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Getting Started with metafrontieR

Source: vignettes/getting-started.Rmd
getting-started.Rmd

What is metafrontieR?

metafrontieR is an R package for implementing metafrontier analysis — a framework for productivity and performance benchmarking of firms (or farms, utilities, hospitals, etc.) that operate under different technologies. This is also referred to as “heterogeneous technology” analysis.

The classic stochastic frontier analysis (SFA) estimates a single frontier for all firms. Metafrontier analysis extends this by:

  1. Estimating group-specific frontiers for each technology sub-group.
  2. Estimating a common metafrontier that envelops all group frontiers.
  3. Computing metatechnology ratios (MTR), which quantify how far each group’s frontier lies below the best-practice metafrontier.

This allows researchers to disentangle:

  • Technical efficiency relative to the group’s own frontier (TE_group).
  • Metafrontier efficiency relative to the common best-practice frontier (TE_meta).
  • Technology gap ratio (MTR = TE_meta / TE_group), which captures how technologically advanced a group’s production possibilities are.

Conceptual Framework

MTRi=TE_metaiTE_groupi\text{MTR}_i = \frac{\text{TE\_meta}_i}{\text{TE\_group}_i}

A MTR close to 1 means the group’s technology is near the metafrontier (advanced technology). A MTR far below 1 means the group operates under a less advanced technology.

Methods Supported

metafrontieR supports four metafrontier estimation methods (metaMethod):

Method Description
"lp" Linear programming deterministic envelope — Battese, Rao & O’Donnell (2004)
"qp" Quadratic programming deterministic envelope
"sfa" (sfaApproach = "huang") Two-stage stochastic metafrontier — Huang, Huang & Liu (2014)
"sfa" (sfaApproach = "ordonnell") Two-stage SFA on LP envelope — O’Donnell, Rao & Battese (2008)

And three group frontier types (groupType):

Group Type When to Use
"sfacross" Technology groups are observed (e.g., a group variable exists)
"sfalcmcross" Technology groups are unobserved — latent class model identifies them
"sfaselectioncross" Sample selection bias is present (e.g., a binary selection indicator)

Installation 

# Install devtools if needed
if (!require("devtools")) install.packages("devtools")

# Install metafrontieR from GitHub
devtools::install_github("SulmanOlieko/metafrontieR")

Note: sfaR is automatically installed as a dependency — you do not need to install it separately.

Quick-Start Example

This minimal example demonstrates the core workflow using the ricephil dataset from the sfaR package, with three Filipino rice farm-size groups (small, medium, large).

Step 1: Load data and create groups 

library(metafrontieR)
data("ricephil", package = "sfaR")

# Create technology groups based on farm area terciles
ricephil$group <- cut(
  ricephil$AREA,
  breaks        = quantile(ricephil$AREA, probs = c(0, 1/3, 2/3, 1), na.rm = TRUE),
  labels        = c("small", "medium", "large"),
  include.lowest = TRUE
)
table(ricephil$group)

Step 2: Fit the metafrontier model 

meta_lp <- sfametafrontier(
  formula    = log(PROD) ~ log(AREA) + log(LABOR) + log(NPK),
  data       = ricephil,
  group      = "group",
  S          = 1,            # production frontier (S=1) or cost frontier (S=-1)
  udist      = "hnormal",
  groupType  = "sfacross",
  metaMethod = "lp"
)

Step 3: Summarise results 

summary(meta_lp)

Step 4: Extract firm-level efficiencies 

eff <- efficiencies(meta_lp)
head(eff)

Key output columns:

Column Description
TE_group_BC Group TE (Battese & Coelli 1988)
TE_meta_BC Metafrontier TE
MTR_BC Metatechnology ratio

What Next?