Using geographically weighted regression to solve the areal interpolation problem

Figures & data

Figure 1. The remotely sensed land cover distribution for Hartford County.

Figure 2. Spatial distribution of population density at the block group level.

Figure 3. Spatial distribution of the GWR coefficient at the block group level in the 50 GWR2 BLKG model: (a) for residential land cover; (b) for rural residential land cover.

Table 1. Results of the block group interpolation

	RMS	Rank	Adj-RMS	Rank	MAE	Rank
Before scaling
OLS1	1310.54	13	38.711	13	1241	12
OLS2	679.02	9	14.742	5	490	10
OLS3	679.10	10	14.993	6	489	9
50 GWR1 TRCT	1197.67	12	37.723	11	1072	11
50 GWR1 BLKG	1195.58	11	38.588	12	1282	13
160 GWR1 TRCT	1395.24	14	40.358	14	1328	14
160 GWR1 BLKG	1395.14	15	40.796	15	1328	15
50 GWR2 TRCT	616.42	2	6.554	1	356	3
50 GWR2 BLKG	614.53	1	7.751	2	356	4
160 GWR2 TRCT	656.83	6	11.784	3	352	1
160 GWR2 BLKG	656.81	5	11.977	4	352	2
50 GWR3 TRCT	621.42	4	21.090	10	445	6
50 GWR3 BLKG	620.08	3	20.259	9	443	5
160 GWR3 TRCT	663.47	7	16.683	8	474	7
160 GWR3 BLKG	663.59	8	16.664	7	474	8
After scaling
Areal weighting	562.22	17	23.666	17	407	13
Dasymetric	343.20	4	14.015	11	237	1
OLS1	335.01	1	15.390	16	249	2
OLS2	515.90	12	13.826	8	354	12
OLS3	514.95	14	14.000	10	353	9
50 GWR1 TRCT	366.26	5	12.720	6	268	5
50 GWR1 BLKG	367.24	6	12.180	5	271	6
160 GWR1 TRCT	339.61	2	14.945	14	251	3
160 GWR1 BLKG	339.81	3	15.022	15	251	4
50 GWR2 TRCT	516.40	16	5.965	1	438	15
50 GWR2 BLKG	515.36	15	6.428	2	436	14
160 GWR2 TRCT	512.84	7	10.963	3	471	16
160 GWR2 BLKG	513.26	8	10.982	4	471	17
50 GWR3 TRCT	514.60	10	14.019	12	353	7
50 GWR3 BLKG	514.57	9	12.955	7	354	10
160 GWR3 TRCT	514.64	11	14.020	13	353	8
160 GWR3 BLKG	514.98	13	13.904	9	354	11
Note: RMS, root mean square; MAE, mean absolute error.

Figure 4. Spatial distribution of error by block group for the 50 GWR2 BLKG model (a) before scaling, (b) after scaling.

Figure 5. Spatial distribution of error by block group for the OLS1 model (a) before scaling, (b) after scaling.

Table 2. Results of pseudo-tract interpolation

	RMS	Rank	Adj-RMS	Rank	MAE	Rank
Before scaling
OLS1	2530.80	13	0.740	13	2281	13
OLS2	1774.31	9	0.352	9	1225	9
OLS3	1777.05	10	0.353	10	1226	10
50 GWR1 TRCT	2248.56	12	0.658	12	1939	12
50 GWR1 PTRC	2229.40	11	0.657	11	1926	11
160 GWR1 TRCT	2678.01	15	0.784	15	2450	15
160 GWR1 PTRC	2674.72	14	0.783	14	2448	14
50 GWR2 TRCT	1445.73	3	0.295	3	984	3
50 GWR2 PTRC	1436.43	2	0.294	2	975	1
160 GWR2 TRCT	1642.93	6	0.325	6	1107	6
160 GWR2 PTRC	1641.56	5	0.325	5	1105	5
50 GWR3 TRCT	1445.96	4	0.296	4	991	4
50 GWR3 PTRC	1434.79	1	0.294	1	982	2
160 GWR3 TRCT	1685.50	8	0.335	8	1131	8
160 GWR3 PTRC	1684.50	7	0.334	7	1130	7
After scaling
Areal weighting	951.94	17	0.247	17	703	17
Dasymetric	485.56	5	0.131	5	380	7
OLS1	661.38	12	0.167	12	521	12
OLS2	484.89	3	0.131	3	380	5
OLS3	485.56	6	0.131	6	380	8
50 GWR1 TRCT	709.86	15	0.174	15	543	15
50 GWR1 PTRC	723.42	16	0.180	16	554	16
160 GWR1 TRCT	675.39	14	0.170	14	530	14
160 GWR1 PTRC	675.00	13	0.170	13	528	13
50 GWR2 TRCT	487.11	9	0.132	9	376	3
50 GWR2 PTRC	485.62	8	0.132	8	379	4
160 GWR2 TRCT	476.52	1	0.129	1	373	1
160 GWR2 PTRC	478.17	2	0.130	2	374	2
50 GWR3 TRCT	485.61	7	0.131	7	381	9
50 GWR3 PTRC	487.57	10	0.132	10	385	11
160 GWR3 TRCT	485.52	4	0.131	4	380	6
160 GWR3 PTRC	489.07	11	0.132	11	382	10
Note: RMS, root mean square; MAE, mean absolute error.

Figure 6. Spatial distribution of error by pseudo-tract for the 50 GWR3 PTRC model (a) before scaling, (b) after scaling.

Figure 7. Spatial distribution of error by pseudo-tract for the 160 GWR2 PTRC model (a) before scaling, (b) after scaling.