| Title: | Fitting Nonlinear Models with Scale Mixture of Skew-Normal Distributions |
| Date: | 2020-12-22 |
| Version: | 0.0-6 |
| Description: | Fit univariate non-linear scale mixture of skew-normal(NL-SMSN) regression, details in Garay, Lachos and Abanto-Valle (2011) <doi:10.1016/j.jkss.2010.08.003> and Lachos, Bandyopadhyay and Garay (2011) <doi:10.1016/j.spl.2011.03.019>. |
| Depends: | R (≥ 2.10.0) |
| Author: | Marcos Prates [aut, cre, trl], Victor Lachos [aut], Aldo Garay [aut] |
| Maintainer: | Marcos Prates <marcosop@est.ufmg.br> |
| License: | GPL (≥ 3.0) |
| Packaged: | 2020-12-22 18:11:42 UTC; marcos |
| Repository: | CRAN |
| NeedsCompilation: | no |
| Date/Publication: | 2021-01-20 18:10:02 UTC |
Oil palm yield
Description
Growth and yield of palm oil
Usage
data(Oil)Format
A data frame with 19 observations of oil characteristics
Author(s)
Aldo Garay amedina@ime.usp.br, Marcos Prates marcosop@est.ufmg.br and Victor Lachos hlachos@ime.unicamp.br
Source
Aldo M. Garay, Victor H. Lachos, Carlos A. Abanto-Valle (2011). "Nonlinear regression models based on scale mixture of skew-normal distributions". Journal of the Korean Stastical Society, 40, 115-124.
Examples
## Not run:
##Load the data
data(Oil)
##Define non linear function
nlf<-function(x,betas){
resp<- betas[1]/(1 +betas[2]*exp(-betas[3]*x))
return(resp)
}
##Set the response y and covariate x
y <- Oil$y
x <- Oil$x
##Set initial values
betas <- c(37,4.81,0.78)
sigma2 <- 2.95
shape <- -2
nu <- 3
## Skew.normal regression
analysis.sn <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2,
shape = shape, nlf = nlf, criteria = TRUE,
family = "Skew.normal", iter.max = 200)
## Skew.t regression
analysis.st <- smsn.nl(y=y, x=x, betas=betas, sigma2=sigma2, shape = shape,
nu = nu, nlf = nlf, criteria = TRUE,
family = "Skew.t", iter.max = 200)
## End(Not run)
Ultrasonic Calibration
Description
The data is a result of a ultrasonic calibration study perfomed by National Institute of Standard and Technology.
Usage
data(Ultrasonic)Format
A data frame with 214 observations with y as the ultrasonic measuraments and x the metal distance
Author(s)
Aldo Garay amedina@ime.usp.br, Marcos Prates marcosop@est.ufmg.br and Victor Lachos hlachos@ime.unicamp.br
Source
Victor H. Lachos, Dipankar Bandyopadhyay and Aldo M. Garay (2011). "Heteroscedastic nonlinear regression models based on scale mixture of skew-normal distributions". Statistics -and Probability Letters, 81, 1208-1217.
Examples
## Not run:
##Load the data
data(Ultrasonic)
##Define non linear function
nlf<-function(x,betas){
resp<- exp(-betas[1]*x)/(betas[2] + betas[3]*x)
return(resp)
}
##Set the response y and covariate x
y <- Ultrasonic$y
x <- Ultrasonic$x
##Set initial values
z <- x
betas <- c(0.1913, 0.0061, 0.0110)
rho <- -0.1
sigma2 <- 3.2726
shape <- 0.1698
nu <- 4
## Skew.normal regression
analysis.sn <- smsn.nl(y = y, x = x, z = z, betas = betas, sigma2 = sigma2, shape = shape,
rho = rho, nlf = nlf, rho.func = 2, reg.type = "Heteroscedastic",
criteria = TRUE, family = "Skew.normal", iter.max = 200)
## Skew.t regression
analysis.st <- smsn.nl(y = y, x = x, z = z, betas = betas, sigma2 = sigma2, shape = shape, nu = nu,
rho = rho, nlf = nlf, rho.func = 1, reg.type = "He",
criteria = TRUE, family = "Skew.t", iter.max = 200)
## End(Not run)
Fit univariate NL-SMSN regression
Description
Return EM algorithm output for NL-SMSN regression for both "Homoscedastic" and "Heteroscedastic" (univaritate case, p=1).
Usage
smsn.nl(y, x = NULL, z = NULL, betas = NULL, sigma2 = NULL,
shape = NULL, rho = NULL,
nu = NULL, nlf = NULL, rho.func = 1,
reg.type = "Homoscedastic", criteria = FALSE,
family = "Skew.t", error = 1e-05, iter.max = 100)
Arguments
y |
the response vector |
x |
the independent covariates |
z |
the independent covariates for sigma2. "Heteroscedastic" model ONLY! |
betas |
regression coefficient(s) vector |
sigma2 |
initial value for the scale parameter |
shape |
initial value for the skewness parameter |
rho |
initial value for "Heteroscedastic" coefficient rho. "Heteroscedastic" model ONLY! |
nu |
the parameter of the scale variable (vector or scalar) of the SMSN family (kurtosis parameter). For the "Skew.cn" must be a vector of length 2 and values in (0,1) |
nlf |
non linear function for the regression |
rho.func |
Choose the type of heteroscedasticity for sigma2. If rho.func == 1 ( f(z,rho) = exp(z*rho) ) and rho.func == 2 ( f(z,rho) = z^rho ). |
reg.type |
the type of possible regression: "Homoscedastic" or "Ho"; "Heteroscedastic" or "He". |
criteria |
if TRUE, loglik, AIC, BIC will be calculated |
family |
distribution famility to be used in fitting ("t", "Skew.t", "Skew.cn", "Skew.slash", "Skew.normal", "Normal") |
error |
the covergence maximum error |
iter.max |
maximum iterations of the EM algorithm |
Value
Estimated values of the location, scale, skewness, regression coefficients and "Heteroscedastic" coefficient (when reg.type = "He").
Author(s)
Aldo Garay amedina@ime.usp.br, Marcos Prates marcosop@est.ufmg.br and Victor Lachos hlachos@ime.unicamp.br
References
Aldo M. Garay, Victor H. Lachos, Carlos A. Abanto-Valle (2011). "Nonlinear regression models based on scale mixture of skew-normal distributions". Journal of the Korean Stastical Society, 40, 115-124.\
Victor H. Lachos, Dipankar Bandyopadhyay and Aldo M. Garay (2011). "Heteroscedastic nonlinear regression models based on scale mixture of skew-normal distributions". Statistics -and Probability Letters, 81, 1208-1217.
Examples
##see examples in \code{\link{Oil}} and \code{\link{Ultrasonic}}