--- title: "Compare Size Effect of Spatial Units(SESU)" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{sesu} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- **gdverse** provides the `sesu_opgd()` and `sesu_gozh()` function to support the selection of optimal spatial analysis scales which based on **OPGD** and **GOZH** respectively. Please refer to the help documentation of the corresponding function for more details. Here, we use [FVC raster data](https://github.com/SpatLyu/rdevdata/blob/main/FVC.tif) as an example to demonstrate the optimal spatial analysis scale selection function in **gdverse**. ## Processing data First, we construct FVC data under different spatial units using the original data. ``` r library(terra) library(tidyverse) library(gdverse) fvcpath = "https://github.com/SpatLyu/rdevdata/raw/main/FVC.tif" fvc = terra::rast(paste0("/vsicurl/",fvcpath)) fvc ## class : SpatRaster ## dimensions : 418, 568, 13 (nrow, ncol, nlyr) ## resolution : 1000, 1000 (x, y) ## extent : -92742.16, 475257.8, 3591385, 4009385 (xmin, xmax, ymin, ymax) ## coord. ref. : Asia_North_Albers_Equal_Area_Conic ## source : FVC.tif ## names : fvc, premax, premin, presum, tmpmax, tmpmin, ... ## min values : 0.1363270, 109.8619, 2.00000, 3783.904, 9.289694, -11.971293, ... ## max values : 0.9596695, 249.9284, 82.74928, 8549.112, 26.781870, 1.322163, ... ``` The original data resolution is `1000`m, and then we construct the data under `2000-10000` m spatial units with 1000 spatial unit interval. ``` r su = seq(1000,10000,by = 1000) fvc1000 = tibble::as_tibble(terra::as.data.frame(fvc,na.rm = T)) fvc_other = 2:10 %>% purrr::map(\(.x) terra::aggregate(fvc,fact=.x ,fun="mean") %>% terra::as.data.frame(na.rm = T) %>% tibble::as_tibble()) fvc = c(list(fvc1000),fvc_other) str(fvc) ## List of 10 ## $ : tibble [136,243 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:136243] 0.198 0.193 0.192 0.189 0.208 ... ## ..$ premax: num [1:136243] 163 161 160 159 164 ... ## ..$ premin: num [1:136243] 7.95 6.8 5.24 5 9.98 ... ## ..$ presum: num [1:136243] 3956 3892 3842 3808 4051 ... ## ..$ tmpmax: num [1:136243] 20.8 20.7 20.9 21.1 20.6 ... ## ..$ tmpmin: num [1:136243] -7.53 -7.55 -7.48 -7.39 -7.59 ... ## ..$ tmpavg: num [1:136243] 8.05 8.02 8.15 8.35 7.97 ... ## ..$ pop : num [1:136243] 1.903 1.203 0.547 0.542 10.392 ... ## ..$ ntl : num [1:136243] 6.6 4.91 3.75 3.99 7.1 ... ## ..$ lulc : num [1:136243] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:136243] 1758 1754 1722 1672 1780 ... ## ..$ slope : num [1:136243] 2.65 3.45 3.96 2.9 1.94 ... ## ..$ aspect: num [1:136243] 176.4 169.6 138.5 110.9 99.5 ... ## $ : tibble [33,722 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:33722] 0.195 0.184 0.157 0.204 0.208 ... ## ..$ premax: num [1:33722] 162 159 167 165 165 ... ## ..$ premin: num [1:33722] 7.37 5.14 4.21 10.98 9.8 ... ## ..