lowe: Lowe productivity and profitability index
In productivity: Indices of Productivity Using Data Envelopment Analysis (DEA)
Description
Usage
Arguments
Details
Value
Warning
Note
Author(s)
References
See Also
Examples
Description
Using Data Envelopment Analysis (DEA), this function measures
productivity and profitability in levels and changes with Lowe index.
Deflated shadow prices of inputs and outputs can also be computed.
Usage
1
2
3
4
5
6
7
lowe(data, id.var, time.var, x.vars, y.vars, w.vars, p.vars, tech.change = TRUE,
tech.reg = TRUE, rts = c("vrs", "crs", "nirs", "ndrs"), orientation = c("out",
"in", "in-out"), parallel = FALSE, cores = max(1, detectCores() - 1), scaled = TRUE,
by.id = NULL, by.year = NULL, shadow = FALSE)
## S3 method for class 'Lowe'
print(x, digits = NULL, ...)
Arguments
data
A dataframe containing the required information for measuring productivity and
profitability.
id.var
Firms' ID variable. Can be an integer or a text string.
time.var
Time period variable. Can be an integer or a text string.
x.vars
Input quantity variables. Can be a vector of text strings or integers.
y.vars
Output quantity variables. Can be a vector of text strings or
integers.
w.vars
Input price variables. Can be a vector of text strings or integers.
p.vars
Output price variables. Can be a vector of text strings or integers.
tech.change
Logical. If TRUE (default), the model allows for technological change.
If FALSE, technological change is prohibited. See also the Details section.
tech.reg
Logical. If TRUE (default), the model allows for negative technological change
(i.e. technological regress). If FALSE, only positive technological change (i.e. technological progress)
is allowed. See also the Details section.
rts
Character string specifying the returns to scale assumption.
The default value is "vrs" (variable returns to scale). Other possible options
are "crs" (constant returns to scale), "nirs" (non-increasing returns to scale),
or "ndrs" (non-decreasing returns to scale).
orientation
Character string specifying the orientation.
The default value is "out" (output-orientation). Other possible options
are "in" (input-orientation), and "in-out" (both input- and output-orientations).
For "in-out", the geometric mean of input- and output-orientations' results is returned.
parallel
Logical. Allows parallel computation. If FALSE (default) the estimation is conducted
in sequential mode. If TRUE, parallel mode is activated using the number of cores specified in cores.
When the sample size is small, it is recommended to keep the parallel option to its default value (FALSE).
cores
Integer. Used only if parallel = TRUE. It specifies the number of cores to be used
for parallel computation. By default, cores = max(1, detectCores() - 1).
scaled
Logical. If TRUE (default), input and output quantities are rescaled. If FALSE, a warning message
is displayed when very large (>1e5) and/or very small (<1e-4) values are present in the input and output quantity variables.
See also the Details section.
by.id
Integer specifying the reference observation used for computing the indices (Optional).
by.id must range between one and the total number of firms per period. See also the Details section.
by.year
Integer specifying the reference year used for computing the indices (Optional).
by.year must range between one and the total number of time periods. See also the Details section.
shadow
Logical. Default is FALSE (no shadow prices are returned). When set to TRUE, input and output
shadow prices are returned. These shadow prices are informative only and may be subject to the linear programming solver used.
x
An object of class 'Lowe'.
digits
The minimum number of significant digits to be printed in values.
Default = max(3, getOption("digits") - 3).
...
Currently not used.
Details
When tech.change is set to FALSE, this overrides the effect of tech.reg.
Setting scaled = FALSE (no rescaling of data) may lead to numerical problems in solving LP
problems while optimizing DEA models. In extreme cases it may also prevent models from being optimized.
By default by.id = NULL and by.year = NULL. This means that in the computation of
change indices, each observation is by default compared to itself in the first period. by.id and
by.year allow to specify a reference (e.g. a specific observation in a specific period).
If by.id is specified and by.year = NULL, then the reference observation is by.id
in the first period. If by.year is specified and by.id = NULL, then each observation is compared
to itself in the specified period of time.
The Lowe index is also a fixed-weights-based TFP index as the F<c3><a4>re-Primont. The Lowe index uses the average observed
input and output prices as aggregators.
Value
lowe() returns a list of class 'Lowe' for which a summary of productivity and profitability
measures in levels and changes, as well as a summary shadow prices (if shadow = TRUE), is printed.
