maxLik package to perform its estimations.
sgt.mle(X.f, mu.f = mu ~ mu, sigma.f = sigma ~ sigma,
lambda.f = lambda ~ lambda, p.f = p ~ p, q.f = q ~ q,
data = parent.frame(), start, subset,
method = c("Nelder-Mead", "BFGS"), itnmax = NULL,
hessian.method="Richardson",
gradient.method="Richardson",
mean.cent = TRUE, var.adj = TRUE, ...)X should be on the left-hand side and the right-hand side should be the data or function of the data that should be used.mu, sigma, lambda, p, and q should be on the left-hand side of these formulas respectively.formula and weights. Can also be a list or an environment.optimx function in the optimx package. See ?optimx for a list of methods that can be used.
Note that the method that achieves the highest log-likelihood value is the method that is printed and reported.
The default method is to use both "Nelder-Mead" and the "BFGS" methods.method, gives the maximum number of iterations or function values for the corresponding method. If a single number is provided, this will be used for all methods.hessian function in the numDeriv package. See ?hessian for details.grad function in the numDeriv package. See ?grad for details.?dsgt).control argument in the optimx function in the optimx package. See ?optimx for a list of arguments that can be used in the control argument.sgt.mle returns a list of class "sgtest".
A list of class "sgtest" has the following components:
convcode returned from the optimx function in the optimx package of the method that achieved the greatest log-likelihood value. See ?optimx for the different convcode values.data.frame of class "optimx" that contains the results of the optimx maximization for every method (not just the method that achieved the highest log-likelihood value). See ?optimx for details.start. If there is a name of a parameter or some data found on the right-hand side of one of the formulas but not found in data and not found in start, then an error is given.
This function simply uses the optimx function in the optimx package to maximize the skewed generalized t distribution log-likelihood function. It takes the method that returned the highest log-likelihood, and saves these results as the final estimates.
optimx package and its documentation. The sgt.mle simply uses its functions to maximize the skewed generalized t log-likelihood. Also, the sgt.mle function uses the numDeriv package to compute the final hessian and gradients of the estimates.
# SINGLE VARIABLE ESTIMATION:
### generate random variable
set.seed(7900)
n = 1000
x = rsgt(n, mu = 2, sigma = 2, lambda = -0.25, p = 1.7, q = 7)
### Get starting values and estimate the parameter values
start = list(mu = 0, sigma = 1, lambda = 0, p = 2, q = 10)
result = sgt.mle(X.f = ~ x, start = start, method = "nlminb")
print(result)
print(summary(result))
# REGRESSION MODEL ESTIMATION:
### Generate Random Data
set.seed(1253)
n = 1000
x1 = rnorm(n)
x2 = runif(n)
y = 1 + 2*x1 + 3*x2 + rnorm(n)
data = as.data.frame(cbind(y, x1, x2))
### Estimate Linear Regression Model
reg = lm(y ~ x1 + x2, data = data)
coef = as.numeric(reg$coefficients)
rmse = summary(reg)$sigma
start = c(b0 = coef[1], b1 = coef[2], b2 = coef[3],
g0 = log(rmse)+log(2)/2, g1 = 0, g2 = 0, d0 = 0,
d1 = 0, d2 = 0, p = 2, q = 10)
### Set up Model
X.f = X ~ y - (b0 + b1*x1 + b2*x2)
mu.f = mu ~ 0
sigma.f = sigma ~ exp(g0 + g1*x1 + g2*x2)
lambda.f = lambda ~ (exp(d0 + d1*x1 + d2*x2)-1)/(exp(d0 + d1*x1 + d2*x2)+1)
### Estimate Regression with a skewed generalized t error term
### This estimates the regression model from the Davis,
### McDonald, and Walton (2015) paper cited in the references section
### q is in reality infinite since the error term is normal
result = sgt.mle(X.f = X.f, mu.f = mu.f, sigma.f = sigma.f,
lambda.f = lambda.f, data = data, start = start,
var.adj = FALSE, method = "nlm")
print(result)
print(summary(result))
Run the code above in your browser using DataLab