-
Notifications
You must be signed in to change notification settings - Fork 0
/
README.Rmd
118 lines (86 loc) · 4.58 KB
/
README.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
---
output: github_document
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# Mixtures of Non-Homogeneous Linear Regression Models
<!-- badges: start -->
[](https://CRAN.R-project.org/package=mixnhreg) [](https://github.com/jobstdavid/mixnhreg/actions) [](https://github.com/jobstdavid/mixnhreg)
<!-- badges: end -->
## Overview
The R package `mixnhreg` allows to estimate mixtures of non-homogenous linear regression models. Linear predictors are separately employed for the location, scale and weight parameter of each mixture component allowing for heteroscedastic mixture regression models.
The infrastructure offers:
- predefined mixture distributions, such as e.g. mixture normal distribution.
- the possibility for the user to extending the zoo of usable mixture distributions by its own.
The model estimation supports:
- numerical optimization algorithms such as e.g. BFGS or Nelder-Mead.
- non-cyclic gradient boosting and therefore a variable selection procedure.
- different loss functions for the model estimation, i.e. negative log-likelihood or continuous ranked probability score.
## Installation
You can install the development version from GitHub with:
``` r
# install.packages("remotes")
remotes::install_github("jobstdavid/mixnhreg")
```
## Example
```{r example0, eval = T, echo = FALSE}
set.seed(2025)
```
### Model estimation
```{r example1, eval = T}
library(mixnhreg)
# load data
data("station")
# fit mixture normal distribution with two components via BFGS
(fit_optim <- mixnhreg(formula = obs ~ sin1 + cos1 + temp_mean | temp_ctrl,
scale.formula = ~ sin1 + cos1 + log(temp_sd) | 1,
weight.formula = ~ sin1 + cos1 | 1,
data = station,
control = control_optim()))
# fit mixture normal distribution with two components via gradient-boosting
(fit_boost <- mixnhreg(formula = obs ~ sin1 + cos1 + temp_mean | temp_ctrl,
scale.formula = ~ sin1 + cos1 + log(temp_sd) | 1,
weight.formula = ~ sin1 + cos1 | 1,
data = station,
control = control_boost(mstop = "cv")))
```
### Model prediction
```{r example2, eval = T}
# parameter predictions
par_optim <- predict(fit_optim, type = "parameter")
par_boost <- predict(fit_boost, type = "parameter")
# get observations and mean forecasts
obs <- na.omit(station$obs)
mean_optim <- rowSums(par_optim$location * par_optim$weight)
mean_boost <- rowSums(par_boost$location * par_boost$weight)
```
### Residual plot
```{r example3, out.width = "100%", fig.align = 'center', eval = T}
plot(obs - mean_optim,
xlab = "Index",
ylab = "Observation - Mean",
pch = 19,
col = adjustcolor("red", alpha = 0.5))
points(obs - mean_boost,
pch = 19,
col = adjustcolor("steelblue", alpha = 0.25))
legend("bottomright",
legend = c("optim", "boost"),
pch = 19,
col = c("red", "steelblue"))
grid()
```
## Contact
Feel free to contact [jobstd\@uni-hildesheim.de](mailto:jobstd@uni-hildesheim.de) if you have any questions or suggestions.
## References
* Grimit E.P., Gneiting T., Berrocal V., Johnson N.A. (2006). The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification. Quarterly Journal of the Royal Meteorological Society, 132, pp. 2925–2942. doi: <https://doi.org/10.1256/qj.05.235>.
* Hepp, T., J. Zierk, and E. Bergherr (2023). "Component-wise boosting for mixture distributional regression models". In: Proceedings of the 37th International Workshop on Statistical Modelling. url: https://iwsm2023.statistik.tu-dortmund.de/.
* Jobst, D. (2024). Gradient-Boosted Mixture Regression Models for Postprocessing Ensemble Weather Forecasts. doi: <https://doi.org/10.48550/arXiv.2412.09583>.
* Messner, J. W., G. J. Mayr, and A. Zeileis (2017). "Nonhomogeneous Boosting for Predictor Selection in Ensemble Postprocessing". In: Monthly Weather Review 145.1, pp. 137–147. doi: <https://doi.org/10.1175/mwr-d-16-0088.1>.
* Thomas, J. et al. (2017). "Gradient boosting for distributional regression: faster tuning and improved variable selection via noncyclical updates". In: Statistics and Computing 28.3, pp. 673–687. doi: <https://doi.org/10.1007/s11222-017-9754-6>.