This list contains the following items:
Levels
Several elements are provided, depending on the orientation specified:
REV Revenues
COST Costs
PROF Profitability
P Aggregated output prices
W Aggregated input prices
TT Terms of trade (i.e. P/W)
AO Aggregated outputs
AI Aggregated inputs
TFP Total Factor Productivity (TFP)
MP Maximum productivity
TFPE TFP efficiency score
OTE Output-oriented technical efficiency score (orientation = "out")
OSE Output-oriented scale efficiency score (orientation = "out")
OME Output-oriented mix efficiency score (orientation = "out")
ROSE Residual output-oriented scale efficiency score (orientation = "out")
OSME Output-oriented scale-mix efficiency score (orientation = "out")
ITE Input-oriented technical efficiency score (orientation = "in")
ISE Input-oriented scale efficiency score (orientation = "in")
IME Input-oriented mix efficiency score (orientation = "in")
RISE Residual input-oriented scale efficiency score (orientation = "in")
ISME Input-oriented scale-mix efficiency score (orientation = "in")
OTE.ITE Geometric mean of OTE and ITE (orientation = "in-out")
OSE.ISE Geometric mean of OSE and ISE (orientation = "in-out")
OME.IME Geometric mean of OME and IME (orientation = "in-out")
ROSE.RISE Geometric mean of ROSE and RISE (orientation = "in-out")
OSME.ISME Geometric mean of OSME and ISME (orientation = "in-out")
RME Residual mix efficiency score
RE Revenue efficiency (orientation = "out")
CE Cost efficiency (orientation = "in")
RE.CE Geometric mean of RE and CE (orientation = "in-out")
Changes
Change indices of the different elements of Levels are provided.
Each change is prefixed by "d" (e.g. profitability change is denoted dPROF,
output-oriented efficiency change is denoted dOTE, etc.).
Shadowp
Returned only if shadow = TRUE. It contains the deflated cost input (x.vars) shadow prices and the
deflated revenue output (y.vars) shadow prices.
From an object of class 'Lowe' obtained from lowe(), the
-
Levels function extracts individual productivity and profitability levels;
-
Changes function extracts individual productivity and profitability change indices; and
If shadow = TRUE, the Shadowp function extracts individual input and output deflated shadow prices.
Warning
The lowe() function will not work with unbalanced panel data.
The Lowe index may be sensitive to the rescaling.
For extreme efficient observations, the problem of multiple solutions may arise and the values of
shadow prices may differ depending on the linear programming solver used (here lpSolveAPI).
Note
All output-oriented efficiency scores are computed a la Shephard, while all
input-oriented efficiency scores are computed a la Farrell.
Hence, all efficiency scores are greater than zero and are lower or equal to one.
Author(s)
K Herv<c3><a9> Dakpo, Yann Desjeux, Laure Latruffe
References
O'Donnell C.J. (2008), An aggregate quantity-price framework for measuring
and decomposing productivity and profitability change. School of Economics,
University of Queensland, Australia.
URL: https://www.uq.edu.au/economics/cepa/docs/WP/WP072008.pdf
O'Donnell C.J. (2011), The sources of productivity change in the manufacturing
sectors of the U.S. economy. School of Economics, University of Queensland, Australia.
URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP072011.pdf
O'Donnell C.J. (2012), Nonparametric estimates of the components of productivity
and profitability change in U.S. Agriculture. American Journal of Agricultural
Economics, 94(4), 873–890.
https://doi.org/10.1093/ajae/aas023
See Also
See Levels to retrieve a data frame with Lowe
productivity and profitability in levels and components.
See Changes to retrieve a data frame with Lowe
productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices, provided that shadow = TRUE.
See also fareprim for computations with an alternative transitive index.
Examples
1
2
3
4
5
6
7
8
## Lowe profitability and productivity levels and changes' computations
## Not run:
Lowe.prod <- lowe(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10),
y.vars = c(4:6), w.vars = c(14:17), p.vars = c(11:13), orientation = "in-out", by.id = 1,
by.year = 1)
Lowe.prod
## End(Not run)
Example output
* Please cite the 'productivity' package as:
Dakpo K.H., Desjeux Y. and Latruffe L. (2018). productivity: Indices of Productivity and Profitability Using Data Envelopment Analysis (DEA). R package version 1.1.0.
See also: citation("productivity")
* For any questions, suggestions, or comments on the 'productivity' package, please make use of Tracker facilities at:
https://r-forge.r-project.org/projects/productivity/
sh: 1: wc: Permission denied
sh: 1: cannot create /dev/null: Permission denied
Loading required package: foreach
Loading required package: iterators
Loading required package: parallel
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DONE!
