examples/bigKRLS_boston_kcv.md
In rdrr1990/bigKRLS: Optimized Kernel Regularized Least Squares
K folds crossvalidating with bigKRLS
This little demo shows how to use and interpret crossvalidate.bigKRLS on the Boston housing data. (medv is median house value).
library(pacman)
p_load(bigKRLS, tidyverse, knitr, MASS)
opts_chunk$set(tidy = TRUE, comment = "")
glimpse(Boston)
Observations: 506
Variables: 14
$ crim <dbl> 0.00632, 0.02731, 0.02729, 0.03237, 0.06905, 0.02985, ...
$ zn <dbl> 18.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.5, 12.5, 12.5, 12.5,...
$ indus <dbl> 2.31, 7.07, 7.07, 2.18, 2.18, 2.18, 7.87, 7.87, 7.87, ...
$ chas <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
$ nox <dbl> 0.538, 0.469, 0.469, 0.458, 0.458, 0.458, 0.524, 0.524...
$ rm <dbl> 6.575, 6.421, 7.185, 6.998, 7.147, 6.430, 6.012, 6.172...
$ age <dbl> 65.2, 78.9, 61.1, 45.8, 54.2, 58.7, 66.6, 96.1, 100.0,...
$ dis <dbl> 4.0900, 4.9671, 4.9671, 6.0622, 6.0622, 6.0622, 5.5605...
$ rad <int> 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, ...
$ tax <dbl> 296, 242, 242, 222, 222, 222, 311, 311, 311, 311, 311,...
$ ptratio <dbl> 15.3, 17.8, 17.8, 18.7, 18.7, 18.7, 15.2, 15.2, 15.2, ...
$ black <dbl> 396.90, 396.90, 392.83, 394.63, 396.90, 394.12, 395.60...
$ lstat <dbl> 4.98, 9.14, 4.03, 2.94, 5.33, 5.21, 12.43, 19.15, 29.9...
$ medv <dbl> 24.0, 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, ...
y <- as.matrix(Boston$medv)
X <- as.matrix(Boston %>% dplyr::select(-medv))
out <- crossvalidate.bigKRLS(y, X, seed = 1234, Kfolds = 5)
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s <- summary(out)
s[["overview"]]
| | Fold 1 | Fold 2 | Fold 3 | Fold 4 | Fold 5 |
|:------------------------|:--------|:---------|:---------|:--------|:--------|
| MSE (In Sample) | 5.547 | 5.339 | 5.332 | 4.303 | 5.504 |
| MSE (Out of Sample) | 8.464 | 10.896 | 8.970 | 17.715 | 7.753 |
| MSE AME (In Sample) | 815.101 | 1388.626 | 1080.492 | 489.638 | 801.770 |
| MSE AME (Out of Sample) | 754.644 | 1724.905 | 1328.164 | 392.617 | 753.858 |
| R2 (In Sample) | 0.937 | 0.938 | 0.940 | 0.944 | 0.935 |
| R2 (Out of Sample) | 0.883 | 0.868 | 0.871 | 0.857 | 0.910 |
| R2 AME (In Sample) | 0.068 | 0.048 | 0.070 | 0.046 | 0.068 |
| R2 AME (Out of Sample) | 0.085 | 0.120 | 0.019 | 0.356 | 0.108 |
The predictiveness of the model is relatively stable across models (85-90% of variance explained). The model fits the best for Fold 5 (lowest Mean Squared Error and highest R2 out of sample). The model is massively non-additive in that giant gaps between how much the model as a whole explains vs. how much the average marginal effects (AMEs) explain. Put differently, most of the variance is explained by interactions. The AMEs are most informative for Fold 4.
