README.md
In ElliottMardones/test10: foRgotten
test10
Description
The foRgotten library extends the theory of forgotten effects with the
aggregation of multiple key informants for complete graphs and chained
bipartite graphs. Provides analysis tools for direct effects and
forgotten effects.
The package allows for:
- Calculation of the average incidence by edges for direct effects.
- Calculation of the average incidence per row and column for direct
effects.
- Calculation of the median betweenness centrality per node for direct
effects.
- Calculation of the forgotten effects.
- Use of complete graphs and chained bipartite graphs.
Authors
Elliott Jamil Mardones Arias
School of Computer Science
Universidad Católica de Temuco
Rudecindo Ortega 02351
Temuco, Chile
emardones2016@inf.uct.cl
Julio Rojas-Mora Department of Computer Science
Universidad Católica de Temuco
Rudecindo Ortega 02351 Temuco, Chile
and Centro de Políticas Públicas
Universidad Católica de Temuco
Temuco, Chile
jrojas@inf.uct.cl
Installation
You can install the stable version of \ from CRAN with:
# install.packages(“foRgotten”)
and the development version from GitHub with:
#install.packages(“devtools”)
#devtools::install_github("ElliottMardones/foRgotten")
Usage
library(test10)#cambiar a foRgotten despues
Functions
The package provides five functions:
?directEffects
#> starting httpd help server ... done
Computes the mean incidence, lower confidence interval, and p-value with
multiple key informants for complete graphs and chained bipartite
graphs. For more details, see help (de.sq).
?bootMargin
Computes the mean incidence for each cause and each effect, confidence
intervals, and p-value with multiple key informants for complete graphs
and chain bipartite graphs. For more details, see help(bootMargin).
?centrality
Performs the computation of median betweenness centrality with multiple
key informants for complete graphs and chain bipartite graphs. For more
details, see help(centrality).
?fe.sq
It performs the calculation of the forgotten effects proposed by
Kaufmann and Gil-Aluja (1988) with multiple key informants for complete
graphs, with the frequency of appearance of the forgotten effect, mean
incidence, confidence intervals, and standard error. For more details,
see help(fe.sq).
?fe.rect
It performs the calculation of the forgotten effects proposed by
Kaufmann and Gil-Aluja (1988) with multiple key informants for chain
bipartite graphs, with the frequency of appearance of the forgotten
effect, mean incidence, confidence intervals, and standard error. For
more details, see help(fe.rect)
DataSet
The library provides 3 three-dimensional incidence matrices which are
called AA, AB and BB. The data are those used in the study
“Application of the Forgotten Effects Theory For Assessing the Public
Policy on Air Pollution Of the Commune of Valdivia, Chile” developed by
Manna, E. M et al (2018).
The data consists of 16 incentives, 4 behaviors and 10 key informants,
where each of the key informants presented the data with a minimum and
maximum value for each incident. The description of the data can be seen
in Tables 1 and 2 of Manna, E. M et al (2018).
The book store presents the data with the average between the minimum
and maximum value for each incidence, A being the equivalent to
incentives and B to behaviors. For more details of the data you can
consult:
help(AA)
help(AB)
help(BB)
Examples
directEffects()
The directEffects() function calculates the mean incidence, left
one-sided confidence interval, and p-value with multiple key informants
for complete graphs and chain bipartite graphs.
The function contemplates two modalities, the first is focused on
complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the significant direct effects of the incidence matrix
AA, which is described in DataSet, we use the parameter CC, which
allows us to enter a three-dimensional matrix, where each submatrix
along the z-axis is a square incidence matrix and reflective, or a list
of data.frame containing square and reflective incidence matrices. Each
matrix represents a complete graph. The CE and EE parameters are
used to perform the calculation with chain bipartite graphs, therefore
it is necessary that these parameters are not used.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
The directEffects() function makes use of the “boot.one.bca”
function of the wBoot package to implement the bootstrap method with
BCa adjusted boot and with a left one-sided hypothesis test based on the
Z-test. The conf.level parameter defines the confidence level and
reps the number of bootstrap replicas. By default conf.level = 0.95
and reps = 10000.
For example, let thr = 0.5 and reps = 1000, we get:
result <- directEffects(CC = AA, thr = 0.5, reps = 1000)
The function returns a list object with the $DirectEffects data subset
that contains the following values:
- From: Origin of the incident
- To: Destination of the incident
- Mean: Average incidence
- UCI: Upper Confidence Interval
- p.value: the calculated p-value
The results obtained correspond to 240 first-order incidents. Equivalent
to the number of edges minus the incidence on itself of each edge. The
first 6 values are:
head(result$DirectEffects)
#> From To Mean UCI p.value
#> 1 I1 I2 0.525 0.6300 0.575
#> 2 I1 I3 0.450 0.5861 0.293
#> 3 I1 I4 0.525 0.6654 0.609
#> 4 I1 I5 0.465 0.6450 0.375
#> 5 I1 I6 0.645 0.7850 0.895
#> 6 I1 I7 0.815 0.8700 1.000
If any of the occurrences have "NA" and "NaN" values in the UCI and
p.value fields, it indicates that the values for that occurrence have
repeated values. This prevents bootstrapping.
The delete parameter allows assigning zeros to edges whose incidences
are significantly less than thr to the p-value set in the conf.level
parameter. Also, this allows you to remove non-significant results from
the $DirectEffects subset.
For example, let thr = 0.5 and conf.level = 0.95, mean incidences
less than 0.5 or incidents with p.value less than 1 - conf.level
will be eliminated.
result <- directEffects(CC = AA, thr = 0.5, reps = 1000, delete = TRUE)
#> deleting data...
The function reports by console when significant edges have been
removed. The number of significant direct effects decreased from 240 to
205 for delete = TRUE.
Note: However, this does not guarantee that a non-significant
variable in 1st order does not generate 2nd order effects, since they
are extracted from the empirical distribution of the key informants.
For delete = TRUE, the function returns $Data, the three-dimensional
matrix entered in the CC parameter but assigning 0 to the
non-significant edges.
For chain bipartite graphs To calculate the significant direct effects
of the incidence matrices AA, AB and BB, which are described in
DataSet, we make use of the already described parameter CC. The EE
parameter is equivalent to the CC parameter. The CE parameter allows
you to enter a three-dimensional matrix, where each sub-matrix along the
z-axis is a rectangular incidence matrix or a list of data.frame
containing rectangular incidence matrices. Each matrix represents a
bipartite graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- directEffects(CC = AA, CE = AB, EE = BB, reps = 1000)
The results obtained correspond to 312 first-order incidents. Using the
delete = TRUE parameter, the number of first-order significant
occurrences was reduced to 271.
For delete = TRUE, the function returns $CC, $CE, and $EE, which
are the three-dimensional matrices entered in the parameters CC, CE,
and EE, but assigning 0 to the non-significant edges.
For chain bipartite graphs
To calculate the significant direct effects of the incidence matrices
AA, ABand BB, which are described in DataSet, we make use of the
already described parameter CC. The EEparameter is equivalent to the
CCparameter. The CEparameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- directEffects(CC = AA, CE = AB, EE = BB, thr = 0.5, reps = 1000)
The results obtained correspond to 312 first-order incidents. Using the
delete = TRUE parameter, the number of first order significant
occurrences was reduced to 271.
For delete = TRUE, the function returns $CC, $CE and $EE, which
are the three-dimensional matrices entered in the parameters CC,
CEand EE, but assigning 0 to the non-significant edges.
bootMargin()
The bootMargin() function calculates the mean incidence of each cause
and each effect, confidence intervals, and p-value with multiple experts
for complete graphs and chain bipartite graphs.
The function contemplates two modalities, the first is focused on
complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the average incidence of each cause and each effect of the
AA incidence matrix, which is described in DataSet, we use the CC
parameter, which allows us to enter a three-dimensional matrix, where
each sub-matrix along the z-axis is a reflexive square incidence matrix
or a list of data.frame containing square and reflexive incidence
matrices. Each matrix represents a complete graph. The CE and EE
parameters are used to perform the calculation with chain bipartite
graphs, therefore it is necessary that these parameters are not used.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
The bootMargin() function makes use of the “boot.one.bca” function
from the wBoot package to implement the bootstrap resampling method
with BCa adjusted boot and with a two-sided hypothesis test based on the
Z-test. The conf.level parameter defines the confidence level and
reps the number of bootstrap replicas. By default conf.level = 0.95
and reps = 10000.
