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README.md
In eat: Efficiency Analysis Trees
eat
The EAT algorithm performs a regression tree based on CART methodology
under a new approach that guarantees obtaining a frontier as estimator
that fulfills the property of free disposability. This new technique has
been baptized as Efficiency Analysis Trees. Some of its main functions
are:
-
To create homogeneous groups of DMUs in terms of their inputs and to
know for each of these groups, what is the maximum expected output.
-
To know which DMUs exercise best practices and which of them do not
obtain a performance according to their resources level.
-
To know what variables are more relevant in obtaining efficient
levels of output.
Installation
You can install the released version of eat from
CRAN with:
install.packages("eat")
And the development version from
GitHub with:
devtools::install_github("MiriamEsteve/EAT")
Example
library(eat)
data("PISAindex")
- EAT model with 1 input (
NBMC) and 1 output (S_PISA)
single_model <- EAT(data = PISAindex,
x = 15, # input
y = 3) # output
#> [conflicted] Will prefer dplyr::filter over any other package
- Print an
EAT object
print(single_model)
#> [1] y: [ 551 ] || R: 11507.5 n(t): 72
#>
#> | [2] PFC < 77.2 --> y: [ 478 ] || R: 2324.47 n(t): 34
#>
#> | | [4] PFC < 65.45 --> y: [ 428 ] <*> || R: 390.17 n(t): 16
#>
#> | | [5] PFC >= 65.45 --> y: [ 478 ] <*> || R: 637.08 n(t): 18
#>
#> | [3] PFC >= 77.2 --> y: [ 551 ] <*> || R: 2452.83 n(t): 38
#>
#> <*> is a leaf node
- Summary of an
EAT object
summary(single_model)
#>
#> Formula: S_PISA ~ PFC
#>
#> # ========================== #
#> # Summary for leaf nodes #
#> # ========================== #
#>
#> id n(t) % S_PISA R(t)
#> 3 38 53 551 2452.83
#> 4 16 22 428 390.17
#> 5 18 25 478 637.08
#>
#> # ========================== #
#> # Tree #
#> # ========================== #
#>
#> Interior nodes: 2
#> Leaf nodes: 3
#> Total nodes: 5
#>
#> R(T): 3480.08
#> numStop: 5
#> fold: 5
#> max.depth:
#> max.leaves:
#>
#> # ========================== #
#> # Primary & surrogate splits #
#> # ========================== #
#>
#> Node 1 --> {2,3} || PFC --> {R: 4777.31, s: 77.2}
#>
#> Node 2 --> {4,5} || PFC --> {R: 1027.25, s: 65.45}
- Number of leaf nodes of an
EAT object
size(single_model)
#> The number of leaf nodes of the EAT model is: 3
- Frontier levels of output for an
EAT object
frontier.levels(single_model)
#> The frontier levels of the outputs at the leaf nodes are:
#> S_PISA
#> 1 551
#> 2 428
#> 3 478
- Descriptive analysis for an
EAT object
descriptiveEAT <- descrEAT(single_model)
descriptiveEAT
#> Node n(t) % mean var sd min Q1 median Q3 max RMSE
#> 1 1 72 100 455.06 2334.59 48.32 336 416.75 466.0 495.25 551 107.27
#> 2 2 34 47 416.88 1223.02 34.97 336 397.25 415.5 435.75 478 70.16
#> 3 3 38 53 489.21 851.95 29.19 419 478.00 494.0 504.50 551 68.17
#> 4 4 16 22 394.62 684.65 26.17 336 381.50 398.0 414.00 428 41.90
#> 5 5 18 25 436.67 889.29 29.82 386 415.25 433.5 468.00 478 50.48
- Plot the frontier
frontier(object = single_model,
FDH = TRUE,
observed.data = TRUE,
rwn = TRUE)
#> Warning: ggrepel: 8 unlabeled data points (too many overlaps). Consider
#> increasing max.overlaps
- EAT model with 13 inputs and 3 outputs
multioutput <- EAT(data = PISAindex,
x = 6:18,
y = 3:5)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, fold = fold, : Rows with NA values have been omitted .
