smoothp {sglg}

smoothp

Description

Tool that supports the selection of the smoothing parameters in semi-parametric generalized log-gamma models. The selection is based on the AIC, BIC, or Generalized Cross Validation methods.

Usage

smoothp(formula, npc, data, method = "PAIC", basis, interval, step)

Arguments

formula

a symbolic description of the systematic component of the model to be fitted.

npc

a data frame with potential nonparametric variables of the systematic part of the model to be fitted.

data

a data frame which contains the variables in the model.

method

There are three possible criteria to estimate the smoothing parameters: Penalized Akaike Criterion 'PAIC', Penalized Bayesian Criterion 'PBIC' and Generalized Cross Validation 'GCV'. The default method is 'PAIC'.

basis

a name of the cubic spline basis to be used in the model. Supported basis include deBoor and Gu basis.

interval

an optional numerical vector of length 2. In this interval is the maximum likelihood estimate of the shape parameter of the model. By default is [0.1,2].

step

an optional positive value. This parameter represents the length of the step of the partition of the interval parameter. By default is 0.2.

Author(s)

Carlos Alberto Cardozo Delgado <[e-mail]>

References

Carlos Alberto Cardozo Delgado, Semi-parametric generalized log-gamma regression models. Ph.D. thesis. Sao Paulo University.

Cardozo C.A., Paula G., and Vanegas L. (2022). Generalized log-gamma additive partial linear models with P-spline smoothing. Statistical Papers.

Examples

set.seed(1)
rows<- 150
t_beta <- c(0.5,2)
t_sigma <- 0.5
t_lambda <- 1
x1 <- runif(rows,-3,3)
x2 <- rbinom(rows,1,0.5)
X <- cbind(x1,x2)
t <- as.matrix((2*1:rows - 1)/(2*rows))
colnames(t) <- "t"
f_t <- cos(4*pi*t)
error <- rglg(rows,0,1,t_lambda)
y <- X %*%t_beta + f_t + t_sigma*error
colnames(y) <- "y"
data <- data.frame(y,X,t)
fit1 <- sglg(y ~ x1 + x2 - 1,npc=t,data=data,basis = "deBoor",alpha0=1)
fit1$AIC
# We can get (probably) better values of alpha with the function smoothp
smoothp(y ~ x1 + x2 - 1,npc=t,data=data,basis = "deBoor")
fit2 <- sglg(y ~ x1 + x2 - 1,npc=t,data=data,basis = "Gu",alpha0=0.5)
fit2$BIC
# Again using the smooth function
smoothp(y ~ x1 + x2 - 1,npc=t,data=data,basis = "Gu",method='PBIC')
#################################################
# An example with two non-parametric components #
#################################################
set.seed(2)
t_2 <- as.matrix(rnorm(rows,sd=0.5))
colnames(t_2) <- 't_2'
f_t_2 <- exp(t_2)
error <- rglg(rows,0,1,t_lambda)
y_2 <- X %*%t_beta + f_t + f_t_2 + t_sigma*error
colnames(y_2) <- 'y_2'
data2 <- data.frame(y_2,X,t,t_2)
npcs <- cbind(t,t_2)
# Some intuition about the best alpha values
smoothp(y ~ x1 + x2 - 1,npc=npcs,data=data, method='GCV')