The goal of dirinla is to analyze compositional data with a Dirichlet regression using the integrated nested Laplace approximation via the R-INLA package.
Package documentation can be found at https://inlabru-org.github.io/dirinla/
Installation
It is not yet in CRAN, but you can install the latest bugfix release of dirinla from github with:
# install.packages("remotes")
remotes::install_github("inlabru-org/dirinla", ref = "master")The latest development version can be installed via inlabru-org.r-universe.dev:
# Enable universe(s) by inlabru-org
options(repos = c(
inlabruorg = 'https://inlabru-org.r-universe.dev',
INLA = 'https://inla.r-inla-download.org/R/testing',
CRAN = 'https://cloud.r-project.org'))
# Install the package
install.packages('dirinla')or directly from github:
# install.packages("remotes")
remotes::install_github("inlabru-org/dirinla", ref = "devel")Example
This is a basic example which shows you how to solve a common problem:
Loading libraries
library(dirinla)
library(INLA)
library(DirichletReg)Simulating from a Dirichlet likelihood
set.seed(1000)
N <- 50 #number of data
V <- as.data.frame(matrix(runif((4) * N, 0, 1), ncol = 4)) #Covariates
names(V) <- paste0('v', 1:4)
formula <- y ~ 1 + v1 | 1 + v2 | 1 + v3 | 1 + v4
(names_cat <- formula_list(formula))
#> $`category 1`
#> [1] "intercept" "v1"
#>
#> $`category 2`
#> [1] "intercept" "v2"
#>
#> $`category 3`
#> [1] "intercept" "v3"
#>
#> $`category 4`
#> [1] "intercept" "v4"
x <- c(-1.5, 1, -3, 1.5,
2, -3 , -1, 5)
mus <- exp(x) / sum(exp(x))
C <- length(names_cat)
A_construct <-
data_stack_dirich(y = as.vector(rep(NA, N * C)),
covariates = names_cat,
data = V,
d = C,
n = N)
A_construct[1:8, ]
#> 8 x 8 sparse Matrix of class "dgCMatrix"
#>
#> [1,] 1 0.3278787 . . . . . .
#> [2,] . . 1 0.7267993 . . . .
#> [3,] . . . . 1 0.5993679 . .
#> [4,] . . . . . . 1 0.3224284
#> [5,] 1 0.7588465 . . . . . .
#> [6,] . . 1 0.6820559 . . . .
#> [7,] . . . . 1 0.4516818 . .
#> [8,] . . . . . . 1 0.5613199
eta <- A_construct %*% x
alpha <- exp(eta)
alpha <- matrix(alpha,
ncol = C,
byrow = TRUE)
y_o <- rdirichlet(N, alpha)
colnames(y_o) <- paste0("y", 1:C)
head(y_o)
#> y1 y2 y3 y4
#> [1,] 1.139109e-04 2.413110e-01 0.345644051 0.4129310
#> [2,] 7.342592e-02 3.633687e-03 0.193128806 0.7298116
#> [3,] 2.079875e-02 4.007038e-05 0.323599848 0.6555613
#> [4,] 1.361278e-05 3.894290e-02 0.172308411 0.7887351
#> [5,] 2.339991e-02 4.035880e-03 0.055003377 0.9175608
#> [6,] 8.910796e-01 6.743970e-10 0.000663061 0.1082573Fitting a simple model
y <- y_o
model.inla <- dirinlareg(
formula = y ~ 1 + v1 | 1 + v2 | 1 + v3 | 1 + v4,
y = y,
data.cov = V,
prec = 0.0001,
verbose = TRUE)
#>
#>
#> ---------------------- Looking for the mode -----------------
#>
#> Iter = 1, |grad| = 824.56, log.post = -457.73, |x_new - x_old| = 13.92583, |f_new - f_old| = 368.13749
#> Iter = 2, |grad| = 136.74, log.post = -577.55, |x_new - x_old| = 3.65634, |f_new - f_old| = 119.82746
#> Iter = 3, |grad| = 120.98, log.post = -671.77, |x_new - x_old| = 3.31293, |f_new - f_old| = 94.22001
#> Iter = 4, |grad| = 96.8, log.post = -739.43, |x_new - x_old| = 2.81732, |f_new - f_old| = 67.65798
#> Iter = 5, |grad| = 70.76, log.post = -785.42, |x_new - x_old| = 2.1453, |f_new - f_old| = 45.99234
#> Iter = 6, |grad| = 48.13, log.post = -809.29, |x_new - x_old| = 1.3377, |f_new - f_old| = 23.86892
#> Iter = 7, |grad| = 24.92, log.post = -814.96, |x_new - x_old| = 0.55663, |f_new - f_old| = 5.67249
#> Iter = 8, |grad| = 5.97, log.post = -815.24, |x_new - x_old| = 0.10262, |f_new - f_old| = 0.27719
#> Iter = 9, |grad| = 0.3, log.post = -815.24, |x_new - x_old| = 0.00994, |f_new - f_old| = 0.00062
#> Iter = 10, |grad| = 0, log.post = -815.24, |x_new - x_old| = 0.00011, |f_new - f_old| = 0
#> Iter = 11, |grad| = 0, log.post = -815.24, |x_new - x_old| = 0, |f_new - f_old| = 0
#>
#> Great news! The mode has been properly located!
