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Estimate a stochastic frontier production function using a maximum likelihood method.
sfa(x, y, beta0 = NULL, lambda0 = 1, resfun = ebeta,
TRANSPOSE = FALSE, DEBUG=FALSE,
control=list(), hessian=2)
te.sfa(object)
teBC.sfa(object)
teMode.sfa(object)
teJ.sfa(object)
te.add.sfa(object)
sigma2u.sfa(object)
sigma2v.sfa(object)
sigma2.sfa(object)
lambda.sfa(object)
Input as a K x m matrix of observations on m inputs from K firms; (firm x input); MUST be a matrix. No constant for the intercept should be included in x as it is added by default.
Output; K times 1 matrix (one output)
Optional initial parameter values
Optional initial ratio of variances
Function to calculate the residuals, default is a
linear model with an intercept. Must be called as
resfun(x,y,parm) where parm=c(beta,lambda) or
parm=c(beta), and return the residuals as an array of length
corresponding to the length of output y.
If TRUE, data is transposed, i.e. input is now m x K matrix
Set to TRUE to get various debugging information written on the console
List of control parameters to ucminf
How the Hessian is delivered, see the ucminf documentation
Object of class ‘sfa’ as output from the
function sfa
The values returned from sfa is the same as for ucminf,
i.e. a list with components plus some especially relevant for sfa:
The best set of parameters found c(beta,lambda).
The value of minus log-likelihood function corresponding to 'par'.
The parameters for the function
The estimate of the total variance
The estimate of lambda
The number of observations
The degrees of freedom for the model
The residuals as a K times 1 matrix/vector,
can also be obtained by residuals(sfa-object)
Fitted values
The variance-covarians matrix for all estimated parameters incl. lambda
An integer code. '0' indicates successful
convergence. Some of the error codes taken from
ucminf are
'1' Stopped by small gradient (grtol).
'2' Stopped by small step (xtol).
'3' Stopped by function evaluation limit (maxeval).
'4' Stopped by zero step from line search
More codes are found in ucminf
A character string giving any additional information returned by the optimizer, or 'NULL'.
The object returned by ucminf, for further information
on this see ucminf
The optimization is done by the R method ucminf from
the package with the same name. The efficiency terms are assumed to
be half--normal distributed.
Changing the maximum steplength, the trust rgion, might be important, and this can be done by the option 'control= list(stepmax=0.1)'. The default value is 0.1 and that value is suitable for parameters around 1; for smaller parameters a lower value should be used. Notice that the step length is updated by the optimizing program and thus must be set for every call of the function sfa if it is to be set.
The generic functions print.sfa, summary.sfa,
fitted.sfa, residuals.sfa, logLik.sfa, and
coef.sfa all work as expected.
The methods te.sfa, teMode.sfa etc. calculates the
efficiency corresponding to different methods
Bogetoft and Otto; Benchmarking with DEA, SFA, and R, Springer 2011; chapters 7 and 8.
See the method ucminf for the possible optimization
methods and further options to use in the option control.
The method sfa in the package frontier gives another
way to estimate stochastic production functions.
# NOT RUN {
# Example from the book by Coelli et al.
# d <- read.csv("c:/0work/rpack/front41Data.csv", header = TRUE, sep = ",")
# x <- cbind(log(d$capital), log(d$labour))
# y <- matrix(log(d$output))
n <- 50
x1 <- 1:50 + rnorm(50,0,10)
x2 <- 100 + rnorm(50,0,10)
x <- cbind(x1,x2)
y <- 0.5 + 1.5*x1 + 2*x2 + rnorm(n,0,1) - pmax(0,rnorm(n,0,1))
sfa(x,y)
summary(sfa(x,y))
# Estimate efficiency for each unit
o <- sfa(x,y)
eff(o)
te <- te.sfa(o)
teM <- teMode.sfa(o)
teJ <- teJ.sfa(o)
cbind(eff(o),te,Mode=eff(o, type="Mode"),teM,teJ)[1:10,]
sigma2.sfa(o) # Estimated varians
lambda.sfa(o) # Estimated lambda
# }
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