- Ranking of importance of variables for EAT
rankingEAT(object = multioutput,
barplot = TRUE,
threshold = 70,
digits = 2)
#> $scores
#> Importance
#> AAE 100.00
#> WS 98.45
#> S 84.51
#> NBMC 83.37
#> HW 83.31
#> ABK 67.97
#> GDP_PPP 65.37
#> AIC 64.89
#> EQ 57.11
#> PR 57.05
#> I 57.05
#> PS 45.41
#> PFC 31.67
#>
#> $barplot
- Plot an EAT model
plotEAT(object = multioutput)
- Tuning an EAT model
n <- nrow(PISAindex) # Observations in the dataset
t_index <- sample(1:n, n * 0.7) # Training indexes
training <- PISAindex[t_index, ] # Training set
test <- PISAindex[-t_index, ] # Test set
bestEAT(training = training,
test = test,
x = 6:18,
y = 3:5,
numStop = c(5, 7, 10),
fold = c(5, 7))
#> Warning in preProcess(test, x, y, na.rm = na.rm): Rows with NA values have been omitted .
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> numStop fold RMSE leaves
#> 1 7 5 66.94 10
#> 2 7 7 66.94 10
#> 3 5 7 71.87 8
#> 4 5 5 84.60 7
#> 5 10 5 85.06 5
#> 6 10 7 85.06 5
- Efficiency scores EAT
single_model <- EAT(data = PISAindex,
x = 15, # input
y = 3) # output
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
scores_EAT <- efficiencyEAT(data = PISAindex,
x = 15,
y = 3,
object = single_model,
scores_model = "BCC.OUT",
digits = 3,
FDH = TRUE)
#> EAT_BCC_OUT FDH_BCC_OUT
#> SGP 1.000 1.000
#> JPN 1.042 1.000
#> KOR 1.062 1.000
#> EST 1.040 1.000
#> NLD 1.095 1.095
#> POL 1.078 1.000
#> CHE 1.113 1.113
#> CAN 1.064 1.064
#> DNK 1.118 1.118
#> SVN 1.087 1.024
#> BEL 1.104 1.062
#> FIN 1.056 1.056
#> SWE 1.104 1.104
#> GBR 1.091 1.091
#> NOR 1.124 1.124
#> DEU 1.095 1.095
#> IRL 1.111 1.069
#> AUT 1.124 1.082
#> CZE 1.109 1.044
#> LVA 1.131 1.066
#> FRA 1.118 1.075
#> ISL 1.160 1.116
#> NZL 1.085 1.043
#> PRT 1.120 1.055
#> AUS 1.095 1.054
#> RUS 1.000 1.000
#> ITA 1.021 1.021
#> SVK 1.187 1.037
#> LUX 1.155 1.155
#> HUN 1.146 1.000
#> LTU 1.143 1.060
#> ESP 1.141 1.075
#> USA 1.098 1.056
#> BLR 1.015 1.015
#> MLT 1.193 1.106
#> HRV 1.006 1.006
#> ISR 1.193 1.106
#> TUR 1.021 1.000
#> UKR 1.019 1.000
#> CYP 1.255 1.182
#> GRC 1.058 1.058
#> SRB 1.086 1.000
#> MYS 1.091 1.068
#> ALB 1.026 1.000
#> BGR 1.127 1.127
#> ARE 1.270 1.177
#> MNE 1.152 1.128
#> ROU 1.122 1.122
#> KAZ 1.204 1.179
#> MDA 1.000 1.000
#> AZE 1.075 1.048
#> THA 1.005 1.005
#> URY 1.293 1.200
#> CHL 1.241 1.169
#> QAT 1.315 1.239
#> MEX 1.021 1.021
#> BIH 1.075 1.048
#> CRI 1.149 1.149
#> JOR 1.114 1.093
#> PER 1.059 1.032
#> GEO 1.117 1.089
#> MKD 1.036 1.036
#> LBN 1.115 1.115
#> COL 1.036 1.036
#> BRA 1.183 1.158
#> ARG 1.183 1.158
#> IDN 1.081 1.081
#> SAU 1.238 1.215
#> MAR 1.135 1.135
#> PAN 1.173 1.173
#> PHL 1.199 1.168
#> DOM 1.274 1.241
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> EAT 1.114 0.074 1 1.061 1.110 1.110 1.315
#> FDH 1.081 0.065 1 1.030 1.069 1.069 1.241
- Efficiency scores CEAT
scores_CEAT <- efficiencyCEAT(data = PISAindex,
x = 15,
y = 3,
object = single_model,
scores_model = "BCC.INP",
digits = 3,