summary(out)
Overview of Model Performance
N: 506
Kfolds: 5
Seed: 1234
Fold 1 Fold 2 Fold 3 Fold 4 Fold 5
MSE (In Sample) 5.5473 5.34e+00 5.33e+00 4.3028 5.5040
MSE (Out of Sample) 8.4643 1.09e+01 8.97e+00 17.7145 7.7533
MSE AME (In Sample) 815.1014 1.39e+03 1.08e+03 489.6375 801.7701
MSE AME (Out of Sample) 754.6435 1.72e+03 1.33e+03 392.6165 753.8584
R2 (In Sample) 0.9365 9.38e-01 9.40e-01 0.9438 0.9345
R2 (Out of Sample) 0.8830 8.68e-01 8.71e-01 0.8567 0.9102
R2 AME (In Sample) 0.0400 2.69e-02 4.97e-02 0.0169 0.0414
R2 AME (Out of Sample) 0.0853 1.20e-01 1.86e-02 0.3563 0.1085
MSE denotes Mean Squared Error. AME implies calculations done with Average Marginal Effects only.
Summary of Training Model1:
MODEL SUMMARY:
lambda: 0.2145
N: 404
N Effective: 310.8598
R2: 0.9365
R2AME**: 0.04
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0977 0.0324 -3.0207 0.0027
zn -0.0118 0.0108 -1.0968 0.2736
indus 0.0038 0.0332 0.1153 0.9083
chas* 103.6046 18.9535 5.4662 0.0000
nox -10.4226 2.7829 -3.7453 0.0002
rm 4.4998 0.3261 13.8007 0.0000
age -0.0418 0.0082 -5.1280 0.0000
dis -1.2196 0.1250 -9.7595 0.0000
rad 0.1590 0.0404 3.9340 0.0001
tax -0.0104 0.0016 -6.2975 0.0000
ptratio -0.2368 0.0692 -3.4223 0.0007
black 0.0013 0.0037 0.3400 0.7341
lstat -0.3262 0.0392 -8.3303 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.3903 -0.1510 -0.0604 -0.0156 0.0713
zn -0.0534 -0.0296 -0.0087 -0.0012 0.0459
indus -0.1600 -0.0659 -0.0155 0.0550 0.2094
chas* -68.0724 29.2456 95.8535 179.0750 297.9587
nox -31.2882 -14.0401 -8.9859 -3.9585 6.0274
rm -1.8657 0.5196 4.1433 8.1936 11.5775
age -0.1160 -0.0725 -0.0414 -0.0115 0.0476
dis -2.7053 -1.6986 -1.1764 -0.6760 -0.0046
rad -0.0130 0.0940 0.1613 0.2340 0.3409
tax -0.0247 -0.0160 -0.0103 -0.0032 0.0007
ptratio -1.2797 -0.5753 -0.1221 0.1730 0.3994
black -0.0071 -0.0022 0.0011 0.0048 0.0103
lstat -1.1181 -0.4552 -0.2188 -0.0766 0.0395
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model2:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 313.9762
R2: 0.9377
R2AME**: 0.0269
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0517 0.0240 -2.1497 0.0324
zn -0.0092 0.0101 -0.9120 0.3625
indus 0.0020 0.0336 0.0608 0.9515
chas* 147.9221 24.3181 6.0828 0.0000
nox -13.0208 2.7971 -4.6551 0.0000
rm 4.4851 0.3136 14.3003 0.0000
age -0.0310 0.0080 -3.8886 0.0001
dis -1.1857 0.1231 -9.6309 0.0000
rad 0.1869 0.0391 4.7763 0.0000
tax -0.0086 0.0016 -5.2814 0.0000
ptratio -0.3032 0.0735 -4.1265 0.0000
black 0.0018 0.0038 0.4702 0.6385
lstat -0.3683 0.0392 -9.4026 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2288 -0.0955 -0.0174 0.0029 0.0503
zn -0.0514 -0.0330 -0.0111 -0.0015 0.0545
indus -0.1600 -0.0727 -0.0138 0.0559 0.2338
chas* -141.6465 33.1156 111.6110 294.1739 472.7116