Lowe productivity and profitability levels (summary):
REV COST PROF P
Min. : 51852 Min. : 65626 Min. :0.4827 Min. :1027059
1st Qu.: 1493904 1st Qu.: 1617473 1st Qu.:0.7983 1st Qu.:1415786
Median : 3926819 Median : 4277850 Median :0.8901 Median :1553516
Mean : 4889511 Mean : 5137308 Mean :0.9190 Mean :1579664
3rd Qu.: 6154740 3rd Qu.: 6450927 3rd Qu.:1.0143 3rd Qu.:1716471
Max. :35628145 Max. :24027241 Max. :1.5416 Max. :2384726
W TT AO AI
Min. : 487397 Min. :0.7701 Min. : 0.02356 Min. : 0.04291
1st Qu.:1025751 1st Qu.:1.1812 1st Qu.: 0.97224 1st Qu.: 1.54111
Median :1177871 Median :1.3256 Median : 2.69449 Median : 3.82375
Mean :1167683 Mean :1.4100 Mean : 3.17071 Mean : 4.48176
3rd Qu.:1311215 3rd Qu.:1.5544 3rd Qu.: 4.01923 3rd Qu.: 5.64282
Max. :1991798 Max. :3.3208 Max. :21.35709 Max. :19.26621
TFP MP TFPE OTE.ITE
Min. :0.2586 Min. :1.108 Min. :0.1924 Min. :0.5321
1st Qu.:0.5445 1st Qu.:1.242 1st Qu.:0.4333 1st Qu.:0.8194
Median :0.6442 Median :1.282 Median :0.4976 Median :0.9267
Mean :0.6917 Mean :1.282 Mean :0.5405 Mean :0.8980
3rd Qu.:0.7980 3rd Qu.:1.345 3rd Qu.:0.6148 3rd Qu.:1.0000
Max. :1.4479 Max. :1.448 Max. :1.0000 Max. :1.0000
OSE.ISE OME.IME ROSE.RISE OSME.ISME
Min. :0.7772 Min. :0.5011 Min. :0.3867 Min. :0.2732
1st Qu.:0.9686 1st Qu.:0.7011 1st Qu.:0.6863 1st Qu.:0.4883
Median :0.9959 Median :0.7815 Median :0.7543 Median :0.5698
Mean :0.9759 Mean :0.7878 Mean :0.7531 Mean :0.6004
3rd Qu.:1.0000 3rd Qu.:0.8760 3rd Qu.:0.8289 3rd Qu.:0.7053
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
RME RE.CE
Min. :0.2755 Min. :0.3313
1st Qu.:0.5077 1st Qu.:0.5891
Median :0.5895 Median :0.6983
Mean :0.6148 Mean :0.7110
3rd Qu.:0.7156 3rd Qu.:0.8123
Max. :1.0000 Max. :1.0000
Lowe productivity and profitability changes (summary):
dREV dCOST dPROF dP
Min. : 0.01645 Min. :0.02133 Min. :0.4712 Min. :0.8241
1st Qu.: 0.47396 1st Qu.:0.52570 1st Qu.:0.7793 1st Qu.:1.1360
Median : 1.24584 Median :1.39036 Median :0.8689 Median :1.2465
Mean : 1.55127 Mean :1.66970 Mean :0.8971 Mean :1.2675
3rd Qu.: 1.95269 3rd Qu.:2.09664 3rd Qu.:0.9901 3rd Qu.:1.3772
Max. :11.30357 Max. :7.80919 Max. :1.5048 Max. :1.9134
dW dTT dAO dAI
Min. :0.4866 Min. :0.6189 Min. :0.009317 Min. :0.01397
1st Qu.:1.0240 1st Qu.:0.9493 1st Qu.:0.384438 1st Qu.:0.50172
Median :1.1759 Median :1.0653 Median :1.065443 Median :1.24484
Mean :1.1657 Mean :1.1332 Mean :1.253746 Mean :1.45906
3rd Qu.:1.3090 3rd Qu.:1.2492 3rd Qu.:1.589266 3rd Qu.:1.83705
Max. :1.9885 Max. :2.6689 Max. :8.444922 Max. :6.27223
dTFP dMP dTFPE dOTE.ITE
Min. :0.3141 Min. :1.000 Min. :0.2588 Min. :0.5962
1st Qu.:0.6614 1st Qu.:1.121 1st Qu.:0.5831 1st Qu.:0.9181
Median :0.7824 Median :1.157 Median :0.6696 Median :1.0383
Mean :0.8401 Mean :1.157 Mean :0.7273 Mean :1.0062
3rd Qu.:0.9692 3rd Qu.:1.214 3rd Qu.:0.8273 3rd Qu.:1.1204
Max. :1.7586 Max. :1.307 Max. :1.3456 Max. :1.1204
dOSE.ISE dOME.IME dROSE.RISE dOSME.ISME
Min. :0.7782 Min. :0.5389 Min. :0.4318 Min. :0.3281
1st Qu.:0.9698 1st Qu.:0.7541 1st Qu.:0.7663 1st Qu.:0.5865
Median :0.9971 Median :0.8406 Median :0.8423 Median :0.6844
Mean :0.9771 Mean :0.8474 Mean :0.8410 Mean :0.7211
3rd Qu.:1.0012 3rd Qu.:0.9422 3rd Qu.:0.9256 3rd Qu.:0.8470
Max. :1.0012 Max. :1.0755 Max. :1.1166 Max. :1.2010
dRME dRE.CE
Min. :0.3305 Min. :0.3993
