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Extracting Efficiencies and MTRs

Source: vignettes/efficiency-extraction.Rmd
efficiency-extraction.Rmd

Overview

Once a metafrontier model has been fitted, a range of S3 methods are available to extract and inspect results. This vignette demonstrates all of them using a simple sfacross + LP example.

Setup: Fit a Model 

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

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
)

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

summary() — Full Model Summary

Prints the complete model output including group-specific SFA results, metafrontier coefficients (if available), and efficiency statistics by group.

summary(meta_lp)

efficiencies() — Firm-Level Efficiency and MTR Scores

Returns a data frame with one row per observation containing all efficiency estimates and metatechnology ratios. All estimators are available for all groupType values, though the exact columns vary slightly by model type.

eff <- efficiencies(meta_lp)
head(eff)

Column Reference

Column sfacross sfalcmcross sfaselectioncross
id ✓ ✓ ✓
group / Group_c ✓ ✓ ✓
u_g ✓ ✓ ✓
TE_group_JLMS ✓ ✓ ✓
TE_group_BC ✓ ✓ ✓
TE_group_BC_reciprocal ✓ ✓ ✓
uLB_g, uUB_g ✓ — —
m_g, TE_group_mode ✓ — —
PosteriorProb_c, PosteriorProb_c1 … — ✓ —
u_meta ✓ ✓ ✓
TE_meta_JLMS ✓ ✓ ✓
TE_meta_BC ✓ ✓ ✓
MTR_JLMS ✓ ✓ ✓
MTR_BC ✓ ✓ ✓

Subsetting by Group 

# All small farms
eff_small <- eff[eff$group == "small", ]

# Descriptive statistics
summary(eff_small[, c("TE_group_BC", "TE_meta_BC", "MTR_BC")])

# Group-level means
aggregate(cbind(TE_group_BC, TE_meta_BC, MTR_BC) ~ group, data = eff, FUN = mean)

Visualising the Distribution 

# MTR distribution by group (base R)
boxplot(MTR_BC ~ group, data = eff,
        main = "Metatechnology Ratio by Farm Size",
        xlab = "Group", ylab = "MTR (BC)",
        col  = c("#e8f5ef", "#b2dfdb", "#80cbc4"))

# Histogram of TE_meta_BC
hist(eff$TE_meta_BC, breaks = 30,
     main = "Distribution of Metafrontier TE",
     xlab = "TE_meta_BC", col = "#2d8f65", border = "white")

coef() — Estimated Coefficients

Returns the metafrontier coefficient vector (for QP and SFA methods; NULL for LP).

# First fit a QP model
meta_qp <- sfametafrontier(
  formula    = log(PROD) ~ log(AREA) + log(LABOR) + log(NPK),
  data       = ricephil, group = "group", S = 1, udist = "hnormal",
  groupType  = "sfacross", metaMethod = "qp"
)
coef(meta_qp)

vcov() — Variance-Covariance Matrix

Returns the variance-covariance matrix of the metafrontier coefficients (for models that estimate metafrontier parameters).

vcov(meta_qp)

logLik() — Log-Likelihood

Returns the total log-likelihood value of the model (sum of group-level log-likelihoods plus the metafrontier log-likelihood where applicable).

logLik(meta_lp)

ic() — Information Criteria

Returns all three information criteria: AIC, BIC, and HQIC.

ic(meta_lp)
#>        AIC       BIC      HQIC
#> 1  184.579  253.710   212.113

nobs() — Number of Observations 

nobs(meta_lp)  # Total observations across all groups

fitted() — Fitted Values

Returns the fitted frontier values from the model.

fv <- fitted(meta_lp)
head(fv)

residuals() — Residuals

Returns the composite error residuals from the group-level stochastic frontier models.

res <- residuals(meta_lp)
head(res)

Comparing Multiple Models

You can compare information criteria across methods to select the best model:

meta_lp    <- sfametafrontier(log(PROD) ~ log(AREA) + log(LABOR) + log(NPK),
                               data = ricephil, group = "group", S = 1,
                               udist = "hnormal", groupType = "sfacross",
                               metaMethod = "lp")
meta_qp    <- sfametafrontier(log(PROD) ~ log(AREA) + log(LABOR) + log(NPK),
                               data = ricephil, group = "group", S = 1,
                               udist = "hnormal", groupType = "sfacross",
                               metaMethod = "qp")
meta_huang <- sfametafrontier(log(PROD) ~ log(AREA) + log(LABOR) + log(NPK),
                               data = ricephil, group = "group", S = 1,
                               udist = "hnormal", groupType = "sfacross",
                               metaMethod = "sfa", sfaApproach = "huang")

# Combined information criteria table
models <- list(LP = meta_lp, QP = meta_qp, Huang = meta_huang)
do.call(rbind, lapply(names(models), function(nm) {
  ic_vals <- ic(models[[nm]])
  data.frame(Model = nm, AIC = ic_vals[["AIC"]],
             BIC = ic_vals[["BIC"]], HQIC = ic_vals[["HQIC"]])
}))