The goal of acmvup is to provide some useful functions that are implemented following the additive covariance modeling via unconstrained parametrization idea. You will find more detail in my master thesis.
You can install the released version of acmvup from Github with:
library("devtools")
install_github("PeppeSaccardi/acmvup")This is a basic example which shows you how to compute the log-likelihood function value, gradient and hessian
library(acmvup)
set.seed(1234)
# Let generate synthetic data, using p = 3
data <- matrix(rnorm(300), ncol=3)
# Then we need the lists containing the covariates for all the
# unconstrained parameters that we want to model
lista_d <- list()
lista_phi <- list()
lista_d[[1]] <- matrix(c(rep(1,100),rnorm(100)), byrow = FALSE, ncol=2)
lista_d[[2]] <- matrix(c(rep(1,100),rnorm(200)), byrow = FALSE, ncol=3)
lista_d[[3]] <- matrix(rep(1,100), byrow = FALSE, ncol=1)
lista_phi[[1]] <- matrix(c(rep(1,100),rnorm(200)),byrow = FALSE, ncol=3)
lista_phi[[2]] <- matrix(rep(1,100),ncol=1)
lista_phi[[3]] <- matrix(c(rep(1,100),rnorm(100)),byrow = FALSE, ncol=2)Now we are able to use the functions implemented in the package to compute the log-likelihood function value, gradient and hessian, for instance in a suitable random point
par <- rnorm(12)
ll <- optimal_loglik(par,data,lista_phi,lista_d)
gll <- optimal_grad(par,data,lista_phi,lista_d)
hll <- optimal_hessian(par,data,lista_phi,lista_d)Therefore for our example
print(paste0("The log-likelihood value is ",ll))
#> [1] "The log-likelihood value is -1082.81516785296"
print("The gradient vector is ")
#> [1] "The gradient vector is "
gll
#> [1] 380.3925537 51.8455975 167.4419360 -215.2302577 71.1800255
#> [6] -206.7230241 -17.9633814 0.5270398 725.7886307 503.6839641
#> [11] -266.7740084 262.2474045
print("The hessian matrix is ")
#> [1] "The hessian matrix is "
hll
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] -129.213953 -10.32009 3.795308 0.000000 0.000000 0.00000
#> [2,] -10.320090 -97.83978 28.219271 0.000000 0.000000 0.00000
#> [3,] 3.795308 28.21927 -127.188731 0.000000 0.000000 0.00000
#> [4,] 0.000000 0.00000 0.000000 -309.969137 9.849759 -13.36294
#> [5,] 0.000000 0.00000 0.000000 9.849759 -320.007963 -51.85966
#> [6,] 0.000000 0.00000 0.000000 -13.362941 -51.859657 -246.46343
#> [7,] 0.000000 0.00000 0.000000 0.000000 0.000000 0.00000
#> [8,] 0.000000 0.00000 0.000000 0.000000 0.000000 0.00000
#> [9,] -380.392554 -51.84560 -167.441936 0.000000 0.000000 0.00000
#> [10,] -223.845450 -106.43793 -107.343399 0.000000 0.000000 0.00000
#> [11,] 112.712387 47.58699 16.062310 0.000000 0.000000 0.00000
#> [12,] 0.000000 0.00000 0.000000 215.230258 -71.180026 206.72302
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.000000 0.000000 -380.3926 -223.8454 112.71239 0.00000
#> [2,] 0.000000 0.000000 -51.8456 -106.4379 47.58699 0.00000
#> [3,] 0.000000 0.000000 -167.4419 -107.3434 16.06231 0.00000
#> [4,] 0.000000 0.000000 0.0000 0.0000 0.00000 215.23026
#> [5,] 0.000000 0.000000 0.0000 0.0000 0.00000 -71.18003
#> [6,] 0.000000 0.000000 0.0000 0.0000 0.00000 206.72302
#> [7,] -32.036619 -0.121783 0.0000 0.0000 0.00000 0.00000
#> [8,] -0.121783 -36.842355 0.0000 0.0000 0.00000 0.00000
#> [9,] 0.000000 0.000000 -775.7886 -502.5947 273.61786 0.00000
#> [10,] 0.000000 0.000000 -502.5947 -1196.5624 352.93666 0.00000
#> [11,] 0.000000 0.000000 273.6179 352.9367 -848.71568 0.00000
#> [12,] 0.000000 0.000000 0.0000 0.0000 0.00000 -312.24740