DEA = TRUE)
#> CEAT_BCC_INP DEA_BCC_INP
#> SGP 0.878 1.000
#> JPN 0.872 0.986
#> KOR 0.878 0.989
#> EST 0.857 0.969
#> NLD 0.736 0.824
#> POL 0.862 0.968
#> CHE 0.697 0.777
#> CAN 0.768 0.865
#> DNK 0.693 0.772
#> SVN 0.821 0.920
#> BEL 0.735 0.821
#> FIN 0.787 0.888
#> SWE 0.724 0.809
#> GBR 0.750 0.840
#> NOR 0.680 0.757
#> DEU 0.723 0.809
#> IRL 0.731 0.816
#> AUT 0.712 0.792
#> CZE 0.788 0.880
#> LVA 0.758 0.843
#> FRA 0.725 0.808
#> ISL 0.669 0.739
#> NZL 0.769 0.862
#> PRT 0.776 0.865
#> AUS 0.754 0.845
#> RUS 0.846 0.936
#> ITA 0.756 0.832
#> SVK 0.717 0.787
#> LUX 0.660 0.729
#> HUN 0.779 0.864
#> LTU 0.768 0.851
#> ESP 0.755 0.838
#> USA 0.756 0.846
#> BLR 0.750 0.826
#> MLT 0.703 0.771
#> HRV 0.792 0.875
#> ISR 0.703 0.771
#> TUR 0.866 0.953
#> UKR 0.831 0.916
#> CYP 0.628 0.678
#> GRC 0.754 0.822
#> SRB 0.767 0.829
#> MYS 0.734 0.792
#> ALB 1.000 1.000
#> BGR 0.661 0.691
#> ARE 0.616 0.663
#> MNE 0.698 0.698
#> ROU 0.662 0.701
#> KAZ 0.696 0.696
#> MDA 0.771 0.825
#> AZE 0.967 0.967
#> THA 0.744 0.787
#> URY 0.602 0.637
#> CHL 0.638 0.692
#> QAT 0.591 0.599
#> MEX 0.746 0.755
#> BIH 0.782 0.782
#> CRI 0.615 0.615
#> JOR 0.682 0.731
#> PER 0.795 0.795
#> GEO 0.798 0.798
#> MKD 0.768 0.768
#> LBN 0.735 0.735
#> COL 0.739 0.739
#> BRA 0.697 0.697
#> ARG 0.693 0.693
#> IDN 0.735 0.735
#> SAU 0.674 0.674
#> MAR 0.748 0.748
#> PAN 0.770 0.770
#> PHL 0.780 0.780
#> DOM 0.804 0.804
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> CEAT 0.749 0.077 0.591 0.698 0.749 0.749 1
#> DEA 0.805 0.094 0.599 0.739 0.801 0.801 1
- Efficiency jitter plot
efficiencyJitter(object = single_model,
df_scores = scores_EAT$EAT_BCC_OUT,
scores_model = "BCC.OUT",
lwb = 1.2)
- Efficiency density plot
efficiencyDensity(df_scores = scores_EAT[, 3:4],
model = c("EAT", "FDH"))
- RFEAT model
forest <- RFEAT(data = PISAindex,
x = 6:18, # input
y = 5, # output
numStop = 5,
m = 30,
s_mtry = "BRM",
na.rm = TRUE)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
- Print a
RFEAT object
print(forest)
#>
#> Formula: M_PISA ~ NBMC + WS + S + PS + ABK + AIC + HW + EQ + PR + PFC + I + AAE + GDP_PPP
#>
#> # ========================== #
#> # Forest #
#> # ========================== #
#>
#> Error: 738.42
#> numStop: 5
#> No. of trees (m): 30
#> No. of inputs tried (s_mtry): BRM
- Plot the Out-of-Bag error for a forest made up of k trees
plotRFEAT(forest)
- RFEAT ranking
rankingRFEAT(object = forest, barplot = TRUE,
digits = 2)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> $scores
#> Importance
#> PS 14.25
#> PR 14.08
#> AAE 13.97
#> EQ 11.86
#> S 10.80
#> HW 9.36
#> AIC 6.36
#> I 4.49
#> NBMC 3.26
#> WS -1.79
#> GDP_PPP -4.68
#> PFC -4.77
#> ABK -6.11
#>
#> $barplot
- Tuning a RFEAT model
bestRFEAT(training = training,
test = test,
x = 6:18,
y = 3:5,
numStop = c(5, 10),
m = c(30, 40),
s_mtry = c("BRM", "3"))
#> Warning in preProcess(test, x, y, na.rm = na.rm): Rows with NA values have been omitted .
