# 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. ```r 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 ```r 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

smoothp function