$ presum: num [1:33722] 3935 3799 3975 4134 4089 ... ## ..$ tmpmax: num [1:33722] 20.9 21.3 21.1 20.4 20.9 ... ## ..$ tmpmin: num [1:33722] -7.39 -7.21 -7.3 -7.62 -7.33 ... ## ..$ tmpavg: num [1:33722] 8.17 8.5 8.49 7.78 8.2 ... ## ..$ pop : num [1:33722] 18.69 0.91 8.94 10.31 6.46 ... ## ..$ ntl : num [1:33722] 6.15 4.32 2.14 4.64 6.79 ... ## ..$ lulc : num [1:33722] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:33722] 1720 1638 1662 1835 1717 ... ## ..$ slope : num [1:33722] 3.89 2.63 3.06 3.37 3.93 ... ## ..$ aspect: num [1:33722] 114 158 136 102 120 ... ## $ : tibble [14,840 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:14840] 0.205 0.197 0.175 0.163 0.21 ... ## ..$ premax: num [1:14840] 165 161 160 162 165 ... ## ..$ premin: num [1:14840] 10.35 6.02 4.97 4.48 11.04 ... ## ..$ presum: num [1:14840] 4098 3908 3848 3910 4131 ... ## ..$ tmpmax: num [1:14840] 20.7 21.2 21.5 21.3 20.4 ... ## ..$ tmpmin: num [1:14840] -7.46 -7.19 -7.07 -7.24 -7.52 ... ## ..$ tmpavg: num [1:14840] 8.04 8.44 8.67 8.52 7.84 ... ## ..$ pop : num [1:14840] 12.33 13.78 4.59 6.52 2.97 ... ## ..$ ntl : num [1:14840] 6.37 7.79 7.23 9.96 4.59 ... ## ..$ lulc : num [1:14840] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:14840] 1762 1654 1600 1649 1805 ... ## ..$ slope : num [1:14840] 3.41 3.19 2.61 3.06 3.76 ... ## ..$ aspect: num [1:14840] 126 130 179 201 146 ... ## $ : tibble [8,268 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:8268] 0.2 0.174 0.175 0.182 0.193 ... ## ..$ premax: num [1:8268] 164 161 165 171 164 ... ## ..$ premin: num [1:8268] 7.57 5.37 6.07 5.78 9.32 ... ## ..$ presum: num [1:8268] 4022 3896 4026 4177 4072 ... ## ..$ tmpmax: num [1:8268] 21 21.6 21.3 20.8 21 ... ## ..$ tmpmin: num [1:8268] -7.22 -6.96 -7.15 -7.46 -7.15 ... ## ..$ tmpavg: num [1:8268] 8.36 8.81 8.57 8.19 8.35 ... ## ..$ pop : num [1:8268] 5.82 15.87 20.4 8.66 1.55 ... ## ..$ ntl : num [1:8268] 8.33 8.39 13.18 2.69 11 ... ## ..$ lulc : num [1:8268] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:8268] 1684 1567 1642 1690 1693 ... ## ..$ slope : num [1:8268] 3.43 2.13 3.48 3.22 3.56 ... ## ..$ aspect: num [1:8268] 115 159 224 207 133 ... ## $ : tibble [5,240 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:5240] 0.188 0.162 0.168 0.186 0.189 ... ## ..$ premax: num [1:5240] 163 162 168 174 164 ... ## ..$ premin: num [1:5240] 6.86 5.23 4.15 5.99 7.86 ... ## ..$ presum: num [1:5240] 3992 3922 4040 4254 4047 ... ## ..$ tmpmax: num [1:5240] 21.2 21.7 21.2 20.8 21.2 ... ## ..$ tmpmin: num [1:5240] -7.09 -6.9 -7.22 -7.42 -7 ... ## ..$ tmpavg: num [1:5240] 8.54 8.92 8.53 8.21 8.58 ... ## ..$ pop : num [1:5240] 5.64 23.14 9.73 6.84 2.36 ... ## ..$ ntl : num [1:5240] 9.1 10.45 5.58 2.89 12.3 ... ## ..$ lulc : num [1:5240] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:5240] 1645 1539 1611 1677 1643 ... ## ..