probability
wiesehahn
2020-08-31
Last updated: 2020-09-02
Checks: 7 0
Knit directory: baumarten/analysis/
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Probabilities
Probability distribution
Relative probability distributions for correctly und uncorrectly classified forest stands by tree species
Reduced number of classes
What happens to prediction probabilities if the number of predicted tree species is reduced?
To test this I trained the model on just four species (beech, spruce, pine, oak)
6-Class-Accuracy
The effect on validation accuracy, including all 6 tree species is tested.
Error Matrix| Baumart | BU | DGL | FI | KI | LAE | TEI |
|---|---|---|---|---|---|---|
| BU | 2308 | 2 | 8 | 4 | 356 | 148 |
| DGL | 0 | 0 | 0 | 0 | 0 | 0 |
| FI | 0 | 394 | 2786 | 22 | 55 | 1 |
| KI | 16 | 97 | 49 | 538 | 307 | 2 |
| LAE | 0 | 0 | 0 | 0 | 0 | 0 |
| TEI | 83 | 35 | 5 | 4 | 251 | 1673 |
We can see, that Douglas fir is mainly classified as Spruce, while Larch is classified as either Beech, Pine or Oak!
Respective Accuracy| Accuracy | Kappa | AccuracyLower | AccuracyUpper |
|---|---|---|---|
| 0.7988845 | 0.7340012 | 0.7905195 | 0.8070587 |
4-Class-Accuracy
The effect on validation accuracy, including only the classes on which the model was trained.
Error Matrix| Baumart | BU | DGL | FI | KI | LAE | TEI |
|---|---|---|---|---|---|---|
| BU | 2308 | 0 | 8 | 4 | 0 | 148 |
| DGL | 0 | 0 | 0 | 0 | 0 | 0 |
| FI | 0 | 0 | 2786 | 22 | 0 | 1 |
| KI | 16 | 0 | 49 | 538 | 0 | 2 |
| LAE | 0 | 0 | 0 | 0 | 0 | 0 |
| TEI | 83 | 0 | 5 | 4 | 0 | 1673 |
| Accuracy | Kappa | AccuracyLower | AccuracyUpper |
|---|---|---|---|
| 0.9552766 | 0.936171 | 0.9504019 | 0.9598003 |
Boxplots
Correct probabilities
propabilities of predicted tree species which were classified correct
Reducing the number of predicted tree species results in higher model certainties for all species.
Uncorrect probabilties
propabilities of predicted tree species which were classified uncorrect (e.g. predicted probability of beech which is in fact oak)
Quite unsurprisingly the (false) probabilities of uncorrectly classified forest stands rise with reduced number of species if we are considering all reference data, including Larch and Douglas fir. These stands are classified as one of the other four species and hence are uncorrect by default.
propabilities of reference tree species which were classified uncorrect (e.g. probability of oak which was predicted as beech)
Probabilities for the (true) reference species, which were classified uncorrectly as another species increased slighty with reduced number of predicted species. This is mainly due to the fact that probabilities are split among four instead of six species.
R version 4.0.2 (2020-06-22)
Platform: i386-w64-mingw32/i386 (32-bit)
Running under: Windows 10 x64 (build 18362)
Matrix products: default
locale:
[1] LC_COLLATE=German_Germany.1252 LC_CTYPE=German_Germany.1252
[3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C
[5] LC_TIME=German_Germany.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ranger_0.12.1 caret_6.0-86 lattice_0.20-41 recipes_0.1.13
[5] dplyr_1.0.0 here_0.1 plotly_4.9.2.1 ggplot2_3.3.2
[9] readr_1.3.1 kableExtra_1.1.0 viridis_0.5.1 viridisLite_0.3.0
[13] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] httr_1.4.2 tidyr_1.1.0 jsonlite_1.7.0
[4] splines_4.0.2 foreach_1.5.0 prodlim_2019.11.13
[7] highr_0.8 stats4_4.0.2 yaml_2.2.1
[10] ipred_0.9-9 pillar_1.4.6 backports_1.1.7
[13] glue_1.4.1 pROC_1.16.2 digest_0.6.25
[16] RColorBrewer_1.1-2 promises_1.1.1 rvest_0.3.6
[19] colorspace_1.4-1 htmltools_0.5.0 httpuv_1.5.4
[22] Matrix_1.2-18 plyr_1.8.6 timeDate_3043.102
[25] pkgconfig_2.0.3 purrr_0.3.4 scales_1.1.1
[28] webshot_0.5.2 whisker_0.4 later_1.1.0.1
[31] gower_0.2.2 lava_1.6.7 git2r_0.27.1
[34] tibble_3.0.3 farver_2.0.3 generics_0.0.2
[37] ellipsis_0.3.1 withr_2.2.0 nnet_7.3-14
[40] lazyeval_0.2.2 survival_3.2-3 magrittr_1.5
[43] crayon_1.3.4 evaluate_0.14 fs_1.4.2
[46] nlme_3.1-148 MASS_7.3-51.6 xml2_1.3.2
[49] class_7.3-17 tools_4.0.2 data.table_1.12.8
[52] hms_0.5.3 lifecycle_0.2.0 stringr_1.4.0
[55] munsell_0.5.0 e1071_1.7-3 compiler_4.0.2
[58] rlang_0.4.7 grid_4.0.2 iterators_1.0.12
[61] rstudioapi_0.11 htmlwidgets_1.5.1 crosstalk_1.1.0.1
[64] labeling_0.3 rmarkdown_2.3 ModelMetrics_1.2.2.2
[67] gtable_0.3.0 codetools_0.2-16 reshape2_1.4.4
[70] R6_2.4.1 gridExtra_2.3 lubridate_1.7.9
[73] knitr_1.29 rprojroot_1.3-2 stringi_1.4.6
[76] Rcpp_1.0.5 vctrs_0.3.2 rpart_4.1-15
[79] tidyselect_1.1.0 xfun_0.15