1st Qu.:0.6089 1st Qu.:0.7098
Median :0.7071 Median :0.8415
Mean :0.7375 Mean :0.8568
3rd Qu.:0.8583 3rd Qu.:0.9789
Max. :1.1995 Max. :1.2051
productivity documentation built on May 1, 2019, 8:19 p.m.
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Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples
Description
Using Data Envelopment Analysis (DEA), this function measures productivity and profitability in levels and changes with Lowe index.
Deflated shadow prices of inputs and outputs can also be computed.
Usage
1 2 3 4 5 6 7 | lowe(data, id.var, time.var, x.vars, y.vars, w.vars, p.vars, tech.change = TRUE,
tech.reg = TRUE, rts = c("vrs", "crs", "nirs", "ndrs"), orientation = c("out",
"in", "in-out"), parallel = FALSE, cores = max(1, detectCores() - 1), scaled = TRUE,
by.id = NULL, by.year = NULL, shadow = FALSE)
## S3 method for class 'Lowe'
print(x, digits = NULL, ...)
|
Arguments
data |
A dataframe containing the required information for measuring productivity and profitability. |
id.var |
Firms' ID variable. Can be an integer or a text string. |
time.var |
Time period variable. Can be an integer or a text string. |
x.vars |
Input quantity variables. Can be a vector of text strings or integers. |
y.vars |
Output quantity variables. Can be a vector of text strings or integers. |
w.vars |
Input price variables. Can be a vector of text strings or integers. |
p.vars |
Output price variables. Can be a vector of text strings or integers. |
tech.change |
Logical. If |
tech.reg |
Logical. If |
rts |
Character string specifying the returns to scale assumption.
The default value is |
orientation |
Character string specifying the orientation.
The default value is |
parallel |
Logical. Allows parallel computation. If |
cores |
Integer. Used only if |
scaled |
Logical. If |
by.id |
Integer specifying the reference observation used for computing the indices (Optional).
|
by.year |
Integer specifying the reference year used for computing the indices (Optional).
|
shadow |
Logical. Default is |
x |
An object of class |
digits |
The minimum number of significant digits to be printed in values.
Default = |
... |
Currently not used. |
Details
When tech.change is set to FALSE, this overrides the effect of tech.reg.
Setting scaled = FALSE (no rescaling of data) may lead to numerical problems in solving LP
problems while optimizing DEA models. In extreme cases it may also prevent models from being optimized.
By default by.id = NULL and by.year = NULL. This means that in the computation of
change indices, each observation is by default compared to itself in the first period. by.id and
by.year allow to specify a reference (e.g. a specific observation in a specific period).
If by.id is specified and by.year = NULL, then the reference observation is by.id
in the first period. If by.year is specified and by.id = NULL, then each observation is compared
to itself in the specified period of time.
The Lowe index is also a fixed-weights-based TFP index as the F<c3><a4>re-Primont. The Lowe index uses the average observed input and output prices as aggregators.
Value
lowe() returns a list of class 'Lowe' for which a summary of productivity and profitability
measures in levels and changes, as well as a summary shadow prices (if shadow = TRUE), is printed.