nox -32.5640 -19.2169 -12.9771 -5.1220 5.2963
rm -1.1989 1.0614 3.7261 7.9043 11.2197
age -0.0964 -0.0568 -0.0372 -0.0094 0.0687
dis -2.5854 -1.6466 -1.0910 -0.6789 -0.1640
rad 0.0142 0.1224 0.1789 0.2572 0.3693
tax -0.0223 -0.0138 -0.0084 -0.0022 0.0022
ptratio -1.2227 -0.6010 -0.1910 0.0713 0.2279
black -0.0146 -0.0030 0.0041 0.0075 0.0126
lstat -1.1521 -0.5104 -0.2757 -0.1081 0.0384
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model3:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 312.0236
R2: 0.9397
R2AME**: 0.0497
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0679 0.0252 -2.6980 0.0074
zn -0.0118 0.0105 -1.1221 0.2627
indus -0.0175 0.0330 -0.5306 0.5961
chas* 130.8481 23.8693 5.4819 0.0000
nox -7.3249 2.8442 -2.5754 0.0105
rm 4.5547 0.3115 14.6239 0.0000
age -0.0415 0.0082 -5.0442 0.0000
dis -1.0450 0.1243 -8.4035 0.0000
rad 0.1334 0.0396 3.3670 0.0009
tax -0.0103 0.0016 -6.2477 0.0000
ptratio -0.3054 0.0717 -4.2578 0.0000
black 0.0032 0.0037 0.8674 0.3864
lstat -0.3375 0.0398 -8.4821 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2665 -0.1124 -0.0443 -0.0080 0.0522
zn -0.0458 -0.0312 -0.0086 -0.0010 0.0390
indus -0.1760 -0.0973 -0.0320 0.0393 0.1923
chas* -112.2719 30.8496 118.4596 242.5509 401.1752
nox -29.3183 -11.4084 -6.1125 0.0483 9.2596
rm -1.1173 1.3039 4.1210 7.9353 11.1596
age -0.1098 -0.0684 -0.0463 -0.0203 0.0512
dis -2.1330 -1.5585 -1.0529 -0.5551 0.0137
rad 0.0002 0.0884 0.1395 0.1802 0.2705
tax -0.0267 -0.0155 -0.0100 -0.0029 0.0006
ptratio -1.3377 -0.5942 -0.1856 0.0899 0.3627
black -0.0135 -0.0008 0.0044 0.0083 0.0135
lstat -1.0287 -0.4540 -0.2768 -0.1079 0.0490
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model4:
MODEL SUMMARY:
lambda: 0.2235
N: 405
N Effective: 311.3317
R2: 0.9438
R2AME**: 0.0169
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0575 0.0236 -2.4341 0.0155
zn -0.0146 0.0092 -1.5960 0.1116
indus -0.0076 0.0297 -0.2550 0.7989
chas* 76.2714 19.6619 3.8791 0.0001
nox -9.3801 2.4636 -3.8075 0.0002
rm 4.6342 0.2778 16.6812 0.0000
age -0.0391 0.0071 -5.5207 0.0000
dis -0.8727 0.1072 -8.1380 0.0000
rad 0.1596 0.0361 4.4222 0.0000
tax -0.0092 0.0015 -6.1669 0.0000
ptratio -0.2719 0.0621 -4.3755 0.0000
black 0.0021 0.0035 0.5899 0.5557
lstat -0.3188 0.0350 -9.1168 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2153 -0.0979 -0.0333 -0.0015 0.0232
zn -0.0552 -0.0336 -0.0154 -0.0039 0.0519
indus -0.1482 -0.0723 -0.0242 0.0345 0.1882
chas* -164.7485 14.6677 96.0850 153.0838 245.1769
nox -25.7832 -15.6798 -9.3561 -2.4803 7.1671
rm -1.4179 1.4054 4.1174 7.8686 11.2416
age -0.0982 -0.0656 -0.0477 -0.0183 0.0471
dis -1.5947 -1.2085 -0.8921 -0.5497 -0.0349
rad -0.0099 0.0884 0.1644 0.2346 0.3192
tax -0.0214 -0.0141 -0.0094 -0.0035 0.0006
ptratio -1.2984 -0.5896 -0.1512 0.0863 0.3100
