722.087 954520.608
NO_Of_UNITS -231.180 89.033 -0.050 -2.597 0.010 -405.830 -56.530
FAMILY_FRIENDLY 140340.770 47020.551 0.055 2.985 0.003 48103.399 232578.141
FREEHOLD 359913.008 49220.224 0.140 7.312 0.000 263360.671 456465.345
-----------------------------------------------------------------------------------------------------------------Variable Selection
Forward
condo_fw_mlr <- ols_step_forward_p(
condo_mlr,
p_val = 0.05,
details = FALSE
)
condo_fw_mlr
Stepwise Summary
-----------------------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------------------------
0 Base Model 44449.068 44459.608 40371.745 0.00000 0.00000
1 AREA_SQM 43587.753 43603.562 39510.883 0.45184 0.45146
2 PROX_CBD 43243.523 43264.602 39167.182 0.56928 0.56868
3 PROX_PARK 43177.691 43204.039 39101.331 0.58915 0.58829
4 FREEHOLD 43125.474 43157.092 39049.179 0.60438 0.60327
5 AGE 43069.222 43106.109 38993.167 0.62010 0.61878
6 PROX_ELDERLYCARE 43046.515 43088.672 38970.548 0.62659 0.62502
7 PROX_SHOPPING_MALL 43020.990 43068.417 38945.209 0.63367 0.63188
8 PROX_URA_GROWTH_AREA 43009.092 43061.788 38933.407 0.63720 0.63517
9 PROX_MRT 42999.058 43057.024 38923.483 0.64023 0.63796
10 PROX_BUS_STOP 42984.951 43048.186 38909.581 0.64424 0.64175
11 FAMILY_FRIENDLY 42981.085 43049.590 38905.797 0.64569 0.64296
12 NO_Of_UNITS 42975.246 43049.021 38900.092 0.64762 0.64465
13 PROX_CHILDCARE 42971.858 43050.902 38896.812 0.64894 0.64573
14 PROX_PRIMARY_SCH 42966.758 43051.072 38891.872 0.65067 0.64723
-----------------------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751998.679
R-Squared 0.651 MSE 571471422208.591
Adj. R-Squared 0.647 Coef. Var 43.168
Pred R-Squared 0.638 AIC 42966.758
MAE 414819.628 SBC 43051.072
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000
Residual 8.120609e+14 1421 571471422208.591
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200
AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382
PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176
PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677
FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821
AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740
PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510
PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288
PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936
PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980
PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082
FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560
NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961
PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613
PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424
-----------------------------------------------------------------------------------------------------------------plot(condo_fw_mlr)
Backward
condo_bw_mlr <- ols_step_backward_p(
condo_mlr,
p_val = 0.05,
details = FALSE
)
condo_bw_mlr
Stepwise Summary
-----------------------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
-----------------------------------------------------------------------------------------
0 Full Model 42970.175 43075.567 38895.493 0.65179 0.64736
1 PROX_TOP_PRIMARY_SCH 42968.188 43068.310 38893.478 0.65178 0.64761
2 PROX_SUPERMARKET 42966.534 43061.387 38891.789 0.65170 0.64777
3 PROX_HAWKER_MARKET 42965.558 43055.141 38890.764 0.65145 0.64777
4 PROX_KINDERGARTEN 42966.758 43051.072 38891.872 0.65067 0.64723
-----------------------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751998.679
R-Squared 0.651 MSE 571471422208.591
Adj. R-Squared 0.647 Coef. Var 43.168
Pred R-Squared 0.638 AIC 42966.758
MAE 414819.628 SBC 43051.072
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000
Residual 8.120609e+14 1421 571471422208.591
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200
AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382
AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740
PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176
PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613
PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510
PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936
PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980
PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677
PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424
PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288
PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082
NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961
FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560
FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821
-----------------------------------------------------------------------------------------------------------------plot(condo_bw_mlr)
Bi-direction
condo_bi_mlr <- ols_step_both_p(
condo_mlr,
p_val = 0.05,
details = FALSE
)
condo_bi_mlr
Stepwise Summary
---------------------------------------------------------------------------------------------
Step Variable AIC SBC SBIC R2 Adj. R2
---------------------------------------------------------------------------------------------
0 Base Model 44449.068 44459.608 40371.745 0.00000 0.00000
1 AREA_SQM (+) 43587.753 43603.562 39510.883 0.45184 0.45146
2 PROX_CBD (+) 43243.523 43264.602 39167.182 0.56928 0.56868
3 PROX_PARK (+) 43177.691 43204.039 39101.331 0.58915 0.58829
4 FREEHOLD (+) 43125.474 43157.092 39049.179 0.60438 0.60327
5 AGE (+) 43069.222 43106.109 38993.167 0.62010 0.61878
6 PROX_ELDERLYCARE (+) 43046.515 43088.672 38970.548 0.62659 0.62502
7 PROX_SHOPPING_MALL (+) 43020.990 43068.417 38945.209 0.63367 0.63188
8 PROX_URA_GROWTH_AREA (+) 43009.092 43061.788 38933.407 0.63720 0.63517
9 PROX_MRT (+) 42999.058 43057.024 38923.483 0.64023 0.63796
10 PROX_BUS_STOP (+) 42984.951 43048.186 38909.581 0.64424 0.64175
11 FAMILY_FRIENDLY (+) 42981.085 43049.590 38905.797 0.64569 0.64296
12 NO_Of_UNITS (+) 42975.246 43049.021 38900.092 0.64762 0.64465
13 PROX_CHILDCARE (+) 42971.858 43050.902 38896.812 0.64894 0.64573
14 PROX_PRIMARY_SCH (+) 42966.758 43051.072 38891.872 0.65067 0.64723
15 PROX_KINDERGARTEN (+) 42965.558 43055.141 38890.764 0.65145 0.64777
---------------------------------------------------------------------------------------------
Final Model Output
------------------
Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751161.087
R-Squared 0.651 MSE 570600646491.086
Adj. R-Squared 0.648 Coef. Var 43.135
Pred R-Squared 0.638 AIC 42965.558
MAE 413583.799 SBC 43055.141
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.514394e+15 15 1.009596e+14 176.936 0.0000
Residual 8.102529e+14 1420 570600646491.086
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 459826.675 114616.014 4.012 0.000 234991.777 684661.574
AREA_SQM 12720.174 368.610 0.581 34.509 0.000 11997.096 13443.252
PROX_CBD -75676.065 5816.474 -0.258 -13.011 0.000 -87085.870 -64266.259
PROX_PARK 575749.528 65523.382 0.151 8.787 0.000 447216.504 704282.552
FREEHOLD 360203.286 48768.851 0.140 7.386 0.000 264536.552 455870.021
AGE -24697.719 2752.751 -0.167 -8.972 0.000 -30097.615 -19297.824
PROX_ELDERLYCARE 182435.081 39910.469 0.088 4.571 0.000 104145.268 260724.893
PROX_SHOPPING_MALL -224513.955 36588.872 -0.117 -6.136 0.000 -296288.004 -152739.906
PROX_URA_GROWTH_AREA 40145.474 11758.824 0.062 3.414 0.001 17078.942 63212.007
PROX_MRT -311753.202 57670.032 -0.119 -5.406 0.000 -424880.814 -198625.590
PROX_BUS_STOP 711858.014 135420.040 0.140 5.257 0.000 446213.188 977502.840
FAMILY_FRIENDLY 144034.218 46874.683 0.057 3.073 0.002 52083.153 235985.283
NO_Of_UNITS -236.270 88.032 -0.051 -2.684 0.007 -408.956 -63.583
PROX_CHILDCARE -336118.857 108331.761 -0.088 -3.103 0.002 -548626.339 -123611.374
PROX_PRIMARY_SCH 162183.897 60202.895 0.063 2.694 0.007 44087.730 280280.063
PROX_KINDERGARTEN 141915.768 79726.155 0.029 1.780 0.075 -14477.927 298309.464
-----------------------------------------------------------------------------------------------------------------plot(condo_bi_mlr)
Model Selection
compare_performance() of performance package is used to compare the performance of the models.
metric <- compare_performance(condo_mlr,
condo_fw_mlr$model,
condo_bw_mlr$model,
condo_bi_mlr$model)gsub() is used to tidy the test value in Name field.