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> numStop m s_mtry RMSE
#> 1 5 40 3 57.44
#> 2 5 40 BRM 57.72
#> 3 5 30 BRM 58.39
#> 4 5 30 3 59.13
#> 5 10 30 BRM 62.43
#> 6 10 40 BRM 63.18
#> 7 10 40 3 65.02
#> 8 10 30 3 68.43
- RFEAT scores
efficiencyRFEAT(data = PISAindex,
x = 6:18, # input
y = 5, # output
object = forest,
FDH = TRUE)
#> RFEAT_BCC_OUT FDH_BCC_OUT
#> SGP 0.936 1.000
#> JPN 1.024 1.000
#> KOR 1.004 1.000
#> EST 0.982 1.000
#> NLD 0.999 1.000
#> POL 0.982 1.000
#> CHE 1.026 1.002
#> CAN 1.010 1.008
#> DNK 1.017 1.014
#> SVN 1.004 1.000
#> BEL 1.006 1.000
#> FIN 1.021 1.018
#> SWE 1.029 1.028
#> GBR 1.019 1.000
#> NOR 1.039 1.030
#> DEU 1.028 1.032
#> IRL 1.031 1.032
#> AUT 1.024 1.034
#> CZE 1.014 1.000
#> LVA 0.997 1.000
#> FRA 1.037 1.000
#> ISL 1.070 1.042
#> NZL 1.048 1.045
#> PRT 0.995 1.000
#> AUS 1.054 1.051
#> RUS 0.963 1.000
#> ITA 1.011 1.000
#> SVK 0.997 1.000
#> LUX 1.053 1.000
#> HUN 1.008 1.000
#> LTU 1.020 1.000
#> ESP 1.030 1.000
#> USA 1.033 1.000
#> BLR 0.992 1.000
#> MLT 1.026 1.000
#> HRV 1.034 1.000
#> ISR 1.050 1.000
#> TUR 0.979 1.000
#> UKR 0.981 1.000
#> CYP 1.095 1.000
#> GRC 1.063 1.007
#> SRB 1.002 1.000
#> MYS 0.998 1.000
#> ALB 0.982 1.000
#> BGR 1.031 1.000
#> ARE 1.014 1.000
#> MNE 1.022 1.000
#> ROU 1.031 1.000
#> KAZ 1.018 1.000
#> MDA 1.003 1.000
#> AZE 0.972 1.000
#> THA 0.991 1.000
#> URY 1.045 1.000
#> CHL 1.097 1.005
#> QAT 1.070 1.000
#> MEX 1.005 1.000
#> BIH 1.042 1.000
#> CRI 1.085 1.000
#> JOR 1.046 1.000
#> PER 0.997 1.000
#> GEO 1.060 1.000
#> MKD 1.052 1.000
#> LBN 1.037 1.000
#> COL 1.055 1.000
#> BRA 1.074 1.000
#> ARG 1.157 1.000
#> IDN 1.034 1.000
#> SAU 1.100 1.000
#> MAR 1.031 1.000
#> PAN 1.116 1.000
#> PHL 1.049 1.000
#> DOM 1.145 1.000
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> RFEAT 1.029 0.039 0.936 1.003 1.026 1.026 1.157
#> FDH 1.005 0.012 1.000 1.000 1.000 1.000 1.051
- EAT and RFEAT predictions
input <- c(6, 7, 8, 12, 17)
output <- 3:5
EAT_model <- EAT(data = PISAindex, x = input, y = output)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, fold = fold, : Rows with NA values have been omitted .
RFEAT_model <- RFEAT(data = PISAindex, x = input, y = output)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, na.rm = na.rm): Rows with NA values have been omitted .
# PREDICTIONS
predictions_EAT <- predict(object = EAT_model, newdata = PISAindex[, input])
predictions_RFEAT <- predict(object = RFEAT_model, newdata = PISAindex[, input])
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eat
The EAT algorithm performs a regression tree based on CART methodology
under a new approach that guarantees obtaining a frontier as estimator
that fulfills the property of free disposability. This new technique has
been baptized as Efficiency Analysis Trees. Some of its main functions
are:
-
To create homogeneous groups of DMUs in terms of their inputs and to know for each of these groups, what is the maximum expected output.