This list contains the following items:
Levels |
Several elements are provided, depending on the
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Changes |
Change indices of the different elements of | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Shadowp |
Returned only if |
From an object of class 'Lowe' obtained from lowe(), the
-
Levelsfunction extracts individual productivity and profitability levels; -
Changesfunction extracts individual productivity and profitability change indices; and If
shadow = TRUE, theShadowpfunction extracts individual input and output deflated shadow prices.
Warning
The lowe() function will not work with unbalanced panel data.
The Lowe index may be sensitive to the rescaling.
For extreme efficient observations, the problem of multiple solutions may arise and the values of shadow prices may differ depending on the linear programming solver used (here lpSolveAPI).
Note
All output-oriented efficiency scores are computed a la Shephard, while all input-oriented efficiency scores are computed a la Farrell. Hence, all efficiency scores are greater than zero and are lower or equal to one.
Author(s)
K Herv<c3><a9> Dakpo, Yann Desjeux, Laure Latruffe
References
O'Donnell C.J. (2008), An aggregate quantity-price framework for measuring and decomposing productivity and profitability change. School of Economics, University of Queensland, Australia. URL: https://www.uq.edu.au/economics/cepa/docs/WP/WP072008.pdf
O'Donnell C.J. (2011), The sources of productivity change in the manufacturing sectors of the U.S. economy. School of Economics, University of Queensland, Australia. URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP072011.pdf
O'Donnell C.J. (2012), Nonparametric estimates of the components of productivity and profitability change in U.S. Agriculture. American Journal of Agricultural Economics, 94(4), 873–890. https://doi.org/10.1093/ajae/aas023
See Also
See Levels to retrieve a data frame with Lowe
productivity and profitability in levels and components.
See Changes to retrieve a data frame with Lowe
productivity and profitability changes and components.
See Shadowp to retrieve deflated input and output shadow prices, provided that shadow = TRUE.
See also fareprim for computations with an alternative transitive index.
Examples
1 2 3 4 5 6 7 8 | ## Lowe profitability and productivity levels and changes' computations
## Not run:
Lowe.prod <- lowe(data = usagri, id.var = "States", time.var = "Years", x.vars = c(7:10),
y.vars = c(4:6), w.vars = c(14:17), p.vars = c(11:13), orientation = "in-out", by.id = 1,
by.year = 1)
Lowe.prod
## End(Not run)
|
Example output
* Please cite the 'productivity' package as:
Dakpo K.H., Desjeux Y. and Latruffe L. (2018). productivity: Indices of Productivity and Profitability Using Data Envelopment Analysis (DEA). R package version 1.1.0.
See also: citation("productivity")
* For any questions, suggestions, or comments on the 'productivity' package, please make use of Tracker facilities at:
https://r-forge.r-project.org/projects/productivity/
sh: 1: wc: Permission denied
sh: 1: cannot create /dev/null: Permission denied
Loading required package: foreach
Loading required package: iterators
Loading required package: parallel
Progress: 0%
Progress: 5%
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Progress: 15%
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Progress: 25%
Progress: 30%
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Progress: 40%
Progress: 45%
Progress: 50%
Progress: 55%
Progress: 60%
Progress: 65%
Progress: 70%
Progress: 75%
Progress: 80%
Progress: 85%
Progress: 90%
Progress: 95%
DONE!
