sfm: sfm
In sfa: Stochastic Frontier Analysis

sfm	R Documentation

sfm

Description

Implementation of the cross-sectional stochastic frontier model across an array of distributional assumptions for both v and u (user specified). For panel models, see the psfm() call.

Usage

sfm(formula, model_name, data,maxit.bobyqa,maxit.psoptim,maxit.optim,REPORT,
trace,pgtol,start_val,PSopt,optHessian,inefdec,upper,Method,eta,alpha,verbose=FALSE,
rand.psoptim=NULL)

Arguments

`formula`	a symbolic description for the model to be estimated
`model_name`	model name for the estimation includes the: normal-half normal (NHN), normal-exponential (NE), student's t-half t (THT), Normal-Rayleigh (NR), and the normal-truncated normal (NTN).
`data`	A data set
`maxit.bobyqa`	Maximum number of iterations for the bobyqa optimization routine
`maxit.psoptim`	Maximum number of iterations for the psoptim optimization routine
`maxit.optim`	Maximum number of iterations for the optim optimization routine
`REPORT`	reporting parameter
`trace`	trace
`pgtol`	pgtol
`start_val`	starting value (optional)
`PSopt`	use psoptim optimization routine (T or F)
`optHessian`	Logical. Should a numerically differentiated Hessian matrix be returned while using the optim routine? (for optim routine)
`inefdec`	Production or cost function
`upper`	Vector of upper values for the optim package.
`Method`	The method to be used for optim. See 'Details' within optim.
`eta`	Parameter used for psi-divergence.
`alpha`	Parameter used for MDPD.
`verbose`	Logical. Print optimization progress messages? Default is `FALSE`.
`rand.psoptim`	Integer. seed for replication of psoptim. Default to `NULL`.

Details

The options include the Normal-Half Normal (NHN), Normal-exponential (NE), Student's t-Half t (THT), and the Normal-Truncated Normal (NTN). NHN_Z and NE_Z are extensions for the NHN and NE models that allow for modeling the u-component of those models with determinants of inefficiency.

Outputs include E[exp(-u)|e] given by exp_u_hat, following Battese and Coelli (1988, JoE), where appropriate.

Value

An object of class "sfareg" containing the following components:

`out`	A matrix with parameter estimates, standard errors, and t-values.
`opt`	A list containing the optimization results from the final optimization procedure.
`total_time`	The total computation time for model estimation.
`start_v`	The starting values used in the optimization.
`model_name`	The name of the stochastic frontier model estimated.
`formula`	The formula used in the model specification.
`exp_u_hat`	Predicted technical efficiency (expected values). Available for models: NHN, NHN_Z, NR, NG, and NNAK.
`med_u_hat`	Predicted technical efficiency (median values). Available only for the NHN model.
`coefficients`	A vector of estimated parameters.
`std.errors`	A vector of standard errors for the estimated parameters (NA if `optHessian = FALSE`).
`t.values`	A vector of t-values for the estimated parameters (NA if `optHessian = FALSE`).
`call`	The matched call.

Note

Standard errors require optHessian set to TRUE

Author(s)

David H. Bernstein and Alexander Stead

Examples


library(sfa)     

cs_data_trial   <- data_gen_cs(N= 1000, rand   = 1,  sig_u  = 0.3, sig_v  = 0.3, 
cons   = 0.5,       beta1  = 0.5,   beta2  = 0.5, a      = 4, mu     = 1)

cs.nhnz     <-  sfm(formula    = y_pcs_z ~ x1 +x2| z,    model_name = "NHN",                  
                    data       = cs_data_trial,          PSopt      = TRUE)

sfa documentation built on Jan. 22, 2026, 1:08 a.m.