-
To know which DMUs exercise best practices and which of them do not obtain a performance according to their resources level.
-
To know what variables are more relevant in obtaining efficient levels of output.
Installation
You can install the released version of eat from CRAN with:
install.packages("eat")
And the development version from GitHub with:
devtools::install_github("MiriamEsteve/EAT")
Example
library(eat)
data("PISAindex")
- EAT model with 1 input (
NBMC) and 1 output (S_PISA)
single_model <- EAT(data = PISAindex,
x = 15, # input
y = 3) # output
#> [conflicted] Will prefer dplyr::filter over any other package
- Print an
EATobject
print(single_model)
#> [1] y: [ 551 ] || R: 11507.5 n(t): 72
#>
#> | [2] PFC < 77.2 --> y: [ 478 ] || R: 2324.47 n(t): 34
#>
#> | | [4] PFC < 65.45 --> y: [ 428 ] <*> || R: 390.17 n(t): 16
#>
#> | | [5] PFC >= 65.45 --> y: [ 478 ] <*> || R: 637.08 n(t): 18
#>
#> | [3] PFC >= 77.2 --> y: [ 551 ] <*> || R: 2452.83 n(t): 38
#>
#> <*> is a leaf node
- Summary of an
EATobject
summary(single_model)
#>
#> Formula: S_PISA ~ PFC
#>
#> # ========================== #
#> # Summary for leaf nodes #
#> # ========================== #
#>
#> id n(t) % S_PISA R(t)
#> 3 38 53 551 2452.83
#> 4 16 22 428 390.17
#> 5 18 25 478 637.08
#>
#> # ========================== #
#> # Tree #
#> # ========================== #
#>
#> Interior nodes: 2
#> Leaf nodes: 3
#> Total nodes: 5
#>
#> R(T): 3480.08
#> numStop: 5
#> fold: 5
#> max.depth:
#> max.leaves:
#>
#> # ========================== #
#> # Primary & surrogate splits #
#> # ========================== #
#>
#> Node 1 --> {2,3} || PFC --> {R: 4777.31, s: 77.2}
#>
#> Node 2 --> {4,5} || PFC --> {R: 1027.25, s: 65.45}
- Number of leaf nodes of an
EATobject
size(single_model)
#> The number of leaf nodes of the EAT model is: 3
- Frontier levels of output for an
EATobject
frontier.levels(single_model)
#> The frontier levels of the outputs at the leaf nodes are:
#> S_PISA
#> 1 551
#> 2 428
#> 3 478
- Descriptive analysis for an
EATobject
descriptiveEAT <- descrEAT(single_model)
descriptiveEAT
#> Node n(t) % mean var sd min Q1 median Q3 max RMSE
#> 1 1 72 100 455.06 2334.59 48.32 336 416.75 466.0 495.25 551 107.27
#> 2 2 34 47 416.88 1223.02 34.97 336 397.25 415.5 435.75 478 70.16
#> 3 3 38 53 489.21 851.95 29.19 419 478.00 494.0 504.50 551 68.17
#> 4 4 16 22 394.62 684.65 26.17 336 381.50 398.0 414.00 428 41.90
#> 5 5 18 25 436.67 889.29 29.82 386 415.25 433.5 468.00 478 50.48
- Plot the frontier
frontier(object = single_model,
FDH = TRUE,
observed.data = TRUE,
rwn = TRUE)
#> Warning: ggrepel: 8 unlabeled data points (too many overlaps). Consider
#> increasing max.overlaps
- EAT model with 13 inputs and 3 outputs
multioutput <- EAT(data = PISAindex,
x = 6:18,
y = 3:5)
#> [conflicted] Removing existing preference
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#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, fold = fold, : Rows with NA values have been omitted .