For example, let thr = 0.6 and reps = 1000 we get:
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000)
The function returns a list object with the data subsets $byRow and
$byCol, each of these subsets of data contains the following values:
- Var: Variable name
- Mean: Calculated mean.
- LCI: Lower Confidence Interval
- ICU: Upper Confidence Interval
- p.value: the calculated p-value.
The bootMargin() function allows you to analyze by node or by
variable. The results obtained are:
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 1 I1 0.5255433 0.4675 0.5875 2.91e-02
#> 2 I2 0.5994003 0.5515 0.6579 9.66e-01
#> 3 I3 0.4280310 0.3590 0.4703 7.73e-05
#> 4 I4 0.4905413 0.4008 0.5421 2.94e-05
#> 5 I5 0.5344293 0.4717 0.5977 4.30e-02
#> 6 I6 0.5539760 0.4773 0.6167 1.25e-01
#> 7 I7 0.5315417 0.4818 0.5835 1.10e-02
#> 8 I8 0.5427540 0.4663 0.6134 1.13e-01
#> 9 I9 0.4643607 0.4060 0.5165 4.25e-04
#> 10 I10 0.4731567 0.3930 0.5400 4.28e-04
#> 11 I11 0.5974773 0.5503 0.6423 8.91e-01
#> 12 I12 0.4559787 0.3943 0.4987 6.48e-05
#> 13 I13 0.5539730 0.4700 0.6363 2.52e-01
#> 14 I14 0.2485857 0.2049 0.2980 1.44e-03
#> 15 I15 0.4426557 0.3927 0.4950 1.48e-03
#> 16 I16 0.5140877 0.4532 0.5627 4.41e-04
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 1 I1 0.4803423 0.3666 0.5719 0.011600
#> 2 I2 0.5521307 0.4294 0.6547 0.384000
#> 3 I3 0.4186917 0.3133 0.5110 0.000675
#> 4 I4 0.4692143 0.3539 0.5916 0.039300
#> 5 I5 0.4575023 0.3578 0.5532 0.000559
#> 6 I6 0.5872893 0.3857 0.6677 0.733000
#> 7 I7 0.5562813 0.4408 0.6485 0.417000
#> 8 I8 0.5743783 0.5063 0.6502 0.478000
#> 9 I9 0.4531933 0.3364 0.5476 0.002950
#> 10 I10 0.4636727 0.3800 0.5791 0.018000
#> 11 I11 0.5774543 0.4310 0.6927 0.724000
#> 12 I12 0.4563103 0.3341 0.5764 0.014500
#> 13 I13 0.5636160 0.4761 0.6353 0.330000
#> 14 I14 0.2733193 0.1853 0.3371 0.000199
#> 15 I15 0.4720647 0.3593 0.5930 0.040700
#> 16 I16 0.5914300 0.5164 0.6933 0.915000
The function allows eliminating causes and effects whose average
incidence is not significant at the set thr parameter. For example,
for delete = TRUE, the number of significant variables decreased.
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000, delete = TRUE)
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 2 I2 0.6003730 0.5477 0.6533 0.97300
#> 5 I5 0.5336233 0.4730 0.6047 0.07770
#> 6 I6 0.5536140 0.4790 0.6164 0.17600
#> 7 I7 0.5302397 0.4799 0.5818 0.00816
#> 8 I8 0.5435877 0.4643 0.6093 0.10300
#> 11 I11 0.5974457 0.5538 0.6495 0.94000
#> 13 I13 0.5542533 0.4753 0.6398 0.26500
#> 15 I15 0.4408610 0.3917 0.4939 0.00180
#> 16 I16 0.5129870 0.4541 0.5649 0.00358
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 2 I2 0.5552910 0.4249 0.6597 0.422000
#> 5 I5 0.4609383 0.3559 0.5459 0.000277
#> 6 I6 0.5878387 0.4093 0.6700 0.776000
#> 7 I7 0.5558383 0.4350 0.6575 0.390000
#> 8 I8 0.5744267 0.5113 0.6519 0.487000
#> 11 I11 0.5760340 0.4348 0.6976 0.745000
#> 13 I13 0.5614550 0.4846 0.6372 0.364000
#> 15 I15 0.4726193 0.3480 0.6017 0.061500
#> 16 I16 0.5929490 0.5190 0.6762 0.887000
For delete = TRUE, the function returns$Data, the matrix entered in
the CCparameter, but with the non-significant rows and columns
removed.
For plot = TRUE, the function returns $plot, which contains the
graph generated from the subsets $byRow and $byCol. On the x-axis
are the “Dependence” associated with $byCol and on the y-axis the
“Influence” is associated with $byRow.
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000, delete = TRUE, plot = TRUE)
result$plot
For chain bipartite graphs
To calculate the average incidence of each cause and each effect of the
incidence matrices AA, ABand BB, which are described in DataSet,
we make use of the already described parameter CC. The EEparameter
is equivalent to the CCparameter. The CEparameter allows you to
enter a three-dimensional matrix, where each sub-matrix along the z-axis
is a rectangular incidence matrix or a list of data.frame containing
rectangular incidence matrices. Each matrix represents a bipartite
graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- bootMargin(CC = AA, CE = AB, EE = BB, thr = 0.6, reps = 1000)
The results obtained correspond to all the nodes or variables found in
the entered matrices.
The results for $byRow and $byCol are:
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 1 I1 0.5151763 0.4697 0.5646 0.004940
#> 2 I2 0.6292071 0.5810 0.6773 0.214000
#> 3 I3 0.4569737 0.3939 0.5247 0.001630
#> 4 I4 0.5099500 0.4502 0.5729 0.002360
#> 5 I5 0.5479624 0.4920 0.6071 0.075200
#> 6 I6 0.5819237 0.5146 0.6524 0.621000
#> 7 I7 0.5735553 0.5188 0.6301 0.381000
#> 8 I8 0.5724137 0.5017 0.6371 0.414000
#> 9 I9 0.4796082 0.4162 0.5403 0.002890
#> 10 I10 0.5159689 0.4442 0.5926 0.030100
#> 11 I11 0.6527029 0.5970 0.7190 0.069600
#> 12 I12 0.4782905 0.4124 0.5313 0.000708
#> 13 I13 0.6236258 0.5380 0.7139 0.589000
#> 14 I14 0.2443937 0.2040 0.2807 0.000833
#> 15 I15 0.4595650 0.4187 0.5096 0.001250
#> 16 I16 0.5279329 0.4812 0.5713 0.001540
#> 17 B1 0.6780183 0.6000 0.7200 0.203000
#> 18 B2 0.6784550 0.5700 0.7550 0.152000
#> 19 B3 0.6737850 0.5500 0.7717 0.493000
#> 20 B4 0.8084783 0.8000 0.8150 0.000753
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 1 I1 0.4792417 0.3635 0.5734 6.79e-03
#> 2 I2 0.5564770 0.4295 0.6560 3.96e-01
#> 3 I3 0.4205187 0.3153 0.5110 5.59e-04
#> 4 I4 0.4689753 0.3438 0.5823 2.54e-02
#> 5 I5 0.4617787 0.3550 0.5435 1.29e-03
#> 6 I6 0.5841477 0.4211 0.6725 8.13e-01
#> 7 I7 0.5578120 0.4368 0.6534 3.89e-01
#> 8 I8 0.5741100 0.5117 0.6463 4.53e-01
#> 9 I9 0.4477490 0.3483 0.5648 1.43e-02
#> 10 I10 0.4680223 0.3611 0.5744 1.92e-02
#> 11 I11 0.5800763 0.4337 0.7040 7.48e-01
#> 12 I12 0.4567530 0.3241 0.5566 1.09e-02
#> 13 I13 0.5640473 0.4715 0.6353 2.79e-01
#> 14 I14 0.2744593 0.1881 0.3358 1.46e-04
#> 15 I15 0.4747730 0.3534 0.5854 2.86e-02
#> 16 I16 0.5927650 0.5120 0.6756 8.81e-01
#> 17 B1 0.5394645 0.4434 0.6576 3.19e-01
#> 18 B2 0.6761287 0.6108 0.7687 1.94e-02
#> 19 B3 0.6904068 0.6339 0.7689 8.56e-05
#> 20 B4 0.6276187 0.5391 0.7255 5.28e-01
For delete = TRUE, the function returns $CC, $CE, and $EE, which
are the three-dimensional arrays entered in the CC, CE, and EE
parameters, but with the rows and columns removed.