black -0.0103 -0.0016 0.0023 0.0063 0.0129
lstat -0.8951 -0.4616 -0.2629 -0.1201 0.0199
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model5:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 311.4581
R2: 0.9345
R2AME**: 0.0414
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0748 0.0295 -2.5335 0.0118
zn -0.0080 0.0102 -0.7845 0.4334
indus -0.0035 0.0321 -0.1089 0.9134
chas* 103.3547 20.1556 5.1279 0.0000
nox -9.6089 2.7275 -3.5230 0.0005
rm 4.4201 0.3310 13.3535 0.0000
age -0.0279 0.0086 -3.2618 0.0012
dis -1.0859 0.1202 -9.0362 0.0000
rad 0.1522 0.0413 3.6885 0.0003
tax -0.0091 0.0016 -5.5111 0.0000
ptratio -0.2777 0.0685 -4.0541 0.0001
black 0.0012 0.0039 0.3008 0.7638
lstat -0.3888 0.0401 -9.7057 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.3058 -0.1314 -0.0450 -0.0063 0.0627
zn -0.0415 -0.0256 -0.0060 -0.0001 0.0434
indus -0.1683 -0.0802 -0.0121 0.0516 0.2005
chas* -93.7708 29.8238 94.8950 177.4629 309.1480
nox -32.0905 -14.5180 -8.7140 -1.4732 7.9573
rm -1.4243 1.3069 3.3908 7.7720 11.6479
age -0.0923 -0.0594 -0.0337 -0.0008 0.0619
dis -2.3266 -1.4901 -1.0199 -0.6114 -0.0825
rad -0.0077 0.0856 0.1518 0.2171 0.3327
tax -0.0225 -0.0142 -0.0089 -0.0027 0.0012
ptratio -1.2556 -0.5653 -0.1724 0.0907 0.3276
black -0.0150 -0.0032 0.0024 0.0060 0.0130
lstat -1.2151 -0.4925 -0.3027 -0.1570 -0.0414
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
rdrr1990/bigKRLS documentation built on Aug. 2, 2019, 9:13 a.m.
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K folds crossvalidating with bigKRLS
This little demo shows how to use and interpret crossvalidate.bigKRLS on the Boston housing data. (medv is median house value).
library(pacman)
p_load(bigKRLS, tidyverse, knitr, MASS)
opts_chunk$set(tidy = TRUE, comment = "")
glimpse(Boston)
Observations: 506
Variables: 14
$ crim <dbl> 0.00632, 0.02731, 0.02729, 0.03237, 0.06905, 0.02985, ...
$ zn <dbl> 18.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.5, 12.5, 12.5, 12.5,...
$ indus <dbl> 2.31, 7.07, 7.07, 2.18, 2.18, 2.18, 7.87, 7.87, 7.87, ...
$ chas <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
$ nox <dbl> 0.538, 0.469, 0.469, 0.458, 0.458, 0.458, 0.524, 0.524...
$ rm <dbl> 6.575, 6.421, 7.185, 6.998, 7.147, 6.430, 6.012, 6.172...
$ age <dbl> 65.2, 78.9, 61.1, 45.8, 54.2, 58.7, 66.6, 96.1, 100.0,...
$ dis <dbl> 4.0900, 4.9671, 4.9671, 6.0622, 6.0622, 6.0622, 5.5605...
$ rad <int> 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, ...
$ tax <dbl> 296, 242, 242, 222, 222, 222, 311, 311, 311, 311, 311,...
$ ptratio <dbl> 15.3, 17.8, 17.8, 18.7, 18.7, 18.7, 15.2, 15.2, 15.2, ...
$ black <dbl> 396.90, 396.90, 392.83, 394.63, 396.90, 394.12, 395.60...
$ lstat <dbl> 4.98, 9.14, 4.03, 2.94, 5.33, 5.21, 12.43, 19.15, 29.9...