- Ranking of importance of variables for EAT
rankingEAT(object = multioutput,
barplot = TRUE,
threshold = 70,
digits = 2)
#> $scores
#> Importance
#> AAE 100.00
#> WS 98.45
#> S 84.51
#> NBMC 83.37
#> HW 83.31
#> ABK 67.97
#> GDP_PPP 65.37
#> AIC 64.89
#> EQ 57.11
#> PR 57.05
#> I 57.05
#> PS 45.41
#> PFC 31.67
#>
#> $barplot
- Plot an EAT model
plotEAT(object = multioutput)
- Tuning an EAT model
n <- nrow(PISAindex) # Observations in the dataset
t_index <- sample(1:n, n * 0.7) # Training indexes
training <- PISAindex[t_index, ] # Training set
test <- PISAindex[-t_index, ] # Test set
bestEAT(training = training,
test = test,
x = 6:18,
y = 3:5,
numStop = c(5, 7, 10),
fold = c(5, 7))
#> Warning in preProcess(test, x, y, na.rm = na.rm): Rows with NA values have been omitted .
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#> numStop fold RMSE leaves
#> 1 7 5 66.94 10
#> 2 7 7 66.94 10
#> 3 5 7 71.87 8
#> 4 5 5 84.60 7
#> 5 10 5 85.06 5
#> 6 10 7 85.06 5
- Efficiency scores EAT
single_model <- EAT(data = PISAindex,
x = 15, # input
y = 3) # output
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scores_EAT <- efficiencyEAT(data = PISAindex,
x = 15,
y = 3,
object = single_model,
scores_model = "BCC.OUT",
digits = 3,
FDH = TRUE)
#> EAT_BCC_OUT FDH_BCC_OUT
#> SGP 1.000 1.000
#> JPN 1.042 1.000
#> KOR 1.062 1.000
#> EST 1.040 1.000
#> NLD 1.095 1.095
#> POL 1.078 1.000
#> CHE 1.113 1.113
#> CAN 1.064 1.064
#> DNK 1.118 1.118
#> SVN 1.087 1.024
#> BEL 1.104 1.062
#> FIN 1.056 1.056
#> SWE 1.104 1.104
#> GBR 1.091 1.091
#> NOR 1.124 1.124
#> DEU 1.095 1.095
#> IRL 1.111 1.069
#> AUT 1.124 1.082
#> CZE 1.109 1.044
#> LVA 1.131 1.066
#> FRA 1.118 1.075
#> ISL 1.160 1.116
#> NZL 1.085 1.043
#> PRT 1.120 1.055
#> AUS 1.095 1.054
#> RUS 1.000 1.000
#> ITA 1.021 1.021
#> SVK 1.187 1.037
#> LUX 1.155 1.155
#> HUN 1.146 1.000
#> LTU 1.143 1.060
#> ESP 1.141 1.075
#> USA 1.098 1.056
#> BLR 1.015 1.015
#> MLT 1.193 1.106
#> HRV 1.006 1.006
#> ISR 1.193 1.106
#> TUR 1.021 1.000
#> UKR 1.019 1.000
#> CYP 1.255 1.182
#> GRC 1.058 1.058
#> SRB 1.086 1.000
#> MYS 1.091 1.068
#> ALB 1.026 1.000
#> BGR 1.127 1.127
#> ARE 1.270 1.177
#> MNE 1.152 1.128
#> ROU 1.122 1.122
#> KAZ 1.204 1.179
#> MDA 1.000 1.000
#> AZE 1.075 1.048
#> THA 1.005 1.005
#> URY 1.293 1.200
#> CHL 1.241 1.169
#> QAT 1.315 1.239
#> MEX 1.021 1.021
#> BIH 1.075 1.048
#> CRI 1.149 1.149
#> JOR 1.114 1.093
#> PER 1.059 1.032
#> GEO 1.117 1.089
#> MKD 1.036 1.036
#> LBN 1.115 1.115
#> COL 1.036 1.036
#> BRA 1.183 1.158
#> ARG 1.183 1.158
#> IDN 1.081 1.081
#> SAU 1.238 1.215
#> MAR 1.135 1.135
#> PAN 1.173 1.173
#> PHL 1.199 1.168
#> DOM 1.274 1.241
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> EAT 1.114 0.074 1 1.061 1.110 1.110 1.315
#> FDH 1.081 0.065 1 1.030 1.069 1.069 1.241
- Efficiency scores CEAT
scores_CEAT <- efficiencyCEAT(data = PISAindex,
x = 15,
y = 3,
object = single_model,
scores_model = "BCC.INP",
digits = 3,
DEA = TRUE)
#> CEAT_BCC_INP DEA_BCC_INP