For plot = TRUE, the function returns $plot, which contains the
graph generated from the subsets $byRow and $byCol. On the x-axis
are the “Dependence” associated with $byCol and on the y-axis the
“Influence” is associated with $byRow.
centralitry()
The centrality() function calculates the median betweenness
centrality, confidence intervals, and the selected method for
calculating the centrality distribution for complete graphs and chain
bipartite graphs.
The function contemplates two modalities, the first is focused on
complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the median betweenness centrality of the incidence matrix
AA, which is described in DataSet, we use the parameter CC, which
allows us to enter a three-dimensional matrix, where each submatrix
along the z-axis is a square incidence matrix and reflective, or a list
of data.frame containing square and reflective incidence matrices. Each
matrix represents a complete graph. The CEand EEparameters are used
to perform the calculation with chain bipartite graphs, therefore it is
necessary that these parameters are not used.
The centrality() function makes use of the “boot” function from the
boot package (Canty A, Ripley BD, 2021) to implement the bootstrap
method with BCa tight boot. The number of bootstrap replicas is defined
in the repsparameter. By default reps = 10000.
The model parameter allows bootstrapping with some of the following
statistics: mediate.
median.conpl: Calculate the median of a power distribution according to
Newman M.E (2005).conlnorm: Calculates the median of a power distribution according
to Gillespie CS (2015).
The objective of the model parameter is to determine to which
heavy-tailed distribution the variables or nodes of the entered
parameter correspond.
For example, let model = "median" and reps = 300, we will obtain:
result <- centrality(CC = AA, model = "median", reps = 300)
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I3 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I9 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I12 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I14 has median = 0
The returned object of type data.frame contains the following
components:
- Var: Name of the variable.
- Median: Median calculated.
- LCI: Lower Confidence Interval.
- ICU: Upper Confidence Interval.
- Method: Statistical method used associated with the model parameter.
If the median calculated for any of the betweenness centrality has a
median equal to 0, the LCI and UCI fields will have a value equal to 0.
This is reported with a warning per console.
The results are:
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 21.358333 median
#> 2 I2 12.9875000 2.7055613 25.430556 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 2.079167 median
#> 5 I5 6.2083333 0.4958333 10.250000 median
#> 6 I6 20.2791667 4.8070548 36.000000 median
#> 7 I7 11.0833333 1.7500000 41.000000 median
#> 8 I8 4.7083333 0.1000000 10.333333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 3.1942299 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.7763065 11.000000 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 8.583333 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Now if we use "conpl" in the model parameter and 300 bootstrap
replicas, we get:
result <- centrality(CC = AA, model = "conpl", reps = 300)
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I9 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I12 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 26.221124 median
#> 2 I2 12.9875000 2.2500000 25.166667 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 3.102966 median
#> 5 I5 6.2083333 0.6666667 10.655172 median
#> 6 I6 20.2791667 4.7074397 42.583333 median
#> 7 I7 11.0833333 1.9107598 41.000000 median
#> 8 I8 4.7083333 0.1000000 10.833333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 2.6250000 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.5000000 11.000000 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 7.291667 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Note: If the calculation cannot be performed with model = "conpl"
in some node, the function will perform the calculation with "median".
This change is indicated in the Method field.
Now if we use "conlnorm" in the model parameter and 300 bootstrap
replicas, we get:
result <- centrality(CC = AA, model = "conlnorm", reps = 300)
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I9 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I12 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 21.358333 median
#> 2 I2 12.9875000 2.2500000 24.125000 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 1.995833 median
#> 5 I5 6.2083333 0.4958333 10.000000 median
#> 6 I6 20.2791667 4.4964274 36.000000 median
#> 7 I7 11.0833333 1.5000000 31.700000 median
#> 8 I8 4.7083333 0.1000000 10.833333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 0.6950687 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.0000000 9.916667 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 9.211933 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Note: If the calculation cannot be performed with
model = "conlnorm" in some node, the function will perform the
calculation with “median”. This change is indicated in the Method field
IMPORTANT: The best statistic to use in the model parameter will
depend on the data and the number of bootstrap replicas that you deem
appropriate.
The centrality() function implements the parallel function from the
boot package. The parallelparameter allows you to set the type of
parallel operation that is required. The options are "multicore",
"snow" and "no". By default parallel = "no". The number of
processors to be used in the paralell implementation is defined in the
ncpusparameter. By default ncpus = 1.
The paralleland ncpusoptions are not available on Windows operating
systems.
For chain bipartite graphs
To calculate the median betweenness centrality of the incidence matrices
AA, ABand BB, which are described in DataSet, we make use of the
already described parameter CC. The EEparameter is equivalent to the
CCparameter. The CEparameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
For example, let model = "conpl" and reps = 300, you get:
result <- centrality(CC = AA, CE = AB, EE = BB, model = "conpl", reps = 300)
#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable B1 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 14.0416667 0.0000000 31.883333 median
#> 2 I2 14.6913273 7.9899228 17.799567 conpl
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.9166667 0.1666667 4.708333 median
#> 5 I5 6.2083333 0.6710528 13.041667 median
#> 6 I6 24.6720238 4.5607143 48.975000 median
#> 7 I7 9.2552918 1.1172637 25.079716 conpl
#> 8 I8 8.2761905 3.7500000 21.294048 median
#> 9 I9 0.3750000 0.0000000 3.650000 median
#> 10 I10 1.5714286 0.1666667 8.125000 median
#> 11 I11 21.0241962 13.7066578 21.438612 conpl
#> 12 I12 3.3333333 0.0000000 11.318238 median
#> 13 I13 5.0166667 1.1428571 14.434524 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 9.166667 median
#> 16 I16 18.7916667 2.5833333 39.019637 median
#> 17 B1 0.0000000 0.0000000 0.000000 median
#> 18 B2 2.7833333 1.0000000 5.500000 median
#> 19 B3 2.0000000 0.5000000 3.333333 median
#> 20 B4 1.8666667 0.0000000 6.965270 median
The centrality() function implements the parallel function from the
bootpackage. The parallelparameter allows you to set the type of
parallel operation that is required. The options are "multicore",
"snow" and "no". By default parallel = "no". The number of
processors to be used in the paralellimplementation is defined in the
ncpusparameter. By default ncpus = 1.
The paralleland ncpusoptions are not available on Windows operating
systems.
fe.sq()
The function fe.sq(), calculates the forgotten effects (Kaufmann & Gil
Aluja, 1988) with multiple experts for complete graphs, with calculation
of the frequency of appearance of the forgotten effects, mean incidence,
confidence intervals and standard error
For example, to perform the calculation using the incidence matrix AA,
described in DATASET, we use the parameter CC, which allows us to
enter a three-dimensional matrix, where each sub-matrix along the z axis
is a square and reflective incidence matrix , or a list of data.frame
containing square and reflective incidence matrices. Each matrix
represents a complete graph.
To define the degree of truth in which the incidence is considered
significant, the parameter thris used, which is defined between
[0,1]. By default thr = 0.5.
To define the maximum order of the forgotten effects, use the
maxOrderparameter. By default maxOrder = 2.
The fe.sq() function makes use of the “boot” function from the boot
package (Canty A, Ripley BD, 2021) to implement bootstrap with BCa tight
boot. The number of bootstrap replicas is defined in the reps
parameter. By default reps = 10000.
For example, let thr = 0.5, maxOrder = 3 and reps = 1000, you get:
result <- fe.sq(CC = AA, thr = 0.5, maxOrder = 3, reps = 1000)
The returned object of type list contains two subsets of data. The
$boot data subset is a list of data.frame where each data.frame
represents the order of the calculated forgotten effect, the components
are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate
relationships of the forgotten effects. For example, for order n
there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Mean: Mean effect of the forgotten effect
- LCI: Lower Confidence Intervals.
- UCI: Upper Confidence Intervals.
- SE: Standard error.
The $byExperts data subset is a list of data.frame where each
data.frame represents the order of the forgotten effect calculated
with its associated incidence value for each expert, the components are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate
relationships of the forgotten effects. For example, for order n
there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Expert_x: Dynamic field that represents each of the entered experts.