Lowe productivity and profitability levels (summary):
REV COST PROF P
Min. : 51852 Min. : 65626 Min. :0.4827 Min. :1027059
1st Qu.: 1493904 1st Qu.: 1617473 1st Qu.:0.7983 1st Qu.:1415786
Median : 3926819 Median : 4277850 Median :0.8901 Median :1553516
Mean : 4889511 Mean : 5137308 Mean :0.9190 Mean :1579664
3rd Qu.: 6154740 3rd Qu.: 6450927 3rd Qu.:1.0143 3rd Qu.:1716471
Max. :35628145 Max. :24027241 Max. :1.5416 Max. :2384726
W TT AO AI
Min. : 487397 Min. :0.7701 Min. : 0.02356 Min. : 0.04291
1st Qu.:1025751 1st Qu.:1.1812 1st Qu.: 0.97224 1st Qu.: 1.54111
Median :1177871 Median :1.3256 Median : 2.69449 Median : 3.82375
Mean :1167683 Mean :1.4100 Mean : 3.17071 Mean : 4.48176
3rd Qu.:1311215 3rd Qu.:1.5544 3rd Qu.: 4.01923 3rd Qu.: 5.64282
Max. :1991798 Max. :3.3208 Max. :21.35709 Max. :19.26621
TFP MP TFPE OTE.ITE
Min. :0.2586 Min. :1.108 Min. :0.1924 Min. :0.5321
1st Qu.:0.5445 1st Qu.:1.242 1st Qu.:0.4333 1st Qu.:0.8194
Median :0.6442 Median :1.282 Median :0.4976 Median :0.9267
Mean :0.6917 Mean :1.282 Mean :0.5405 Mean :0.8980
3rd Qu.:0.7980 3rd Qu.:1.345 3rd Qu.:0.6148 3rd Qu.:1.0000
Max. :1.4479 Max. :1.448 Max. :1.0000 Max. :1.0000
OSE.ISE OME.IME ROSE.RISE OSME.ISME
Min. :0.7772 Min. :0.5011 Min. :0.3867 Min. :0.2732
1st Qu.:0.9686 1st Qu.:0.7011 1st Qu.:0.6863 1st Qu.:0.4883
Median :0.9959 Median :0.7815 Median :0.7543 Median :0.5698
Mean :0.9759 Mean :0.7878 Mean :0.7531 Mean :0.6004
3rd Qu.:1.0000 3rd Qu.:0.8760 3rd Qu.:0.8289 3rd Qu.:0.7053
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
RME RE.CE
Min. :0.2755 Min. :0.3313
1st Qu.:0.5077 1st Qu.:0.5891
Median :0.5895 Median :0.6983
Mean :0.6148 Mean :0.7110
3rd Qu.:0.7156 3rd Qu.:0.8123
Max. :1.0000 Max. :1.0000
Lowe productivity and profitability changes (summary):
dREV dCOST dPROF dP
Min. : 0.01645 Min. :0.02133 Min. :0.4712 Min. :0.8241
1st Qu.: 0.47396 1st Qu.:0.52570 1st Qu.:0.7793 1st Qu.:1.1360
Median : 1.24584 Median :1.39036 Median :0.8689 Median :1.2465
Mean : 1.55127 Mean :1.66970 Mean :0.8971 Mean :1.2675
3rd Qu.: 1.95269 3rd Qu.:2.09664 3rd Qu.:0.9901 3rd Qu.:1.3772
Max. :11.30357 Max. :7.80919 Max. :1.5048 Max. :1.9134
dW dTT dAO dAI
Min. :0.4866 Min. :0.6189 Min. :0.009317 Min. :0.01397
1st Qu.:1.0240 1st Qu.:0.9493 1st Qu.:0.384438 1st Qu.:0.50172
Median :1.1759 Median :1.0653 Median :1.065443 Median :1.24484
Mean :1.1657 Mean :1.1332 Mean :1.253746 Mean :1.45906
3rd Qu.:1.3090 3rd Qu.:1.2492 3rd Qu.:1.589266 3rd Qu.:1.83705
Max. :1.9885 Max. :2.6689 Max. :8.444922 Max. :6.27223
dTFP dMP dTFPE dOTE.ITE
Min. :0.3141 Min. :1.000 Min. :0.2588 Min. :0.5962
1st Qu.:0.6614 1st Qu.:1.121 1st Qu.:0.5831 1st Qu.:0.9181
Median :0.7824 Median :1.157 Median :0.6696 Median :1.0383
Mean :0.8401 Mean :1.157 Mean :0.7273 Mean :1.0062
3rd Qu.:0.9692 3rd Qu.:1.214 3rd Qu.:0.8273 3rd Qu.:1.1204
Max. :1.7586 Max. :1.307 Max. :1.3456 Max. :1.1204
dOSE.ISE dOME.IME dROSE.RISE dOSME.ISME
Min. :0.7782 Min. :0.5389 Min. :0.4318 Min. :0.3281
1st Qu.:0.9698 1st Qu.:0.7541 1st Qu.:0.7663 1st Qu.:0.5865
Median :0.9971 Median :0.8406 Median :0.8423 Median :0.6844
Mean :0.9771 Mean :0.8474 Mean :0.8410 Mean :0.7211
3rd Qu.:1.0012 3rd Qu.:0.9422 3rd Qu.:0.9256 3rd Qu.:0.8470
Max. :1.0012 Max. :1.0755 Max. :1.1166 Max. :1.2010
dRME dRE.CE
Min. :0.3305 Min. :0.3993
1st Qu.:0.6089 1st Qu.:0.7098
Median :0.7071 Median :0.8415
Mean :0.7375 Mean :0.8568
3rd Qu.:0.8583 3rd Qu.:0.9789
Max. :1.1995 Max. :1.2051
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