metric$Name <- gsub(".*\\\\([a-zA-Z0-9_]+)\\\\, \\\\model\\\\.*", "\\1", metric$Name)plot(metric)
Visualising Model Parameters
ggcoefstats(condo_bi_mlr$model, sort = "ascending")
Regression Diagnostics
Checking for multicollinearity
check_collinearity(condo_bi_mlr$model)# Check for Multicollinearity
Low Correlation
Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
AREA_SQM 1.15 [1.10, 1.24] 1.07 0.87 [0.81, 0.91]
PROX_CBD 1.60 [1.50, 1.73] 1.27 0.62 [0.58, 0.67]
PROX_PARK 1.21 [1.15, 1.30] 1.10 0.83 [0.77, 0.87]
FREEHOLD 1.46 [1.37, 1.57] 1.21 0.68 [0.64, 0.73]
AGE 1.41 [1.33, 1.52] 1.19 0.71 [0.66, 0.75]
PROX_ELDERLYCARE 1.52 [1.42, 1.63] 1.23 0.66 [0.61, 0.70]
PROX_SHOPPING_MALL 1.49 [1.40, 1.60] 1.22 0.67 [0.62, 0.72]
PROX_URA_GROWTH_AREA 1.33 [1.26, 1.43] 1.16 0.75 [0.70, 0.79]
PROX_MRT 1.96 [1.83, 2.13] 1.40 0.51 [0.47, 0.55]
PROX_BUS_STOP 2.89 [2.66, 3.15] 1.70 0.35 [0.32, 0.38]
FAMILY_FRIENDLY 1.38 [1.30, 1.48] 1.18 0.72 [0.67, 0.77]
NO_Of_UNITS 1.45 [1.37, 1.56] 1.21 0.69 [0.64, 0.73]
PROX_CHILDCARE 3.29 [3.02, 3.59] 1.81 0.30 [0.28, 0.33]
PROX_PRIMARY_SCH 2.21 [2.05, 2.40] 1.49 0.45 [0.42, 0.49]
PROX_KINDERGARTEN 1.11 [1.06, 1.20] 1.05 0.90 [0.84, 0.94]plot(check_collinearity(condo_bi_mlr$model)) +
# theme is used to make the display the column name more friendly
theme(axis.text.x = element_text (
angle = 45, hjust = 1
))
Linearity Assumption test
out <- plot(check_model(condo_bi_mlr$model,
panel = FALSE))
out[[2]] # have 6 plot
Normality Assumption Test
plot(check_normality(condo_bi_mlr$model))
Checking of Outliers
Method => Can be "all" or some of "cook", "pareto", "zscore", "zscore_robust", "iqr", "ci", "eti", "hdi", "bci", "mahalanobis", "mahalanobis_robust", "mcd", "ics", "optics" or "lof".
outliers <- check_outliers(condo_bi_mlr$model,
method = "cook")
outliersOK: No outliers detected.
- Based on the following method and threshold: cook (1).
- For variable: (Whole model)plot(check_outliers(condo_bi_mlr$model,
method = "pareto"))
Visualising spatial non-stationary
First, we will export the residual of the hedonic pricing model and save it as a data frame.
mlr_output <- as.data.frame(condo_fw_mlr$model$residuals) %>%
rename(`FW_MLR_RES` = `condo_fw_mlr$model$residuals`)Next, we will join the newly created data frame with condo_resale_sf object.
condo_resale_sf <- cbind(condo_resale_sf,
mlr_output$FW_MLR_RES) %>%
rename(`MLR_RES` = `mlr_output.FW_MLR_RES`)tmap_mode("plot")
tm_shape(mpsz)+
tmap_options(check.and.fix = TRUE) +
tm_polygons(alpha = 0.4) +
tm_shape(condo_resale_sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile") 
tmap_mode("plot")Spatial Stationary Test
First, we will compute the distance-based weight matrix by using dnearneigh() function of spdep.
condo_resale_sf <- condo_resale_sf %>%
mutate(nb = st_knn(geometry, k=6,
longlat = FALSE),
wt = st_weights(nb,
style = "W"),
.before = 1)Next, global_moran_perm() of sfdep is used to perform global Moran permutation test.
global_moran_perm(condo_resale_sf$MLR_RES,
condo_resale_sf$nb,
condo_resale_sf$wt,
alternative = "two.sided",
nsim = 99)
Monte-Carlo simulation of Moran I
data: x
weights: listw
number of simulations + 1: 100
statistic = 0.32254, observed rank = 100, p-value < 2.2e-16
alternative hypothesis: two.sided