If we look at the data in the $boot$Order_2 data subset, we find 706
2nd order effects and 611 of these effects are unique. The first 6 are:
head(result$boot$Order_2)
#> From Through_1 To Count Mean LCI UCI SE
#> 1 I8 I11 I10 4 0.6125000 0.5625 0.6750000 0.02652208
#> 2 I5 I11 I10 3 0.6166667 0.5500 0.6666667 0.03671591
#> 3 I6 I11 I14 3 0.6833333 0.6000 0.7666667 0.07021737
#> 4 I13 I11 I14 3 0.5833333 0.5500 0.6000000 0.01399985
#> 5 I13 I6 I1 3 0.6333333 0.6000 0.6666667 0.02748039
#> 6 I13 I16 I1 3 0.6333333 0.6000 0.6666667 0.02785307
The relations I8 -> I11 -> I10 appeared 4 times. To know exactly in
which expert these relationships were found, there is the $byExperts
data subset. If we look at the first row of $byExperts$order_2 we can
identify the experts who provided this information.
head(result$byExperts$Order_2)
#> From Through_1 To Count Expert_1 Expert_2 Expert_3 Expert_4 Expert_5
#> 1 I8 I11 I10 4 0.55 0.6 0.00 0.6 0.0
#> 2 I5 I11 I10 3 0.55 0.7 0.00 0.0 0.0
#> 3 I6 I11 I14 3 0.00 0.6 0.85 0.6 0.0
#> 4 I13 I11 I14 3 0.00 0.6 0.00 0.6 0.0
#> 5 I13 I6 I1 3 0.00 0.0 0.60 0.6 0.0
#> 6 I13 I16 I1 3 0.00 0.0 0.00 0.6 0.7
#> Expert_6 Expert_7 Expert_8 Expert_9 Expert_10
#> 1 0.7 0.00 0.0 0 0.0
#> 2 0.0 0.00 0.6 0 0.0
#> 3 0.0 0.00 0.0 0 0.0
#> 4 0.0 0.55 0.0 0 0.0
#> 5 0.0 0.00 0.0 0 0.7
#> 6 0.0 0.00 0.6 0 0.0
IMPORTANT: If any of the $boot values shows "NA" in LCI, UCI and
SE, it indicates that the values of the incidents per expert are the
same or the value is unique. That prevents implementing bootstrap.
The fe.sq() function implements the parallel function from the boot
package. The parallel parameter allows you to set the type of parallel
operation that is required. The options are "multicore", "snow" and
"no". By default parallel = "no". The number of processors to be
used in the paralellimplementation is defined in the ncpusparameter.
By default ncpus = 1.
The parallel and ncpusoptions are not available on Windows operating
systems.
fe.rect()
The function fe.rect(), calculates the forgotten effects (Kaufmann &
Gil Aluja, 1988) with multiple key informants for chain bipartite
graphs, with calculation of the frequency of appearance of the forgotten
effects, mean incidence, confidence intervals and standard error.
To perform the calculation using the incidence matrices AA, ABand
BB, which are described in DataSet, we make use of the already
described parameter CC. The EE parameter is equivalent to the CC
parameter. The CE parameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
To define the maximum order of the forgotten effects, use the
maxOrderparameter. By default maxOrder = 2.
The fe.rect() function makes use of the “boot” function from the
boot package (Canty A, Ripley BD, 2021) to implement bootstrap with BCa
tight boot.. The number of bootstrap replicas is defined in the reps
parameter. By default reps = 10000.
For example, let thr = 0.5, maxOrder = 3 and reps = 1000, you get:
result <- fe.rect(CC = AA,CE = AB, EE = BB, thr = 0.5, maxOrder = 3, reps = 1000)
#> Warning in wrapper.indirectEffects_R(CC = CC, CE = CE, EE = EE, thr = thr, :
#> Expert number 7 has no 2nd maxOrder or higher effects.
The returned object of type list contains two subsets of data. The
$boot data subset is a list of data.frame where each data.frame
represents the order of the calculated forgotten effect, the components
are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate
relationships of the forgotten effects. For example, for order n
there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Mean: Mean effect of the forgotten effect
- LCI: Lower Confidence Intervals.
- UCI: Upper Confidence Intervals.
- SE: Standard error.
The $byExperts data subset is a list of data.frame where each
data.frame represents the order of the forgotten effect calculated
with its associated incidence value for each expert, the components are:
-
From: Indicates the origin of the forgotten effects relationships.
-
Through_x: Dynamic field that represents the intermediate
relationships of the forgotten effects. For example, for order n
there will be “though_1” up to “though_ \”.
-
To: Indicates the end of the forgotten effects relationships.
-
Count: Number of times the forgotten effect was repeated.
-
Expert_x: Dynamic field that represents each of the entered experts.
If we look at the data in the $boot$Order_2 data subset, we find 182
2nd order effects and 162 of these effects are unique. The first 6 are:
head(result$boot$Order_2)
#> From Through_1 To Count Mean LCI UCI SE
#> 1 I5 B4 B1 3 0.6333333 0.60 0.6666667 0.02745863
#> 2 I6 I7 B1 2 0.8000000 0.75 0.8000000 0.03469411
#> 3 I8 I7 B1 2 0.6250000 0.60 0.6250000 0.01775705
#> 4 I12 I2 B1 2 0.7000000 0.65 0.7500000 0.03593144
#> 5 I10 I11 B2 2 0.5750000 0.55 0.5750000 0.01719826
#> 6 I14 I15 B2 2 0.7250000 0.70 0.7500000 0.01807081
The relations I5 -> B4 -> B1 appeared 3 times. To know exactly in which
expert these relationships were found, there is the $byExperts data
subset. If we look at the first row of $byExperts$order_2 we can
identify the experts who provided this information.
head(result$byExperts$Order_2)
#> From Through_1 To Count Expert_1 Expert_2 Expert_3 Expert_4 Expert_5 Expert_6
#> 1 I5 B4 B1 3 0.60 0.7 0 0.60 0.00 0
#> 2 I6 I7 B1 2 0.75 0.0 0 0.85 0.00 0
#> 3 I8 I7 B1 2 0.65 0.6 0 0.00 0.00 0
#> 4 I12 I2 B1 2 0.65 0.0 0 0.75 0.00 0
#> 5 I10 I11 B2 2 0.60 0.0 0 0.00 0.55 0
#> 6 I14 I15 B2 2 0.75 0.0 0 0.00 0.70 0
#> Expert_7 Expert_8 Expert_9 Expert_10
#> 1 0 0 0 0
#> 2 0 0 0 0
#> 3 0 0 0 0
#> 4 0 0 0 0
#> 5 0 0 0 0
#> 6 0 0 0 0
MPORTANT: If any of the $boot values shows "NA" in LCI, UCI and
SE, it indicates that the values of the incidents per expert are the
same or the value is unique. That prevents implementing bootstrap.
The fe.sq() function implements the parallel function from the boot
package. The parallelparameter allows you to set the type of parallel
operation that is required. The options are "multicore", "snow" and
"no". By default parallel = "no". The number of processors to be
used in the paralell implementation is defined in the ncpus
parameter. By default ncpus = 1.
The parallel and ncpus options are not available on Windows
operating systems.
References
-
Kaufmann, A., & Gil Aluja, J. (1988). Modelos para la Investigación
de efectos olvidados, Milladoiro. Santiago de Compostela, España.
-
Manna, E. M., Rojas-Mora, J., & Mondaca-Marino, C. (2018).
Application of the Forgotten Effects Theory for Assessing the Public
Policy on Air Pollution of the Commune of Valdivia, Chile. In From
Science to Society (pp. 61-72). Springer, Cham.
-
Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual
Clarification. Social Networks, 1, 215-239.
-
Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
Journal of Mathematical Sociology 25(2):163-177, 2001.
-
Canty A, Ripley BD (2021). boot: Bootstrap R (S-Plus) Functions. R
package version 1.3-28.
-
Davison AC, Hinkley DV (1997). Bootstrap Methods and Their
Applications. Cambridge University Press, Cambridge. ISBN
0-521-57391-2, http://statwww.epfl.ch/davison/BMA/.
-
Newman, M. E. (2005). Power laws, Pareto distributions and Zipf’s
law. Contemporary physics, 46(5), 323-351.
-
Gillespie, C. S. (2014). Fitting heavy tailed distributions: the
poweRlaw package. arXiv preprint arXiv:1407.3492.
-
ElliottMardones/test10 documentation built on Dec. 17, 2021, 6:26 p.m.
R Package Documentation
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test10
Description
The foRgotten library extends the theory of forgotten effects with the aggregation of multiple key informants for complete graphs and chained bipartite graphs. Provides analysis tools for direct effects and forgotten effects.
The package allows for:
- Calculation of the average incidence by edges for direct effects.
- Calculation of the average incidence per row and column for direct effects.
- Calculation of the median betweenness centrality per node for direct effects.
- Calculation of the forgotten effects.
- Use of complete graphs and chained bipartite graphs.