$ medv <dbl> 24.0, 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, ...
y <- as.matrix(Boston$medv)
X <- as.matrix(Boston %>% dplyr::select(-medv))
out <- crossvalidate.bigKRLS(y, X, seed = 1234, Kfolds = 5)
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s <- summary(out)
s[["overview"]]
| | Fold 1 | Fold 2 | Fold 3 | Fold 4 | Fold 5 | |:------------------------|:--------|:---------|:---------|:--------|:--------| | MSE (In Sample) | 5.547 | 5.339 | 5.332 | 4.303 | 5.504 | | MSE (Out of Sample) | 8.464 | 10.896 | 8.970 | 17.715 | 7.753 | | MSE AME (In Sample) | 815.101 | 1388.626 | 1080.492 | 489.638 | 801.770 | | MSE AME (Out of Sample) | 754.644 | 1724.905 | 1328.164 | 392.617 | 753.858 | | R2 (In Sample) | 0.937 | 0.938 | 0.940 | 0.944 | 0.935 | | R2 (Out of Sample) | 0.883 | 0.868 | 0.871 | 0.857 | 0.910 | | R2 AME (In Sample) | 0.068 | 0.048 | 0.070 | 0.046 | 0.068 | | R2 AME (Out of Sample) | 0.085 | 0.120 | 0.019 | 0.356 | 0.108 |
The predictiveness of the model is relatively stable across models (85-90% of variance explained). The model fits the best for Fold 5 (lowest Mean Squared Error and highest R2 out of sample). The model is massively non-additive in that giant gaps between how much the model as a whole explains vs. how much the average marginal effects (AMEs) explain. Put differently, most of the variance is explained by interactions. The AMEs are most informative for Fold 4.
summary(out)
Overview of Model Performance
N: 506
Kfolds: 5
Seed: 1234
Fold 1 Fold 2 Fold 3 Fold 4 Fold 5
MSE (In Sample) 5.5473 5.34e+00 5.33e+00 4.3028 5.5040
MSE (Out of Sample) 8.4643 1.09e+01 8.97e+00 17.7145 7.7533
MSE AME (In Sample) 815.1014 1.39e+03 1.08e+03 489.6375 801.7701
MSE AME (Out of Sample) 754.6435 1.72e+03 1.33e+03 392.6165 753.8584
R2 (In Sample) 0.9365 9.38e-01 9.40e-01 0.9438 0.9345
R2 (Out of Sample) 0.8830 8.68e-01 8.71e-01 0.8567 0.9102
R2 AME (In Sample) 0.0400 2.69e-02 4.97e-02 0.0169 0.0414
R2 AME (Out of Sample) 0.0853 1.20e-01 1.86e-02 0.3563 0.1085
MSE denotes Mean Squared Error. AME implies calculations done with Average Marginal Effects only.
Summary of Training Model1:
MODEL SUMMARY:
lambda: 0.2145
N: 404
N Effective: 310.8598
R2: 0.9365
R2AME**: 0.04
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0977 0.0324 -3.0207 0.0027
zn -0.0118 0.0108 -1.0968 0.2736
indus 0.0038 0.0332 0.1153 0.9083
chas* 103.6046 18.9535 5.4662 0.0000
nox -10.4226 2.7829 -3.7453 0.0002
rm 4.4998 0.3261 13.8007 0.0000
age -0.0418 0.0082 -5.1280 0.0000
dis -1.2196 0.1250 -9.7595 0.0000
rad 0.1590 0.0404 3.9340 0.0001
tax -0.0104 0.0016 -6.2975 0.0000
ptratio -0.2368 0.0692 -3.4223 0.0007
black 0.0013 0.0037 0.3400 0.7341
lstat -0.3262 0.0392 -8.3303 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.3903 -0.1510 -0.0604 -0.0156 0.0713
zn -0.0534 -0.0296 -0.0087 -0.0012 0.0459
indus -0.1600 -0.0659 -0.0155 0.0550 0.2094
chas* -68.0724 29.2456 95.8535 179.0750 297.9587