$ slope : num [1:5240] 2.96 1.86 3.19 3.32 2.79 ... ## ..$ aspect: num [1:5240] 122 174 192 213 132 ... ## $ : tibble [3,607 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:3607] 0.196 0.169 0.165 0.174 0.188 ... ## ..$ premax: num [1:3607] 165 161 165 168 175 ... ## ..$ premin: num [1:3607] 9.19 5.07 5.89 4.14 5.51 ... ## ..$ presum: num [1:3607] 4081 3885 4035 4064 4281 ... ## ..$ tmpmax: num [1:3607] 20.9 21.7 21.6 21.3 20.7 ... ## ..$ tmpmin: num [1:3607] -7.2 -6.91 -6.99 -7.17 -7.39 ... ## ..$ tmpavg: num [1:3607] 8.3 8.86 8.79 8.63 8.23 ... ## ..$ pop : num [1:3607] 2.69 11.89 27.15 12.59 4.31 ... ## ..$ ntl : num [1:3607] 8.82 9.36 12.72 6.77 2.09 ... ## ..$ lulc : num [1:3607] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:3607] 1705 1557 1577 1585 1680 ... ## ..$ slope : num [1:3607] 3.37 1.92 2.69 2.89 3.33 ... ## ..$ aspect: num [1:3607] 141 130 200 201 218 ... ## $ : tibble [2,634 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:2634] 0.172 0.159 0.177 0.179 0.208 ... ## ..$ premax: num [1:2634] 161 163 166 170 165 ... ## ..$ premin: num [1:2634] 5.53 4.98 4.19 4.17 8.3 ... ## ..$ presum: num [1:2634] 3924 3969 4003 4115 4133 ... ## ..$ tmpmax: num [1:2634] 21.6 21.8 21.2 21.3 21.1 ... ## ..$ tmpmin: num [1:2634] -6.91 -6.9 -7.15 -7.17 -7.06 ... ## ..$ tmpavg: num [1:2634] 8.84 8.96 8.52 8.64 8.46 ... ## ..$ pop : num [1:2634] 4.79 23.35 33.75 6.38 8.72 ... ## ..$ ntl : num [1:2634] 9.65 11.31 11.85 7.32 5.76 ... ## ..$ lulc : num [1:2634] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:2634] 1568 1528 1632 1585 1670 ... ## ..$ slope : num [1:2634] 1.92 2.08 3.24 2.86 2.62 ... ## ..$ aspect: num [1:2634] 129 181 169 222 164 ... ## $ : tibble [2,002 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:2002] 0.169 0.162 0.176 0.184 0.203 ... ## ..$ premax: num [1:2002] 162 163 167 172 165 ... ## ..$ premin: num [1:2002] 5.12 4.14 3.82 4.05 8.5 ... ## ..$ presum: num [1:2002] 3957 3949 4022 4170 4145 ... ## ..$ tmpmax: num [1:2002] 21.6 21.7 21.4 21.2 20.9 ... ## ..$ tmpmin: num [1:2002] -6.92 -6.9 -7.08 -7.21 -7.09 ... ## ..$ tmpavg: num [1:2002] 8.86 8.96 8.68 8.57 8.32 ... ## ..$ pop : num [1:2002] 5.81 15.22 26.95 6.31 11.41 ... ## ..$ ntl : num [1:2002] 9.42 11.06 12.13 6.12 3.6 ... ## ..$ lulc : num [1:2002] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:2002] 1560 1524 1584 1605 1708 ... ## ..$ slope : num [1:2002] 2.16 2.37 2.9 3.02 2.77 ... ## ..$ aspect: num [1:2002] 129 194 172 211 161 ... ## $ : tibble [1,561 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:1561] 0.175 0.169 0.179 0.196 0.198 ... ## ..$ premax: num [1:1561] 163 163 168 164 166 ... ## ..$ premin: num [1:1561] 5.42 3.72 3.66 8.46 5.79 ... ## ..$ presum: num [1:1561] 4014 3950 4050 4134 4138 ... ## ..$ tmpmax: num [1:1561] 21.5 21.7 21.4 20.8 21.4 ... ## ..$ tmpmin: num [1:1561] -6.97 -6.91 -7.05 -7.08 -6.82 ... ## ..