Last updated: 2020-08-05
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Last update:
[1] "Wed Aug 5 18:21:10 2020"This document originated from the fear of having a response variable which is not normally distributed “enough”.
The response variable looks as follows:
When applying the Shapiro-Wilk test we get
Shapiro-Wilk normality test
data: vi_data_corrected_buffer2$defoliation
W = 0.86069, p-value < 2.2e-16Visualizing model residuals of LASSO and RF to see how they differ. The LASSO “predicted vs. fitted” plot shows limited model power.
The following transformations of the response variable were done to check if it they have an effect on the “residuals vs. fitted” and “QQ-Plot” shown above.
One option to enforce more normality of a variable is by applying a power transformation. The Box-Cox power transformation estimates a lambda value from the variable. Next, the transformation can be applied via
\[(y^lambda - 1) / lambda\]
There is a Stackoverflow question that shows how to do this.
Applying it on the response of the data.
| Version | Author | Date |
|---|---|---|
| 7c7c7d9 | pat-s | 2020-02-25 |
[1] 0.7878788
Shapiro-Wilk normality test
data: y_new1
W = 0.84181, p-value < 2.2e-16The “W” value is a little less than before.
There is another way to do this via package car.
Shapiro-Wilk normality test
data: y_new2
W = 0.8433, p-value < 2.2e-16Exploring the residuals of a Lasso model with no transformation of the response variable.
| Version | Author | Date |
|---|---|---|
| 7c7c7d9 | pat-s | 2020-02-25 |
R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)
Matrix products: default
BLAS: /opt/spack/opt/spack/linux-centos7-x86_64/gcc-9.2.0/r-3.6.1-j25wr6zcofibs2zfjwg37357rjj26lqb/rlib/R/lib/libRblas.so
LAPACK: /opt/spack/opt/spack/linux-centos7-x86_64/gcc-9.2.0/r-3.6.1-j25wr6zcofibs2zfjwg37357rjj26lqb/rlib/R/lib/libRlapack.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] tidyselect_0.2.5 MASS_7.3-51.4 ggplot2_3.3.0 drake_7.12.0
loaded via a namespace (and not attached):
[1] fs_1.4.1 filelock_1.0.2 RColorBrewer_1.1-2
[4] progress_1.2.0 httr_1.4.0 rprojroot_1.3-2
[7] tools_3.6.1 backports_1.1.5 R6_2.4.1
[10] lazyeval_0.2.1 colorspace_1.4-0 withr_2.1.2
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[16] compiler_3.6.1 git2r_0.26.1 parallelMap_1.4
[19] glmnet_3.0-2 cli_2.0.2 DiceKriging_1.5.6
[22] plotly_4.8.0 labeling_0.3 scales_1.1.0
[25] checkmate_2.0.0 plot3D_1.1.1 stringr_1.4.0
[28] digest_0.6.25 foreign_0.8-72 txtq_0.1.4
[31] rmarkdown_1.13 rio_0.5.16 smoof_1.5.1
[34] pkgconfig_2.0.3 htmltools_0.3.6 lhs_1.0.1
[37] readxl_1.3.0 htmlwidgets_1.3 rlang_0.4.5
[40] BBmisc_1.11 shape_1.4.4 farver_2.0.3
[43] mlrMBO_1.1.2 jsonlite_1.6 zip_2.0.4
[46] dplyr_0.8.3 car_3.0-3 magrittr_1.5
[49] Matrix_1.2-15 Rcpp_1.0.3 munsell_0.5.0
[52] fansi_0.4.1 abind_1.4-5 lifecycle_0.1.0
[55] stringi_1.3.1 whisker_0.3-2 yaml_2.2.0
[58] carData_3.0-2 storr_1.2.1 RJSONIO_1.3-1.1
[61] grid_3.6.1 misc3d_0.8-4 parallel_3.6.1
[64] promises_1.0.1 forcats_0.4.0 crayon_1.3.4
[67] lattice_0.20-38 haven_2.1.0 splines_3.6.1
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[82] vctrs_0.2.4 httpuv_1.4.5.1 foreach_1.4.4
[85] cellranger_1.1.0 gtable_0.3.0 purrr_0.3.4
[88] tidyr_1.0.0 kernlab_0.9-27 assertthat_0.2.1
[91] openxlsx_4.1.0 xfun_0.5 later_1.0.0
[94] survival_2.43-3 viridisLite_0.3.0 tibble_2.1.3
[97] iterators_1.0.10 workflowr_1.6.1