nox -31.2882 -14.0401 -8.9859 -3.9585 6.0274
rm -1.8657 0.5196 4.1433 8.1936 11.5775
age -0.1160 -0.0725 -0.0414 -0.0115 0.0476
dis -2.7053 -1.6986 -1.1764 -0.6760 -0.0046
rad -0.0130 0.0940 0.1613 0.2340 0.3409
tax -0.0247 -0.0160 -0.0103 -0.0032 0.0007
ptratio -1.2797 -0.5753 -0.1221 0.1730 0.3994
black -0.0071 -0.0022 0.0011 0.0048 0.0103
lstat -1.1181 -0.4552 -0.2188 -0.0766 0.0395
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model2:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 313.9762
R2: 0.9377
R2AME**: 0.0269
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0517 0.0240 -2.1497 0.0324
zn -0.0092 0.0101 -0.9120 0.3625
indus 0.0020 0.0336 0.0608 0.9515
chas* 147.9221 24.3181 6.0828 0.0000
nox -13.0208 2.7971 -4.6551 0.0000
rm 4.4851 0.3136 14.3003 0.0000
age -0.0310 0.0080 -3.8886 0.0001
dis -1.1857 0.1231 -9.6309 0.0000
rad 0.1869 0.0391 4.7763 0.0000
tax -0.0086 0.0016 -5.2814 0.0000
ptratio -0.3032 0.0735 -4.1265 0.0000
black 0.0018 0.0038 0.4702 0.6385
lstat -0.3683 0.0392 -9.4026 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2288 -0.0955 -0.0174 0.0029 0.0503
zn -0.0514 -0.0330 -0.0111 -0.0015 0.0545
indus -0.1600 -0.0727 -0.0138 0.0559 0.2338
chas* -141.6465 33.1156 111.6110 294.1739 472.7116
nox -32.5640 -19.2169 -12.9771 -5.1220 5.2963
rm -1.1989 1.0614 3.7261 7.9043 11.2197
age -0.0964 -0.0568 -0.0372 -0.0094 0.0687
dis -2.5854 -1.6466 -1.0910 -0.6789 -0.1640
rad 0.0142 0.1224 0.1789 0.2572 0.3693
tax -0.0223 -0.0138 -0.0084 -0.0022 0.0022
ptratio -1.2227 -0.6010 -0.1910 0.0713 0.2279
black -0.0146 -0.0030 0.0041 0.0075 0.0126
lstat -1.1521 -0.5104 -0.2757 -0.1081 0.0384
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model3:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 312.0236
R2: 0.9397
R2AME**: 0.0497
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0679 0.0252 -2.6980 0.0074
zn -0.0118 0.0105 -1.1221 0.2627
indus -0.0175 0.0330 -0.5306 0.5961
chas* 130.8481 23.8693 5.4819 0.0000
nox -7.3249 2.8442 -2.5754 0.0105
rm 4.5547 0.3115 14.6239 0.0000
age -0.0415 0.0082 -5.0442 0.0000
dis -1.0450 0.1243 -8.4035 0.0000
rad 0.1334 0.0396 3.3670 0.0009
tax -0.0103 0.0016 -6.2477 0.0000
ptratio -0.3054 0.0717 -4.2578 0.0000
black 0.0032 0.0037 0.8674 0.3864
lstat -0.3375 0.0398 -8.4821 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2665 -0.1124 -0.0443 -0.0080 0.0522
zn -0.0458 -0.0312 -0.0086 -0.0010 0.0390
indus -0.1760 -0.0973 -0.0320 0.0393 0.1923
chas* -112.2719 30.8496 118.4596 242.5509 401.1752
nox -29.3183 -11.4084 -6.1125 0.0483 9.2596
rm -1.1173 1.3039 4.1210 7.9353 11.1596
age -0.1098 -0.0684 -0.0463 -0.0203 0.0512
dis -2.1330 -1.5585 -1.0529 -0.5551 0.0137
rad 0.0002 0.0884 0.1395 0.1802 0.2705
tax -0.0267 -0.0155 -0.0100 -0.0029 0.0006
ptratio -1.3377 -0.5942 -0.1856 0.0899 0.3627
black -0.0135 -0.0008 0.0044 0.0083 0.0135
lstat -1.0287 -0.4540 -0.2768 -0.1079 0.0490
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model4:
MODEL SUMMARY:
lambda: 0.2235
N: 405
N Effective: 311.3317
R2: 0.9438
R2AME**: 0.0169
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0575 0.0236 -2.4341 0.0155
zn -0.0146 0.0092 -1.5960 0.1116
indus -0.0076 0.0297 -0.2550 0.7989
chas* 76.2714 19.6619 3.8791 0.0001
nox -9.3801 2.4636 -3.8075 0.0002
rm 4.6342 0.2778 16.6812 0.0000
age -0.0391 0.0071 -5.5207 0.0000
dis -0.8727 0.1072 -8.1380 0.0000
rad 0.1596 0.0361 4.4222 0.0000
tax -0.0092 0.0015 -6.1669 0.0000
ptratio -0.2719 0.0621 -4.3755 0.0000
black 0.0021 0.0035 0.5899 0.5557
lstat -0.3188 0.0350 -9.1168 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.2153 -0.0979 -0.0333 -0.0015 0.0232
zn -0.0552 -0.0336 -0.0154 -0.0039 0.0519
indus -0.1482 -0.0723 -0.0242 0.0345 0.1882
chas* -164.7485 14.6677 96.0850 153.0838 245.1769
nox -25.7832 -15.6798 -9.3561 -2.4803 7.1671
rm -1.4179 1.4054 4.1174 7.8686 11.2416
age -0.0982 -0.0656 -0.0477 -0.0183 0.0471
dis -1.5947 -1.2085 -0.8921 -0.5497 -0.0349
rad -0.0099 0.0884 0.1644 0.2346 0.3192
tax -0.0214 -0.0141 -0.0094 -0.0035 0.0006
ptratio -1.2984 -0.5896 -0.1512 0.0863 0.3100
black -0.0103 -0.0016 0.0023 0.0063 0.0129
lstat -0.8951 -0.4616 -0.2629 -0.1201 0.0199
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
Summary of Training Model5:
MODEL SUMMARY:
lambda: 0.2145
N: 405
N Effective: 311.4581
R2: 0.9345
R2AME**: 0.0414
Average Marginal Effects:
Estimate Std. Error t value Pr(>|t|)
crim -0.0748 0.0295 -2.5335 0.0118
zn -0.0080 0.0102 -0.7845 0.4334
indus -0.0035 0.0321 -0.1089 0.9134
chas* 103.3547 20.1556 5.1279 0.0000
nox -9.6089 2.7275 -3.5230 0.0005
rm 4.4201 0.3310 13.3535 0.0000
age -0.0279 0.0086 -3.2618 0.0012
dis -1.0859 0.1202 -9.0362 0.0000
rad 0.1522 0.0413 3.6885 0.0003
tax -0.0091 0.0016 -5.5111 0.0000
ptratio -0.2777 0.0685 -4.0541 0.0001
black 0.0012 0.0039 0.3008 0.7638
lstat -0.3888 0.0401 -9.7057 0.0000
Percentiles of Marginal Effects:
5% 25% 50% 75% 95%
crim -0.3058 -0.1314 -0.0450 -0.0063 0.0627
zn -0.0415 -0.0256 -0.0060 -0.0001 0.0434
indus -0.1683 -0.0802 -0.0121 0.0516 0.2005
chas* -93.7708 29.8238 94.8950 177.4629 309.1480
nox -32.0905 -14.5180 -8.7140 -1.4732 7.9573
rm -1.4243 1.3069 3.3908 7.7720 11.6479
age -0.0923 -0.0594 -0.0337 -0.0008 0.0619
dis -2.3266 -1.4901 -1.0199 -0.6114 -0.0825
rad -0.0077 0.0856 0.1518 0.2171 0.3327
tax -0.0225 -0.0142 -0.0089 -0.0027 0.0012
ptratio -1.2556 -0.5653 -0.1724 0.0907 0.3276
black -0.0150 -0.0032 0.0024 0.0060 0.0130
lstat -1.2151 -0.4925 -0.3027 -0.1570 -0.0414
(*) Reported average and percentiles of dy/dx is for discrete change of the dummy variable from min to max (usually 0 to 1)).
(**) Pseudo-R^2 computed using only the Average Marginal Effects.
You may also wish to use predict() for out-of-sample forecasts or shiny.bigKRLS() to interact with results. Type vignette("bigKRLS_basics") for sample syntax. Use save.bigKRLS() to store results and load.bigKRLS() to re-open them.
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