$ tmpavg: num [1:1561] 8.78 8.95 8.76 8.28 8.75 ... ## ..$ pop : num [1:1561] 4.5 17.55 15.72 12.63 7.42 ... ## ..$ ntl : num [1:1561] 8.93 10.71 10.93 2.97 3.35 ... ## ..$ lulc : num [1:1561] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:1561] 1581 1524 1563 1723 1599 ... ## ..$ slope : num [1:1561] 2.3 2.44 2.91 2.8 2.83 ... ## ..$ aspect: num [1:1561] 137 191 175 177 150 ... ## $ : tibble [1,253 × 13] (S3: tbl_df/tbl/data.frame) ## ..$ fvc : num [1:1253] 0.177 0.177 0.178 0.186 0.19 ... ## ..$ premax: num [1:1253] 164 164 169 160 162 ... ## ..$ premin: num [1:1253] 5.22 3.56 3.34 10.52 7.39 ... ## ..$ presum: num [1:1253] 4046 3990 4098 4058 4069 ... ## ..$ tmpmax: num [1:1253] 21.5 21.6 21.5 21.2 21 ... ## ..$ tmpmin: num [1:1253] -6.98 -6.96 -7.07 -6.86 -6.98 ... ## ..$ tmpavg: num [1:1253] 8.77 8.86 8.79 8.68 8.4 ... ## ..$ pop : num [1:1253] 6.1 18.38 8.83 9.96 8.91 ... ## ..$ ntl : num [1:1253] 7.901 11.324 9.294 0.611 2.963 ... ## ..$ lulc : num [1:1253] 10 10 10 10 10 10 10 10 10 10 ... ## ..$ elev : num [1:1253] 1581 1547 1552 1640 1692 ... ## ..$ slope : num [1:1253] 2.41 2.83 3.04 2.29 2.85 ... ## ..$ aspect: num [1:1253] 130 182 211 194 163 ... ``` ## Comparison of Size Effect of Spatial Units based on OPGD model ``` r discvar = names(select(fvc1000,-c(fvc,lulc))) g1 = sesu_opgd(fvc ~ ., data = fvc,su = su,discvar = discvar,cores = 6) g1 ## Size Effect Of Spatial Units Using OPGD Model ## *** Optimal Spatial Unit: 8000 ## Spatial Unit: 1000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.629224208 | 3.28e-10 | ## | lulc | 0.553328610 | 9.11e-10 | ## | premin | 0.418432585 | 9.07e-10 | ## | tmpmin | 0.388351007 | 2.38e-10 | ## | tmpmax | 0.202221646 | 3.41e-10 | ## | elev | 0.201323643 | 4.71e-10 | ## | slope | 0.191360672 | 4.72e-10 | ## | tmpavg | 0.180958844 | 9.66e-10 | ## | pop | 0.162710129 | 1.22e-10 | ## | premax | 0.123992358 | 2.18e-10 | ## | ntl | 0.015565222 | 5.63e-10 | ## | aspect | 0.006274855 | 3.51e-10 | ## ## Spatial Unit: 2000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.63312876 | 3.11e-10 | ## | lulc | 0.58349550 | 8.71e-10 | ## | premin | 0.42455258 | 9.24e-10 | ## | tmpmin | 0.39556928 | 4.95e-10 | ## | tmpmax | 0.21303636 | 8.76e-10 | ## | elev | 0.20843509 | 6.73e-10 | ## | slope | 0.20649212 | 7.76e-10 | ## | tmpavg | 0.19219842 | 6.67e-10 | ## | pop | 0.16400743 | 1.32e-10 | ## | premax | 0.12681440 | 5.15e-10 | ## | ntl | 0.01517344 | 4.57e-10 | ## | aspect | 0.00842302 | 3.92e-10 | ## ## Spatial Unit: 3000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.64197109 | 7.48e-10 | ## | lulc | 0.62197064 | 7.93e-10 | ## | premin | 0.42942177 | 7.84e-10 | ## | tmpmin | 0.40301113 | 6.18e-10 | ## | slope | 0.21920354 | 6.23e-10 | ## | tmpmax | 0.21913037 | 3.22e-10 | ## | elev | 0.21195601 | 4.86e-10 | ## | tmpavg | 0.19120663 | 2.22e-10 | ## | pop | 0.15680652 | 