Authors
Elliott Jamil Mardones Arias School of Computer Science Universidad Católica de Temuco Rudecindo Ortega 02351 Temuco, Chile emardones2016@inf.uct.cl
Julio Rojas-Mora Department of Computer Science Universidad Católica de Temuco Rudecindo Ortega 02351 Temuco, Chile and Centro de Políticas Públicas Universidad Católica de Temuco Temuco, Chile jrojas@inf.uct.cl
Installation
You can install the stable version of \ from CRAN with:
# install.packages(“foRgotten”)
and the development version from GitHub with:
#install.packages(“devtools”)
#devtools::install_github("ElliottMardones/foRgotten")
Usage
library(test10)#cambiar a foRgotten despues
Functions
The package provides five functions:
?directEffects
#> starting httpd help server ... done
Computes the mean incidence, lower confidence interval, and p-value with multiple key informants for complete graphs and chained bipartite graphs. For more details, see help (de.sq).
?bootMargin
Computes the mean incidence for each cause and each effect, confidence intervals, and p-value with multiple key informants for complete graphs and chain bipartite graphs. For more details, see help(bootMargin).
?centrality
Performs the computation of median betweenness centrality with multiple key informants for complete graphs and chain bipartite graphs. For more details, see help(centrality).
?fe.sq
It performs the calculation of the forgotten effects proposed by Kaufmann and Gil-Aluja (1988) with multiple key informants for complete graphs, with the frequency of appearance of the forgotten effect, mean incidence, confidence intervals, and standard error. For more details, see help(fe.sq).
?fe.rect
It performs the calculation of the forgotten effects proposed by Kaufmann and Gil-Aluja (1988) with multiple key informants for chain bipartite graphs, with the frequency of appearance of the forgotten effect, mean incidence, confidence intervals, and standard error. For more details, see help(fe.rect)
DataSet
The library provides 3 three-dimensional incidence matrices which are
called AA, AB and BB. The data are those used in the study
“Application of the Forgotten Effects Theory For Assessing the Public
Policy on Air Pollution Of the Commune of Valdivia, Chile” developed by
Manna, E. M et al (2018).
The data consists of 16 incentives, 4 behaviors and 10 key informants, where each of the key informants presented the data with a minimum and maximum value for each incident. The description of the data can be seen in Tables 1 and 2 of Manna, E. M et al (2018).
The book store presents the data with the average between the minimum and maximum value for each incidence, A being the equivalent to incentives and B to behaviors. For more details of the data you can consult:
help(AA)
help(AB)
help(BB)
Examples
directEffects()
The directEffects() function calculates the mean incidence, left
one-sided confidence interval, and p-value with multiple key informants
for complete graphs and chain bipartite graphs.
The function contemplates two modalities, the first is focused on complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the significant direct effects of the incidence matrix
AA, which is described in DataSet, we use the parameter CC, which
allows us to enter a three-dimensional matrix, where each submatrix
along the z-axis is a square incidence matrix and reflective, or a list
of data.frame containing square and reflective incidence matrices. Each
matrix represents a complete graph. The CE and EE parameters are
used to perform the calculation with chain bipartite graphs, therefore
it is necessary that these parameters are not used.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
The directEffects() function makes use of the “boot.one.bca”
function of the wBoot package to implement the bootstrap method with
BCa adjusted boot and with a left one-sided hypothesis test based on the
Z-test. The conf.level parameter defines the confidence level and
reps the number of bootstrap replicas. By default conf.level = 0.95
and reps = 10000.
For example, let thr = 0.5 and reps = 1000, we get:
result <- directEffects(CC = AA, thr = 0.5, reps = 1000)
The function returns a list object with the $DirectEffects data subset
that contains the following values:
- From: Origin of the incident
- To: Destination of the incident
- Mean: Average incidence
- UCI: Upper Confidence Interval
- p.value: the calculated p-value
The results obtained correspond to 240 first-order incidents. Equivalent to the number of edges minus the incidence on itself of each edge. The first 6 values are:
head(result$DirectEffects)
#> From To Mean UCI p.value
#> 1 I1 I2 0.525 0.6300 0.575
#> 2 I1 I3 0.450 0.5861 0.293
#> 3 I1 I4 0.525 0.6654 0.609
#> 4 I1 I5 0.465 0.6450 0.375
#> 5 I1 I6 0.645 0.7850 0.895
#> 6 I1 I7 0.815 0.8700 1.000
If any of the occurrences have "NA" and "NaN" values in the UCI and
p.value fields, it indicates that the values for that occurrence have
repeated values. This prevents bootstrapping.
The delete parameter allows assigning zeros to edges whose incidences
are significantly less than thr to the p-value set in the conf.level
parameter. Also, this allows you to remove non-significant results from
the $DirectEffects subset.
For example, let thr = 0.5 and conf.level = 0.95, mean incidences
less than 0.5 or incidents with p.value less than 1 - conf.level
will be eliminated.
result <- directEffects(CC = AA, thr = 0.5, reps = 1000, delete = TRUE)
#> deleting data...
The function reports by console when significant edges have been
removed. The number of significant direct effects decreased from 240 to
205 for delete = TRUE.
Note: However, this does not guarantee that a non-significant variable in 1st order does not generate 2nd order effects, since they are extracted from the empirical distribution of the key informants.
For delete = TRUE, the function returns $Data, the three-dimensional
matrix entered in the CC parameter but assigning 0 to the
non-significant edges.
For chain bipartite graphs To calculate the significant direct effects
of the incidence matrices AA, AB and BB, which are described in
DataSet, we make use of the already described parameter CC. The EE
parameter is equivalent to the CC parameter. The CE parameter allows
you to enter a three-dimensional matrix, where each sub-matrix along the
z-axis is a rectangular incidence matrix or a list of data.frame
containing rectangular incidence matrices. Each matrix represents a
bipartite graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- directEffects(CC = AA, CE = AB, EE = BB, reps = 1000)
The results obtained correspond to 312 first-order incidents. Using the
delete = TRUE parameter, the number of first-order significant
occurrences was reduced to 271.
For delete = TRUE, the function returns $CC, $CE, and $EE, which
are the three-dimensional matrices entered in the parameters CC, CE,
and EE, but assigning 0 to the non-significant edges.
For chain bipartite graphs
To calculate the significant direct effects of the incidence matrices
AA, ABand BB, which are described in DataSet, we make use of the
already described parameter CC. The EEparameter is equivalent to the
CCparameter. The CEparameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- directEffects(CC = AA, CE = AB, EE = BB, thr = 0.5, reps = 1000)
The results obtained correspond to 312 first-order incidents. Using the
delete = TRUE parameter, the number of first order significant
occurrences was reduced to 271.
For delete = TRUE, the function returns $CC, $CE and $EE, which
are the three-dimensional matrices entered in the parameters CC,
CEand EE, but assigning 0 to the non-significant edges.
bootMargin()
The bootMargin() function calculates the mean incidence of each cause
and each effect, confidence intervals, and p-value with multiple experts
for complete graphs and chain bipartite graphs.
The function contemplates two modalities, the first is focused on complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the average incidence of each cause and each effect of the
AA incidence matrix, which is described in DataSet, we use the CC
parameter, which allows us to enter a three-dimensional matrix, where
each sub-matrix along the z-axis is a reflexive square incidence matrix
or a list of data.frame containing square and reflexive incidence
matrices. Each matrix represents a complete graph. The CE and EE
parameters are used to perform the calculation with chain bipartite
graphs, therefore it is necessary that these parameters are not used.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
The bootMargin() function makes use of the “boot.one.bca” function
from the wBoot package to implement the bootstrap resampling method
with BCa adjusted boot and with a two-sided hypothesis test based on the
Z-test. The conf.level parameter defines the confidence level and
reps the number of bootstrap replicas. By default conf.level = 0.95
and reps = 10000.
For example, let thr = 0.6 and reps = 1000 we get:
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000)
The function returns a list object with the data subsets $byRow and
$byCol, each of these subsets of data contains the following values:
- Var: Variable name
- Mean: Calculated mean.
- LCI: Lower Confidence Interval
- ICU: Upper Confidence Interval
- p.value: the calculated p-value.