#> SGP 0.878 1.000
#> JPN 0.872 0.986
#> KOR 0.878 0.989
#> EST 0.857 0.969
#> NLD 0.736 0.824
#> POL 0.862 0.968
#> CHE 0.697 0.777
#> CAN 0.768 0.865
#> DNK 0.693 0.772
#> SVN 0.821 0.920
#> BEL 0.735 0.821
#> FIN 0.787 0.888
#> SWE 0.724 0.809
#> GBR 0.750 0.840
#> NOR 0.680 0.757
#> DEU 0.723 0.809
#> IRL 0.731 0.816
#> AUT 0.712 0.792
#> CZE 0.788 0.880
#> LVA 0.758 0.843
#> FRA 0.725 0.808
#> ISL 0.669 0.739
#> NZL 0.769 0.862
#> PRT 0.776 0.865
#> AUS 0.754 0.845
#> RUS 0.846 0.936
#> ITA 0.756 0.832
#> SVK 0.717 0.787
#> LUX 0.660 0.729
#> HUN 0.779 0.864
#> LTU 0.768 0.851
#> ESP 0.755 0.838
#> USA 0.756 0.846
#> BLR 0.750 0.826
#> MLT 0.703 0.771
#> HRV 0.792 0.875
#> ISR 0.703 0.771
#> TUR 0.866 0.953
#> UKR 0.831 0.916
#> CYP 0.628 0.678
#> GRC 0.754 0.822
#> SRB 0.767 0.829
#> MYS 0.734 0.792
#> ALB 1.000 1.000
#> BGR 0.661 0.691
#> ARE 0.616 0.663
#> MNE 0.698 0.698
#> ROU 0.662 0.701
#> KAZ 0.696 0.696
#> MDA 0.771 0.825
#> AZE 0.967 0.967
#> THA 0.744 0.787
#> URY 0.602 0.637
#> CHL 0.638 0.692
#> QAT 0.591 0.599
#> MEX 0.746 0.755
#> BIH 0.782 0.782
#> CRI 0.615 0.615
#> JOR 0.682 0.731
#> PER 0.795 0.795
#> GEO 0.798 0.798
#> MKD 0.768 0.768
#> LBN 0.735 0.735
#> COL 0.739 0.739
#> BRA 0.697 0.697
#> ARG 0.693 0.693
#> IDN 0.735 0.735
#> SAU 0.674 0.674
#> MAR 0.748 0.748
#> PAN 0.770 0.770
#> PHL 0.780 0.780
#> DOM 0.804 0.804
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> CEAT 0.749 0.077 0.591 0.698 0.749 0.749 1
#> DEA 0.805 0.094 0.599 0.739 0.801 0.801 1
- Efficiency jitter plot
efficiencyJitter(object = single_model,
df_scores = scores_EAT$EAT_BCC_OUT,
scores_model = "BCC.OUT",
lwb = 1.2)
- Efficiency density plot
efficiencyDensity(df_scores = scores_EAT[, 3:4],
model = c("EAT", "FDH"))
- RFEAT model
forest <- RFEAT(data = PISAindex,
x = 6:18, # input
y = 5, # output
numStop = 5,
m = 30,
s_mtry = "BRM",
na.rm = TRUE)
#> [conflicted] Removing existing preference
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- Print a
RFEATobject
print(forest)
#>
#> Formula: M_PISA ~ NBMC + WS + S + PS + ABK + AIC + HW + EQ + PR + PFC + I + AAE + GDP_PPP
#>
#> # ========================== #
#> # Forest #
#> # ========================== #
#>
#> Error: 738.42
#> numStop: 5
#> No. of trees (m): 30
#> No. of inputs tried (s_mtry): BRM
- Plot the Out-of-Bag error for a forest made up of k trees
plotRFEAT(forest)
- RFEAT ranking
rankingRFEAT(object = forest, barplot = TRUE,
digits = 2)
#> [conflicted] Removing existing preference
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#> $scores
#> Importance
#> PS 14.25
#> PR 14.08
#> AAE 13.97
#> EQ 11.86
#> S 10.80
#> HW 9.36
#> AIC 6.36
#> I 4.49
#> NBMC 3.26
#> WS -1.79
#> GDP_PPP -4.68
#> PFC -4.77
#> ABK -6.11
#>
#> $barplot
- Tuning a RFEAT model
bestRFEAT(training = training,
test = test,
x = 6:18,
y = 3:5,
numStop = c(5, 10),
m = c(30, 40),
s_mtry = c("BRM", "3"))
#> Warning in preProcess(test, x, y, na.rm = na.rm): Rows with NA values have been omitted .