8.30e-11 | ## | premax | 0.13003298 | 6.23e-10 | ## | ntl | 0.01491232 | 7.09e-10 | ## | aspect | 0.01072380 | 8.94e-10 | ## ## Spatial Unit: 4000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | presum | 0.64524739 | 3.170000e-10 | ## | lulc | 0.64389956 | 8.290000e-10 | ## | premin | 0.43796195 | 9.050000e-10 | ## | tmpmin | 0.41204303 | 8.050000e-10 | ## | slope | 0.22229402 | 4.180000e-10 | ## | tmpmax | 0.22073865 | 6.470000e-10 | ## | elev | 0.21988510 | 2.480000e-10 | ## | tmpavg | 0.20763621 | 7.420000e-10 | ## | pop | 0.17634834 | 9.910000e-10 | ## | premax | 0.13166579 | 5.530000e-10 | ## | ntl | 0.01477475 | 7.090000e-09 | ## | aspect | 0.01154072 | 1.282143e-03 | ## ## Spatial Unit: 5000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.6597260 | 8.780000e-10 | ## | presum | 0.6541838 | 4.580000e-10 | ## | premin | 0.4373717 | 3.480000e-10 | ## | tmpmin | 0.4177628 | 6.000000e-10 | ## | tmpmax | 0.2343576 | 6.050000e-10 | ## | slope | 0.2267634 | 9.450000e-10 | ## | elev | 0.2240745 | 2.460000e-10 | ## | tmpavg | 0.2116508 | 2.750000e-10 | ## | pop | 0.1726795 | 9.350000e-10 | ## | premax | 0.1349719 | 5.030000e-10 | ## | ntl | 0.0154460 | 2.950835e-02 | ## | aspect | 0.0153570 | 4.128000e-09 | ## ## Spatial Unit: 6000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.67492096 | 8.910000e-10 | ## | presum | 0.65750566 | 4.290000e-10 | ## | premin | 0.44335801 | 2.580000e-10 | ## | tmpmin | 0.43163297 | 1.310000e-10 | ## | tmpmax | 0.24076863 | 6.710000e-10 | ## | elev | 0.23852761 | 3.110000e-10 | ## | slope | 0.22697985 | 4.060000e-10 | ## | tmpavg | 0.21342297 | 4.930000e-10 | ## | pop | 0.18423517 | 4.050000e-10 | ## | premax | 0.13713818 | 7.030000e-10 | ## | aspect | 0.02255081 | 3.779087e-06 | ## | ntl | 0.01603905 | 6.398028e-01 | ## ## Spatial Unit: 7000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.69056548 | 8.460000e-10 | ## | presum | 0.65598539 | 8.960000e-10 | ## | premin | 0.45514450 | 7.130000e-10 | ## | tmpmin | 0.42974033 | 3.750000e-10 | ## | tmpmax | 0.24005942 | 3.670000e-10 | ## | elev | 0.23804435 | 4.600000e-10 | ## | slope | 0.22945970 | 9.720000e-10 | ## | tmpavg | 0.21953445 | 6.520000e-10 | ## | pop | 0.20126959 | 4.320000e-10 | ## | premax | 0.13854986 | 3.910000e-10 | ## | aspect | 0.02290143 | 3.512711e-01 | ## | ntl | 0.01658040 | 8.042073e-01 | ## ## Spatial Unit: 8000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.69775844 | 9.850000e-10 | ## | presum | 0.65944760 | 7.100000e-10 | ## | premin | 0.45756622 | 2.730000e-10 | ## | tmpmin | 0.43917313 | 4.880000e-10 | ## | tmpmax | 0.25085786 | 4.230000e-10 | ## | elev | 0.25050941 | 8.020000e-10 | ## | tmpavg | 0.23209570 | 2.550000e-10 | ## | slope | 0.23133961 | 9.130000e-10 | ## | pop | 0.16938255 | 3.810000e-10 | ## | premax | 0.13691004 | 1.970000e-10 | ## | aspect | 0.02574063 | 3.704521e-01 | ## | ntl | 0.01944793 | 1.077426e-06 | ## ## Spatial Unit: 9000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.70417030 | 9.610000e-10 | ## | presum | 0.66087241 | 2.580000e-10 | ## | premin | 0.45670286 | 6.080000e-10 | ## | tmpmin | 0.44659384 | 1.440000e-10 | ## | elev | 0.26455177 | 1.130000e-10 | ## | tmpavg | 0.25275409 | 2.420000e-10 | ## | tmpmax | 0.22761570 | 6.210000e-10 | ## | slope | 0.22627611 | 8.230000e-10 | ## | pop | 0.19692348 | 7.170000e-10 | ## | premax | 0.14497262 | 5.900000e-10 | ## | aspect | 0.02846294 | 6.337773e-01 | ## | ntl | 0.01523619 | 2.710474e-04 | ## ## Spatial Unit: 10000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | lulc | 0.69927128 | 2.871432e-05 | ## | presum | 0.66343981 | 4.000000e-10 | ## | premin | 0.46911366 | 2.190000e-10 | ## | tmpmin | 0.44824499 | 2.090000e-10 | ## | elev | 0.25805475 | 8.600000e-11 | ## | tmpmax | 0.25711048 | 2.570000e-10 | ## | tmpavg | 0.23844293 | 2.680000e-10 | ## | slope | 0.22356559 | 9.870000e-10 | ## | pop | 0.21293610 | 9.630000e-10 | ## | premax | 0.13851805 | 1.160000e-10 | ## | aspect | 0.04068517 | 6.566287e-01 | ## | ntl | 0.02368926 | 9.871909e-01 | plot(g1) ``` ![](../man/figures/sesu/opgd-1.png) ## Comparison of Size Effect of Spatial Units based on GOZH model ``` r g2 = sesu_gozh(fvc ~ ., data = fvc, su = su, cores = 6, increase_rate = 0.005) g2 ## Size Effect Of Spatial Units Using GOZH Model ## *** Optimal Spatial Unit: 4000 ## Spatial Unit: 1000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.7866938 | 3.33e-10 | ## ## Spatial Unit: 2000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.7975525 | 4.96e-10 | ## ## Spatial Unit: 3000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8038107 | 9.51e-10 | ## ## Spatial Unit: 4000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8120727 | 7.54e-10 | ## ## Spatial Unit: 5000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8051771 | 7.15e-10 | ## ## Spatial Unit: 6000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8285607 | 6.23e-10 | ## ## Spatial Unit: 7000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8356357 | 7.91e-10 | ## ## Spatial Unit: 8000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8194033 | 3.28e-10 | ## ## Spatial Unit: 9000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8494805 | 3.79e-10 | ## ## Spatial Unit: 10000 ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | TotalVariable | 0.8182764 | 3.27e-10 | plot(g2) ``` ![](../man/figures/sesu/gozh1-1.png) You can also use the same strategy as `sesu_opgd()` (use the mean of the individual Q statistic for all explanatory variables) in `sesu_gozh()` by assign `strategy` to `1`. ``` r g3 = sesu_gozh(fvc ~ ., data = fvc, su = su, cores = 6, strategy = 1, increase_rate = 0.005) g3 ## Size Effect Of Spatial Units Using GOZH Model ## *** Optimal Spatial Unit: 10000 ## Spatial Unit: 