The bootMargin() function allows you to analyze by node or by
variable. The results obtained are:
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 1 I1 0.5255433 0.4675 0.5875 2.91e-02
#> 2 I2 0.5994003 0.5515 0.6579 9.66e-01
#> 3 I3 0.4280310 0.3590 0.4703 7.73e-05
#> 4 I4 0.4905413 0.4008 0.5421 2.94e-05
#> 5 I5 0.5344293 0.4717 0.5977 4.30e-02
#> 6 I6 0.5539760 0.4773 0.6167 1.25e-01
#> 7 I7 0.5315417 0.4818 0.5835 1.10e-02
#> 8 I8 0.5427540 0.4663 0.6134 1.13e-01
#> 9 I9 0.4643607 0.4060 0.5165 4.25e-04
#> 10 I10 0.4731567 0.3930 0.5400 4.28e-04
#> 11 I11 0.5974773 0.5503 0.6423 8.91e-01
#> 12 I12 0.4559787 0.3943 0.4987 6.48e-05
#> 13 I13 0.5539730 0.4700 0.6363 2.52e-01
#> 14 I14 0.2485857 0.2049 0.2980 1.44e-03
#> 15 I15 0.4426557 0.3927 0.4950 1.48e-03
#> 16 I16 0.5140877 0.4532 0.5627 4.41e-04
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 1 I1 0.4803423 0.3666 0.5719 0.011600
#> 2 I2 0.5521307 0.4294 0.6547 0.384000
#> 3 I3 0.4186917 0.3133 0.5110 0.000675
#> 4 I4 0.4692143 0.3539 0.5916 0.039300
#> 5 I5 0.4575023 0.3578 0.5532 0.000559
#> 6 I6 0.5872893 0.3857 0.6677 0.733000
#> 7 I7 0.5562813 0.4408 0.6485 0.417000
#> 8 I8 0.5743783 0.5063 0.6502 0.478000
#> 9 I9 0.4531933 0.3364 0.5476 0.002950
#> 10 I10 0.4636727 0.3800 0.5791 0.018000
#> 11 I11 0.5774543 0.4310 0.6927 0.724000
#> 12 I12 0.4563103 0.3341 0.5764 0.014500
#> 13 I13 0.5636160 0.4761 0.6353 0.330000
#> 14 I14 0.2733193 0.1853 0.3371 0.000199
#> 15 I15 0.4720647 0.3593 0.5930 0.040700
#> 16 I16 0.5914300 0.5164 0.6933 0.915000
The function allows eliminating causes and effects whose average
incidence is not significant at the set thr parameter. For example,
for delete = TRUE, the number of significant variables decreased.
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000, delete = TRUE)
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 2 I2 0.6003730 0.5477 0.6533 0.97300
#> 5 I5 0.5336233 0.4730 0.6047 0.07770
#> 6 I6 0.5536140 0.4790 0.6164 0.17600
#> 7 I7 0.5302397 0.4799 0.5818 0.00816
#> 8 I8 0.5435877 0.4643 0.6093 0.10300
#> 11 I11 0.5974457 0.5538 0.6495 0.94000
#> 13 I13 0.5542533 0.4753 0.6398 0.26500
#> 15 I15 0.4408610 0.3917 0.4939 0.00180
#> 16 I16 0.5129870 0.4541 0.5649 0.00358
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 2 I2 0.5552910 0.4249 0.6597 0.422000
#> 5 I5 0.4609383 0.3559 0.5459 0.000277
#> 6 I6 0.5878387 0.4093 0.6700 0.776000
#> 7 I7 0.5558383 0.4350 0.6575 0.390000
#> 8 I8 0.5744267 0.5113 0.6519 0.487000
#> 11 I11 0.5760340 0.4348 0.6976 0.745000
#> 13 I13 0.5614550 0.4846 0.6372 0.364000
#> 15 I15 0.4726193 0.3480 0.6017 0.061500
#> 16 I16 0.5929490 0.5190 0.6762 0.887000
For delete = TRUE, the function returns$Data, the matrix entered in
the CCparameter, but with the non-significant rows and columns
removed.
For plot = TRUE, the function returns $plot, which contains the
graph generated from the subsets $byRow and $byCol. On the x-axis
are the “Dependence” associated with $byCol and on the y-axis the
“Influence” is associated with $byRow.
result <- bootMargin(CC = AA, thr = 0.6, reps = 1000, delete = TRUE, plot = TRUE)
result$plot
For chain bipartite graphs
To calculate the average incidence of each cause and each effect of the
incidence matrices AA, ABand BB, which are described in DataSet,
we make use of the already described parameter CC. The EEparameter
is equivalent to the CCparameter. The CEparameter allows you to
enter a three-dimensional matrix, where each sub-matrix along the z-axis
is a rectangular incidence matrix or a list of data.frame containing
rectangular incidence matrices. Each matrix represents a bipartite
graph.
For example, let thr = 0.5 and reps = 1000, you get:
result <- bootMargin(CC = AA, CE = AB, EE = BB, thr = 0.6, reps = 1000)
The results obtained correspond to all the nodes or variables found in the entered matrices.
The results for $byRow and $byCol are:
For $byRow
result$byRow
#> Var Mean LCI UCI p.value
#> 1 I1 0.5151763 0.4697 0.5646 0.004940
#> 2 I2 0.6292071 0.5810 0.6773 0.214000
#> 3 I3 0.4569737 0.3939 0.5247 0.001630
#> 4 I4 0.5099500 0.4502 0.5729 0.002360
#> 5 I5 0.5479624 0.4920 0.6071 0.075200
#> 6 I6 0.5819237 0.5146 0.6524 0.621000
#> 7 I7 0.5735553 0.5188 0.6301 0.381000
#> 8 I8 0.5724137 0.5017 0.6371 0.414000
#> 9 I9 0.4796082 0.4162 0.5403 0.002890
#> 10 I10 0.5159689 0.4442 0.5926 0.030100
#> 11 I11 0.6527029 0.5970 0.7190 0.069600
#> 12 I12 0.4782905 0.4124 0.5313 0.000708
#> 13 I13 0.6236258 0.5380 0.7139 0.589000
#> 14 I14 0.2443937 0.2040 0.2807 0.000833
#> 15 I15 0.4595650 0.4187 0.5096 0.001250
#> 16 I16 0.5279329 0.4812 0.5713 0.001540
#> 17 B1 0.6780183 0.6000 0.7200 0.203000
#> 18 B2 0.6784550 0.5700 0.7550 0.152000
#> 19 B3 0.6737850 0.5500 0.7717 0.493000
#> 20 B4 0.8084783 0.8000 0.8150 0.000753
For $byCol
result$byCol
#> Var Mean LCI UCI p.value
#> 1 I1 0.4792417 0.3635 0.5734 6.79e-03
#> 2 I2 0.5564770 0.4295 0.6560 3.96e-01
#> 3 I3 0.4205187 0.3153 0.5110 5.59e-04
#> 4 I4 0.4689753 0.3438 0.5823 2.54e-02
#> 5 I5 0.4617787 0.3550 0.5435 1.29e-03
#> 6 I6 0.5841477 0.4211 0.6725 8.13e-01
#> 7 I7 0.5578120 0.4368 0.6534 3.89e-01
#> 8 I8 0.5741100 0.5117 0.6463 4.53e-01
#> 9 I9 0.4477490 0.3483 0.5648 1.43e-02
#> 10 I10 0.4680223 0.3611 0.5744 1.92e-02
#> 11 I11 0.5800763 0.4337 0.7040 7.48e-01
#> 12 I12 0.4567530 0.3241 0.5566 1.09e-02
#> 13 I13 0.5640473 0.4715 0.6353 2.79e-01
#> 14 I14 0.2744593 0.1881 0.3358 1.46e-04
#> 15 I15 0.4747730 0.3534 0.5854 2.86e-02
#> 16 I16 0.5927650 0.5120 0.6756 8.81e-01
#> 17 B1 0.5394645 0.4434 0.6576 3.19e-01
#> 18 B2 0.6761287 0.6108 0.7687 1.94e-02
#> 19 B3 0.6904068 0.6339 0.7689 8.56e-05
#> 20 B4 0.6276187 0.5391 0.7255 5.28e-01
For delete = TRUE, the function returns $CC, $CE, and $EE, which
are the three-dimensional arrays entered in the CC, CE, and EE
parameters, but with the rows and columns removed.
For plot = TRUE, the function returns $plot, which contains the
graph generated from the subsets $byRow and $byCol. On the x-axis
are the “Dependence” associated with $byCol and on the y-axis the
“Influence” is associated with $byRow.
centralitry()
The centrality() function calculates the median betweenness
centrality, confidence intervals, and the selected method for
calculating the centrality distribution for complete graphs and chain
bipartite graphs.
The function contemplates two modalities, the first is focused on complete graphs and the second for chain bipartite graphs.