#>
#> Real Hessian has been used 10 times
#> Expected Hessian has been used 40 times
#>
#> ---------------------- INLA call -----------------
#> INLA-Iter = 1, fixed.effects = 8, hyperparameters = 0 ---> PASS
#>
#> ---------------------- Obtaining linear predictor -----------------
summary(model.inla)
#>
#> Call:
#> dirinlareg(formula = y ~ 1 + v1 | 1 + v2 | 1 + v3 | 1 + v4, y = y,
#> data.cov = V, prec = 1e-04, verbose = TRUE)
#>
#>
#> ---- FIXED EFFECTS ----
#> =======================================================================
#> y1
#> -----------------------------------------------------------------------
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> intercept -1.5293 0.2922 -2.1020 -1.5293 -0.9565 -1.5293
#> v1 0.9977 0.5146 -0.0108 0.9977 2.0063 0.9977
#> =======================================================================
#> y2
#> -----------------------------------------------------------------------
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> intercept -2.8538 0.2783 -3.3993 -2.8538 -2.308 -2.8538
#> v2 0.7187 0.4870 -0.2357 0.7187 1.673 0.7187
#> =======================================================================
#> y3
#> -----------------------------------------------------------------------
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> intercept 1.902 0.2448 1.422 1.902 2.382 1.902
#> v3 -3.045 0.3738 -3.777 -3.045 -2.312 -3.045
#> =======================================================================
#> y4
#> -----------------------------------------------------------------------
#> mean sd 0.025quant 0.5quant 0.975quant mode
#> intercept -0.7033 0.3145 -1.320 -0.7033 -0.08698 -0.7033
#> v4 4.5247 0.4313 3.679 4.5247 5.37012 4.5247
#> =======================================================================
#>
#> ---- HYPERPARAMETERS ----
#>
#> No hyperparameters in the model
#> =======================================================================
#> DIC = 1555.1541 , WAIC = 1039.5909 , LCPO = 779.5896
#> Number of observations: 50
#> Number of Categories: 4Predicting for v1 = 0.25, v2 = 0.5, v3 = 0.5, v4 = 0.1
model.prediction <-
predict(model.inla,
data.pred = data.frame(v1 = 0.25,
v2 = 0.5,
v3 = 0.5,
v4 = 0.1))
#>
#>
#> ---------------------- Predicting -----------------
#>
#>
model.prediction$summary_predictive_means
#> $y1
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> [1,] 0.02366365 0.08238497 0.1044544 0.110075 0.1319717 0.3068168
#>
#> $y2
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> [1,] 0.005978457 0.02321143 0.0308166 0.03341506 0.0405673 0.1574295
#>
#> $y3
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> [1,] 0.238645 0.4919207 0.5581122 0.555305 0.6211048 0.8617697
#>
#> $y4
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> [1,] 0.08145221 0.2405351 0.2951816 0.301205 0.3543549 0.6269677