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
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#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> [conflicted] Removing existing preference
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#> numStop m s_mtry RMSE
#> 1 5 40 3 57.44
#> 2 5 40 BRM 57.72
#> 3 5 30 BRM 58.39
#> 4 5 30 3 59.13
#> 5 10 30 BRM 62.43
#> 6 10 40 BRM 63.18
#> 7 10 40 3 65.02
#> 8 10 30 3 68.43
- RFEAT scores
efficiencyRFEAT(data = PISAindex,
x = 6:18, # input
y = 5, # output
object = forest,
FDH = TRUE)
#> RFEAT_BCC_OUT FDH_BCC_OUT
#> SGP 0.936 1.000
#> JPN 1.024 1.000
#> KOR 1.004 1.000
#> EST 0.982 1.000
#> NLD 0.999 1.000
#> POL 0.982 1.000
#> CHE 1.026 1.002
#> CAN 1.010 1.008
#> DNK 1.017 1.014
#> SVN 1.004 1.000
#> BEL 1.006 1.000
#> FIN 1.021 1.018
#> SWE 1.029 1.028
#> GBR 1.019 1.000
#> NOR 1.039 1.030
#> DEU 1.028 1.032
#> IRL 1.031 1.032
#> AUT 1.024 1.034
#> CZE 1.014 1.000
#> LVA 0.997 1.000
#> FRA 1.037 1.000
#> ISL 1.070 1.042
#> NZL 1.048 1.045
#> PRT 0.995 1.000
#> AUS 1.054 1.051
#> RUS 0.963 1.000
#> ITA 1.011 1.000
#> SVK 0.997 1.000
#> LUX 1.053 1.000
#> HUN 1.008 1.000
#> LTU 1.020 1.000
#> ESP 1.030 1.000
#> USA 1.033 1.000
#> BLR 0.992 1.000
#> MLT 1.026 1.000
#> HRV 1.034 1.000
#> ISR 1.050 1.000
#> TUR 0.979 1.000
#> UKR 0.981 1.000
#> CYP 1.095 1.000
#> GRC 1.063 1.007
#> SRB 1.002 1.000
#> MYS 0.998 1.000
#> ALB 0.982 1.000
#> BGR 1.031 1.000
#> ARE 1.014 1.000
#> MNE 1.022 1.000
#> ROU 1.031 1.000
#> KAZ 1.018 1.000
#> MDA 1.003 1.000
#> AZE 0.972 1.000
#> THA 0.991 1.000
#> URY 1.045 1.000
#> CHL 1.097 1.005
#> QAT 1.070 1.000
#> MEX 1.005 1.000
#> BIH 1.042 1.000
#> CRI 1.085 1.000
#> JOR 1.046 1.000
#> PER 0.997 1.000
#> GEO 1.060 1.000
#> MKD 1.052 1.000
#> LBN 1.037 1.000
#> COL 1.055 1.000
#> BRA 1.074 1.000
#> ARG 1.157 1.000
#> IDN 1.034 1.000
#> SAU 1.100 1.000
#> MAR 1.031 1.000
#> PAN 1.116 1.000
#> PHL 1.049 1.000
#> DOM 1.145 1.000
#>
#> Model Mean Std. Dev. Min Q1 Median Q3 Max
#> RFEAT 1.029 0.039 0.936 1.003 1.026 1.026 1.157
#> FDH 1.005 0.012 1.000 1.000 1.000 1.000 1.051
- EAT and RFEAT predictions
input <- c(6, 7, 8, 12, 17)
output <- 3:5
EAT_model <- EAT(data = PISAindex, x = input, y = output)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, fold = fold, : Rows with NA values have been omitted .
RFEAT_model <- RFEAT(data = PISAindex, x = input, y = output)
#> [conflicted] Removing existing preference
#> [conflicted] Will prefer dplyr::filter over any other package
#> Warning in preProcess(data = data, x = x, y = y, numStop = numStop, na.rm = na.rm): Rows with NA values have been omitted .
# PREDICTIONS
predictions_EAT <- predict(object = EAT_model, newdata = PISAindex[, input])
predictions_RFEAT <- predict(object = RFEAT_model, newdata = PISAindex[, input])
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