1000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.61357308 | 2.33e-10 | ## | lulc | 0.54039924 | 7.28e-10 | ## | premin | 0.43005723 | 2.63e-10 | ## | tmpmin | 0.37878995 | 8.57e-10 | ## | elev | 0.19589469 | 8.32e-10 | ## | tmpavg | 0.19354399 | 6.54e-10 | ## | tmpmax | 0.18257181 | 4.90e-10 | ## | pop | 0.18188771 | 6.91e-10 | ## | slope | 0.18039771 | 3.92e-10 | ## | premax | 0.11278088 | 1.60e-10 | ## | ntl | 0.01298068 | 1.34e-10 | ## | aspect | 0.00000000 | NaN | ## ## Spatial Unit: 2000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.62301279 | 2.66e-10 | ## | lulc | 0.55803717 | 8.77e-10 | ## | premin | 0.43544867 | 7.00e-10 | ## | tmpmin | 0.38618203 | 2.45e-10 | ## | tmpmax | 0.21025124 | 2.07e-10 | ## | elev | 0.20314330 | 2.78e-10 | ## | tmpavg | 0.19914975 | 7.39e-10 | ## | slope | 0.19627348 | 7.61e-10 | ## | pop | 0.19602997 | 4.70e-10 | ## | premax | 0.12512115 | 8.76e-10 | ## | ntl | 0.01303962 | 1.61e-10 | ## | aspect | 0.00000000 | NaN | ## ## Spatial Unit: 3000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.62786163 | 2.02e-10 | ## | lulc | 0.57980350 | 4.66e-10 | ## | premin | 0.45295671 | 8.76e-10 | ## | tmpmin | 0.39398883 | 4.53e-10 | ## | tmpmax | 0.22337707 | 2.02e-10 | ## | slope | 0.21773086 | 8.99e-10 | ## | elev | 0.21072544 | 7.80e-10 | ## | tmpavg | 0.20840028 | 7.53e-10 | ## | pop | 0.20403869 | 8.29e-10 | ## | premax | 0.12036298 | 1.69e-10 | ## | ntl | 0.01254965 | 3.91e-10 | ## | aspect | 0.00000000 | NaN | ## ## Spatial Unit: 4000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:--------:| ## | presum | 0.63518731 | 5.71e-10 | ## | lulc | 0.60101282 | 6.31e-10 | ## | premin | 0.44863951 | 5.28e-10 | ## | tmpmin | 0.40118790 | 4.14e-10 | ## | tmpmax | 0.23847408 | 7.87e-10 | ## | pop | 0.22484285 | 5.80e-10 | ## | slope | 0.22361153 | 9.25e-10 | ## | elev | 0.21891887 | 2.58e-10 | ## | tmpavg | 0.21559889 | 3.61e-10 | ## | premax | 0.12272873 | 2.12e-10 | ## | ntl | 0.01215376 | 2.74e-10 | ## | aspect | 0.00000000 | NaN | ## ## Spatial Unit: 5000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:---------:| ## | presum | 0.63722230 | 9.500e-11 | ## | lulc | 0.61064956 | 4.800e-10 | ## | premin | 0.46576994 | 5.480e-10 | ## | tmpmin | 0.41116492 | 2.950e-10 | ## | tmpmax | 0.24778090 | 7.310e-10 | ## | slope | 0.22861668 | 6.050e-10 | ## | pop | 0.22376308 | 3.750e-10 | ## | elev | 0.22370908 | 4.670e-10 | ## | tmpavg | 0.21883019 | 6.540e-10 | ## | premax | 0.12586705 | 1.440e-10 | ## | ntl | 0.02364914 | 1.830e-10 | ## | aspect | 0.01412962 | 8.938e-09 | ## ## Spatial Unit: 6000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | presum | 0.64204895 | 1.520000e-10 | ## | lulc | 0.62821539 | 5.160000e-10 | ## | premin | 0.46963617 | 7.140000e-10 | ## | tmpmin | 0.42078259 | 1.760000e-10 | ## | tmpmax | 0.26097547 | 7.450000e-10 | ## | elev | 0.24349549 | 