smoothp function

smoothp

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.

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.

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')

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.

Author(s)

Carlos Alberto Cardozo Delgado cardozorpackages@gmail.com