For complete graphs
To calculate the median betweenness centrality of the incidence matrix
AA, which is described in DataSet, we use the parameter CC, which
allows us to enter a three-dimensional matrix, where each submatrix
along the z-axis is a square incidence matrix and reflective, or a list
of data.frame containing square and reflective incidence matrices. Each
matrix represents a complete graph. The CEand EEparameters are used
to perform the calculation with chain bipartite graphs, therefore it is
necessary that these parameters are not used.
The centrality() function makes use of the “boot” function from the
boot package (Canty A, Ripley BD, 2021) to implement the bootstrap
method with BCa tight boot. The number of bootstrap replicas is defined
in the repsparameter. By default reps = 10000.
The model parameter allows bootstrapping with some of the following statistics: mediate.
median.conpl: Calculate the median of a power distribution according to Newman M.E (2005).conlnorm: Calculates the median of a power distribution according to Gillespie CS (2015).
The objective of the model parameter is to determine to which heavy-tailed distribution the variables or nodes of the entered parameter correspond.
For example, let model = "median" and reps = 300, we will obtain:
result <- centrality(CC = AA, model = "median", reps = 300)
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I3 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I9 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I12 has median = 0
#> Warning in resultBoot_median(output_resultIgraph, parallel, reps, ncpus, :
#> Variable I14 has median = 0
The returned object of type data.frame contains the following components:
- Var: Name of the variable.
- Median: Median calculated.
- LCI: Lower Confidence Interval.
- ICU: Upper Confidence Interval.
- Method: Statistical method used associated with the model parameter.
If the median calculated for any of the betweenness centrality has a median equal to 0, the LCI and UCI fields will have a value equal to 0. This is reported with a warning per console.
The results are:
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 21.358333 median
#> 2 I2 12.9875000 2.7055613 25.430556 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 2.079167 median
#> 5 I5 6.2083333 0.4958333 10.250000 median
#> 6 I6 20.2791667 4.8070548 36.000000 median
#> 7 I7 11.0833333 1.7500000 41.000000 median
#> 8 I8 4.7083333 0.1000000 10.333333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 3.1942299 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.7763065 11.000000 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 8.583333 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Now if we use "conpl" in the model parameter and 300 bootstrap
replicas, we get:
result <- centrality(CC = AA, model = "conpl", reps = 300)
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I9 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I12 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 26.221124 median
#> 2 I2 12.9875000 2.2500000 25.166667 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 3.102966 median
#> 5 I5 6.2083333 0.6666667 10.655172 median
#> 6 I6 20.2791667 4.7074397 42.583333 median
#> 7 I7 11.0833333 1.9107598 41.000000 median
#> 8 I8 4.7083333 0.1000000 10.833333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 2.6250000 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.5000000 11.000000 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 7.291667 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Note: If the calculation cannot be performed with model = "conpl"
in some node, the function will perform the calculation with "median".
This change is indicated in the Method field.
Now if we use "conlnorm" in the model parameter and 300 bootstrap
replicas, we get:
result <- centrality(CC = AA, model = "conlnorm", reps = 300)
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I9 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I12 has median = 0
#> Warning in conlnorm_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 13.1666667 0.0000000 21.358333 median
#> 2 I2 12.9875000 2.2500000 24.125000 median
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.8333333 0.0000000 1.995833 median
#> 5 I5 6.2083333 0.4958333 10.000000 median
#> 6 I6 20.2791667 4.4964274 36.000000 median
#> 7 I7 11.0833333 1.5000000 31.700000 median
#> 8 I8 4.7083333 0.1000000 10.833333 median
#> 9 I9 0.0000000 0.0000000 0.000000 median
#> 10 I10 1.5000000 0.0000000 8.125000 median
#> 11 I11 15.8333333 0.6950687 30.416667 median
#> 12 I12 0.0000000 0.0000000 0.000000 median
#> 13 I13 4.7916667 0.0000000 9.916667 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 9.211933 median
#> 16 I16 13.1666667 2.5833333 28.458333 median
Note: If the calculation cannot be performed with
model = "conlnorm" in some node, the function will perform the
calculation with “median”. This change is indicated in the Method field
IMPORTANT: The best statistic to use in the model parameter will depend on the data and the number of bootstrap replicas that you deem appropriate.
The centrality() function implements the parallel function from the
boot package. The parallelparameter allows you to set the type of
parallel operation that is required. The options are "multicore",
"snow" and "no". By default parallel = "no". The number of
processors to be used in the paralell implementation is defined in the
ncpusparameter. By default ncpus = 1.
The paralleland ncpusoptions are not available on Windows operating
systems.
For chain bipartite graphs
To calculate the median betweenness centrality of the incidence matrices
AA, ABand BB, which are described in DataSet, we make use of the
already described parameter CC. The EEparameter is equivalent to the
CCparameter. The CEparameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
For example, let model = "conpl" and reps = 300, you get:
result <- centrality(CC = AA, CE = AB, EE = BB, model = "conpl", reps = 300)
#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I3 has median = 0
#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable I14 has median = 0
#> Warning in conpl_function(resultCent = output_resultIgraph, parallel =
#> parallel, : Variable B1 has median = 0
result
#> Var Median LCI UCI Method
#> 1 I1 14.0416667 0.0000000 31.883333 median
#> 2 I2 14.6913273 7.9899228 17.799567 conpl
#> 3 I3 0.0000000 0.0000000 0.000000 median
#> 4 I4 0.9166667 0.1666667 4.708333 median
#> 5 I5 6.2083333 0.6710528 13.041667 median
#> 6 I6 24.6720238 4.5607143 48.975000 median
#> 7 I7 9.2552918 1.1172637 25.079716 conpl
#> 8 I8 8.2761905 3.7500000 21.294048 median
#> 9 I9 0.3750000 0.0000000 3.650000 median
#> 10 I10 1.5714286 0.1666667 8.125000 median
#> 11 I11 21.0241962 13.7066578 21.438612 conpl
#> 12 I12 3.3333333 0.0000000 11.318238 median
#> 13 I13 5.0166667 1.1428571 14.434524 median
#> 14 I14 0.0000000 0.0000000 0.000000 median
#> 15 I15 2.5000000 0.0000000 9.166667 median
#> 16 I16 18.7916667 2.5833333 39.019637 median
#> 17 B1 0.0000000 0.0000000 0.000000 median
#> 18 B2 2.7833333 1.0000000 5.500000 median
#> 19 B3 2.0000000 0.5000000 3.333333 median
#> 20 B4 1.8666667 0.0000000 6.965270 median
The centrality() function implements the parallel function from the
bootpackage. The parallelparameter allows you to set the type of
parallel operation that is required. The options are "multicore",
"snow" and "no". By default parallel = "no". The number of
processors to be used in the paralellimplementation is defined in the
ncpusparameter. By default ncpus = 1.
The paralleland ncpusoptions are not available on Windows operating
systems.
fe.sq()
The function fe.sq(), calculates the forgotten effects (Kaufmann & Gil
Aluja, 1988) with multiple experts for complete graphs, with calculation
of the frequency of appearance of the forgotten effects, mean incidence,
confidence intervals and standard error
For example, to perform the calculation using the incidence matrix AA,
described in DATASET, we use the parameter CC, which allows us to
enter a three-dimensional matrix, where each sub-matrix along the z axis
is a square and reflective incidence matrix , or a list of data.frame
containing square and reflective incidence matrices. Each matrix
represents a complete graph.
To define the degree of truth in which the incidence is considered
significant, the parameter thris used, which is defined between
[0,1]. By default thr = 0.5.
To define the maximum order of the forgotten effects, use the
maxOrderparameter. By default maxOrder = 2.
The fe.sq() function makes use of the “boot” function from the boot
package (Canty A, Ripley BD, 2021) to implement bootstrap with BCa tight
boot. The number of bootstrap replicas is defined in the reps
parameter. By default reps = 10000.
For example, let thr = 0.5, maxOrder = 3 and reps = 1000, you get:
result <- fe.sq(CC = AA, thr = 0.5, maxOrder = 3, reps = 1000)
The returned object of type list contains two subsets of data. The
$boot data subset is a list of data.frame where each data.frame
represents the order of the calculated forgotten effect, the components
are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate relationships of the forgotten effects. For example, for order n there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Mean: Mean effect of the forgotten effect
- LCI: Lower Confidence Intervals.
- UCI: Upper Confidence Intervals.
- SE: Standard error.