2.210000e-10 | ## | slope | 0.23674911 | 4.340000e-10 | ## | tmpavg | 0.22761345 | 6.460000e-10 | ## | pop | 0.21387327 | 6.550000e-10 | ## | premax | 0.13886190 | 4.090000e-10 | ## | aspect | 0.01965907 | 6.615700e-08 | ## | ntl | 0.01281291 | 1.785448e-06 | ## ## Spatial Unit: 7000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:-----------:| ## | presum | 0.65119059 | 4.91000e-10 | ## | lulc | 0.62992351 | 4.00000e-10 | ## | premin | 0.46746888 | 7.35000e-10 | ## | tmpmin | 0.42352245 | 1.48000e-10 | ## | tmpmax | 0.25489327 | 4.11000e-10 | ## | tmpavg | 0.24806555 | 5.10000e-10 | ## | pop | 0.23833151 | 3.69000e-10 | ## | slope | 0.22981037 | 4.83000e-10 | ## | elev | 0.22955762 | 2.97000e-10 | ## | premax | 0.12914079 | 3.95000e-10 | ## | ntl | 0.02573822 | 1.19570e-08 | ## | aspect | 0.02273950 | 4.78275e-07 | ## ## Spatial Unit: 8000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | presum | 0.65830260 | 1.330000e-10 | ## | lulc | 0.62941306 | 5.520000e-10 | ## | premin | 0.47958908 | 3.610000e-10 | ## | tmpmin | 0.43387026 | 1.270000e-10 | ## | tmpmax | 0.27793736 | 3.600000e-10 | ## | elev | 0.26007519 | 2.170000e-10 | ## | tmpavg | 0.24626023 | 7.420000e-10 | ## | slope | 0.23663987 | 4.930000e-10 | ## | pop | 0.22200579 | 8.390000e-10 | ## | premax | 0.14446913 | 5.440000e-10 | ## | ntl | 0.02638165 | 3.322900e-06 | ## | aspect | 0.01993728 | 1.770375e-03 | ## ## Spatial Unit: 9000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | presum | 0.65739289 | 2.420000e-10 | ## | lulc | 0.62688737 | 8.450000e-10 | ## | premin | 0.46785117 | 8.610000e-10 | ## | tmpmin | 0.44858109 | 9.900000e-11 | ## | elev | 0.26629528 | 1.010000e-10 | ## | tmpavg | 0.26423186 | 2.540000e-10 | ## | tmpmax | 0.24490412 | 2.340000e-10 | ## | slope | 0.23372050 | 3.490000e-10 | ## | pop | 0.23158655 | 5.630000e-10 | ## | premax | 0.15605198 | 5.870000e-10 | ## | ntl | 0.02797473 | 1.571733e-04 | ## | aspect | 0.02732356 | 3.071476e-04 | ## ## Spatial Unit: 10000 ## ## | variable | Q-statistic | P-value | ## |:--------:|:-----------:|:------------:| ## | presum | 0.67041293 | 8.870000e-10 | ## | lulc | 0.62850681 | 3.530000e-10 | ## | premin | 0.48291514 | 5.270000e-10 | ## | tmpmin | 0.44485438 | 4.530000e-10 | ## | tmpmax | 0.28867471 | 4.140000e-10 | ## | tmpavg | 0.28656169 | 5.160000e-10 | ## | elev | 0.27080523 | 8.150000e-10 | ## | pop | 0.26912522 | 8.240000e-10 | ## | slope | 0.22656703 | 8.810000e-10 | ## | premax | 0.14956177 | 1.950000e-10 | ## | aspect | 0.03267780 | 2.524895e-03 | ## | ntl | 0.02332034 | 1.395206e-02 | plot(g3) ``` ![](../man/figures/sesu/gozh2-1.png) As shown above, strategy `2` results in a better trade-off between spatial unit expressive detail and explanatory power than strategy `1`. So `sesu_gozh()` defaults to use strategy `2`(using the interactive Q statistic for all explanatory variables)