The $byExperts data subset is a list of data.frame where each
data.frame represents the order of the forgotten effect calculated
with its associated incidence value for each expert, the components are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate relationships of the forgotten effects. For example, for order n there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Expert_x: Dynamic field that represents each of the entered experts.
If we look at the data in the $boot$Order_2 data subset, we find 706
2nd order effects and 611 of these effects are unique. The first 6 are:
head(result$boot$Order_2)
#> From Through_1 To Count Mean LCI UCI SE
#> 1 I8 I11 I10 4 0.6125000 0.5625 0.6750000 0.02652208
#> 2 I5 I11 I10 3 0.6166667 0.5500 0.6666667 0.03671591
#> 3 I6 I11 I14 3 0.6833333 0.6000 0.7666667 0.07021737
#> 4 I13 I11 I14 3 0.5833333 0.5500 0.6000000 0.01399985
#> 5 I13 I6 I1 3 0.6333333 0.6000 0.6666667 0.02748039
#> 6 I13 I16 I1 3 0.6333333 0.6000 0.6666667 0.02785307
The relations I8 -> I11 -> I10 appeared 4 times. To know exactly in
which expert these relationships were found, there is the $byExperts
data subset. If we look at the first row of $byExperts$order_2 we can
identify the experts who provided this information.
head(result$byExperts$Order_2)
#> From Through_1 To Count Expert_1 Expert_2 Expert_3 Expert_4 Expert_5
#> 1 I8 I11 I10 4 0.55 0.6 0.00 0.6 0.0
#> 2 I5 I11 I10 3 0.55 0.7 0.00 0.0 0.0
#> 3 I6 I11 I14 3 0.00 0.6 0.85 0.6 0.0
#> 4 I13 I11 I14 3 0.00 0.6 0.00 0.6 0.0
#> 5 I13 I6 I1 3 0.00 0.0 0.60 0.6 0.0
#> 6 I13 I16 I1 3 0.00 0.0 0.00 0.6 0.7
#> Expert_6 Expert_7 Expert_8 Expert_9 Expert_10
#> 1 0.7 0.00 0.0 0 0.0
#> 2 0.0 0.00 0.6 0 0.0
#> 3 0.0 0.00 0.0 0 0.0
#> 4 0.0 0.55 0.0 0 0.0
#> 5 0.0 0.00 0.0 0 0.7
#> 6 0.0 0.00 0.6 0 0.0
IMPORTANT: If any of the $boot values shows "NA" in LCI, UCI and
SE, it indicates that the values of the incidents per expert are the
same or the value is unique. That prevents implementing bootstrap.
The fe.sq() function implements the parallel function from the boot
package. The parallel parameter allows you to set the type of parallel
operation that is required. The options are "multicore", "snow" and
"no". By default parallel = "no". The number of processors to be
used in the paralellimplementation is defined in the ncpusparameter.
By default ncpus = 1.
The parallel and ncpusoptions are not available on Windows operating
systems.
fe.rect()
The function fe.rect(), calculates the forgotten effects (Kaufmann &
Gil Aluja, 1988) with multiple key informants for chain bipartite
graphs, with calculation of the frequency of appearance of the forgotten
effects, mean incidence, confidence intervals and standard error.
To perform the calculation using the incidence matrices AA, ABand
BB, which are described in DataSet, we make use of the already
described parameter CC. The EE parameter is equivalent to the CC
parameter. The CE parameter allows you to enter a three-dimensional
matrix, where each sub-matrix along the z-axis is a rectangular
incidence matrix, or a list of data.frame containing rectangular
incidence matrices. Each matrix represents a bipartite graph.
To define the degree of truth in which the incidence is considered
significant, the parameter thr is used, which is defined between
[0,1]. By default thr = 0.5.
To define the maximum order of the forgotten effects, use the
maxOrderparameter. By default maxOrder = 2.
The fe.rect() function makes use of the “boot” function from the
boot package (Canty A, Ripley BD, 2021) to implement bootstrap with BCa
tight boot.. The number of bootstrap replicas is defined in the reps
parameter. By default reps = 10000.
For example, let thr = 0.5, maxOrder = 3 and reps = 1000, you get:
result <- fe.rect(CC = AA,CE = AB, EE = BB, thr = 0.5, maxOrder = 3, reps = 1000)
#> Warning in wrapper.indirectEffects_R(CC = CC, CE = CE, EE = EE, thr = thr, :
#> Expert number 7 has no 2nd maxOrder or higher effects.
The returned object of type list contains two subsets of data. The
$boot data subset is a list of data.frame where each data.frame
represents the order of the calculated forgotten effect, the components
are:
- From: Indicates the origin of the forgotten effects relationships.
- Through_x: Dynamic field that represents the intermediate relationships of the forgotten effects. For example, for order n there will be “though_1” up to “though_ \”.
- To: Indicates the end of the forgotten effects relationships.
- Count: Number of times the forgotten effect was repeated.
- Mean: Mean effect of the forgotten effect
- LCI: Lower Confidence Intervals.
- UCI: Upper Confidence Intervals.
- SE: Standard error.
The $byExperts data subset is a list of data.frame where each
data.frame represents the order of the forgotten effect calculated
with its associated incidence value for each expert, the components are:
-
From: Indicates the origin of the forgotten effects relationships.
-
Through_x: Dynamic field that represents the intermediate relationships of the forgotten effects. For example, for order n there will be “though_1” up to “though_ \”.
-
To: Indicates the end of the forgotten effects relationships.
-
Count: Number of times the forgotten effect was repeated.
-
Expert_x: Dynamic field that represents each of the entered experts.
If we look at the data in the $boot$Order_2 data subset, we find 182
2nd order effects and 162 of these effects are unique. The first 6 are:
head(result$boot$Order_2)
#> From Through_1 To Count Mean LCI UCI SE
#> 1 I5 B4 B1 3 0.6333333 0.60 0.6666667 0.02745863
#> 2 I6 I7 B1 2 0.8000000 0.75 0.8000000 0.03469411
#> 3 I8 I7 B1 2 0.6250000 0.60 0.6250000 0.01775705
#> 4 I12 I2 B1 2 0.7000000 0.65 0.7500000 0.03593144
#> 5 I10 I11 B2 2 0.5750000 0.55 0.5750000 0.01719826
#> 6 I14 I15 B2 2 0.7250000 0.70 0.7500000 0.01807081
The relations I5 -> B4 -> B1 appeared 3 times. To know exactly in which
expert these relationships were found, there is the $byExperts data
subset. If we look at the first row of $byExperts$order_2 we can
identify the experts who provided this information.
head(result$byExperts$Order_2)
#> From Through_1 To Count Expert_1 Expert_2 Expert_3 Expert_4 Expert_5 Expert_6
#> 1 I5 B4 B1 3 0.60 0.7 0 0.60 0.00 0
#> 2 I6 I7 B1 2 0.75 0.0 0 0.85 0.00 0
#> 3 I8 I7 B1 2 0.65 0.6 0 0.00 0.00 0
#> 4 I12 I2 B1 2 0.65 0.0 0 0.75 0.00 0
#> 5 I10 I11 B2 2 0.60 0.0 0 0.00 0.55 0
#> 6 I14 I15 B2 2 0.75 0.0 0 0.00 0.70 0
#> Expert_7 Expert_8 Expert_9 Expert_10
#> 1 0 0 0 0
#> 2 0 0 0 0
#> 3 0 0 0 0
#> 4 0 0 0 0
#> 5 0 0 0 0
#> 6 0 0 0 0
MPORTANT: If any of the $boot values shows "NA" in LCI, UCI and
SE, it indicates that the values of the incidents per expert are the
same or the value is unique. That prevents implementing bootstrap.
The fe.sq() function implements the parallel function from the boot
package. The parallelparameter allows you to set the type of parallel
operation that is required. The options are "multicore", "snow" and
"no". By default parallel = "no". The number of processors to be
used in the paralell implementation is defined in the ncpus
parameter. By default ncpus = 1.
The parallel and ncpus options are not available on Windows
operating systems.
References
-
Kaufmann, A., & Gil Aluja, J. (1988). Modelos para la Investigación de efectos olvidados, Milladoiro. Santiago de Compostela, España.
-
Manna, E. M., Rojas-Mora, J., & Mondaca-Marino, C. (2018). Application of the Forgotten Effects Theory for Assessing the Public Policy on Air Pollution of the Commune of Valdivia, Chile. In From Science to Society (pp. 61-72). Springer, Cham.
-
Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.
-
Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001.
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Canty A, Ripley BD (2021). boot: Bootstrap R (S-Plus) Functions. R package version 1.3-28.
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