`bootEGA`

Estimates the number of dimensions of `iter`

bootstraps
using the empirical zero-order correlation matrix (`"parametric"`

) or
`"resampling"`

from the empirical dataset (non-parametric). `bootEGA`

estimates a typical median network structure, which is formed by the median or
mean pairwise (partial) correlations over the *iter* bootstraps (see
**Details** for information about the typical median network structure).

## Usage

```
bootEGA(
data,
n = NULL,
corr = c("auto", "cor_auto", "pearson", "spearman"),
na.data = c("pairwise", "listwise"),
model = c("BGGM", "glasso", "TMFG"),
algorithm = c("leiden", "louvain", "walktrap"),
uni.method = c("expand", "LE", "louvain"),
iter = 500,
type = c("parametric", "resampling"),
ncores,
EGA.type = c("EGA", "EGA.fit", "hierEGA", "riEGA"),
plot.itemStability = TRUE,
typicalStructure = FALSE,
plot.typicalStructure = FALSE,
seed = NULL,
verbose = TRUE,
...
)
```

## Arguments

- data
Matrix or data frame. Should consist only of variables to be used in the analysis

- n
Numeric (length = 1). Sample size if

`data`

provided is a correlation matrix- corr
Character (length = 1). Method to compute correlations. Defaults to

`"auto"`

. Available options:`"auto"`

— Automatically computes appropriate correlations for the data using Pearson's for continuous, polychoric for ordinal, tetrachoric for binary, and polyserial/biserial for ordinal/binary with continuous. To change the number of categories that are considered ordinal, use`ordinal.categories`

(see`polychoric.matrix`

for more details)`"cor_auto"`

— Uses`cor_auto`

to compute correlations. Arguments can be passed along to the function`"pearson"`

— Pearson's correlation is computed for all variables regardless of categories`"spearman"`

— Spearman's rank-order correlation is computed for all variables regardless of categories

For other similarity measures, compute them first and input them into

`data`

with the sample size (`n`

)- na.data
Character (length = 1). How should missing data be handled? Defaults to

`"pairwise"`

. Available options:`"pairwise"`

— Computes correlation for all available cases between two variables`"listwise"`

— Computes correlation for all complete cases in the dataset

- model
Character (length = 1). Defaults to

`"glasso"`

. Available options:`"BGGM"`

— Computes the Bayesian Gaussian Graphical Model. Set argument`ordinal.categories`

to determine levels allowed for a variable to be considered ordinal. See`?BGGM::estimate`

for more details`"glasso"`

— Computes the GLASSO with EBIC model selection. See`EBICglasso.qgraph`

for more details`"TMFG"`

— Computes the TMFG method. See`TMFG`

for more details

- algorithm
Character or

`igraph`

`cluster_*`

function (length = 1). Defaults to`"walktrap"`

. Three options are listed below but all are available (see`community.detection`

for other options):`"leiden"`

— See`cluster_leiden`

for more details`"louvain"`

— By default,`"louvain"`

will implement the Louvain algorithm using the consensus clustering method (see`community.consensus`

for more information). This function will implement`consensus.method = "most_common"`

and`consensus.iter = 1000`

unless specified otherwise`"walktrap"`

— See`cluster_walktrap`

for more details

- uni.method
Character (length = 1). What unidimensionality method should be used? Defaults to

`"louvain"`

. Available options:`"expand"`

— Expands the correlation matrix with four variables correlated 0.50. If number of dimension returns 2 or less in check, then the data are unidimensional; otherwise, regular EGA with no matrix expansion is used. This method was used in the Golino et al.'s (2020)*Psychological Methods*simulation`"LE"`

— Applies the Leading Eigenvector algorithm (`cluster_leading_eigen`

) on the empirical correlation matrix. If the number of dimensions is 1, then the Leading Eigenvector solution is used; otherwise, regular EGA is used. This method was used in the Christensen et al.'s (2023)*Behavior Research Methods*simulation`"louvain"`

— Applies the Louvain algorithm (`cluster_louvain`

) on the empirical correlation matrix. If the number of dimensions is 1, then the Louvain solution is used; otherwise, regular EGA is used. This method was validated Christensen's (2022)*PsyArXiv*simulation. Consensus clustering can be used by specifying either`"consensus.method"`

or`"consensus.iter"`

- iter
Numeric (length = 1). Number of replica samples to generate from the bootstrap analysis. Defaults to

`500`

(recommended)- type
Character (length = 1). What type of bootstrap should be performed? Defaults to

`"parametric"`

. Available options:`"parametric"`

— Generates`iter`

new datasets from (multivariate normal random distributions) based on the original dataset using`mvrnorm`

`"resampling"`

— Generates`iter`

new datasets from random subsamples of the original data

- ncores
Numeric (length = 1). Number of cores to use in computing results. Defaults to

`ceiling(parallel::detectCores() / 2)`

or half of your computer's processing power. Set to`1`

to not use parallel computingIf you're unsure how many cores your computer has, then type:

`parallel::detectCores()`

- EGA.type
Character (length = 1). Type of EGA model to use. Defaults to

`"EGA"`

Available options:`"EGA"`

— Uses standard exploratory graph analysis`"hierEGA"`

— Uses hierarchical exploratory graph analysis`"riEGA"`

— Uses random-intercept exploratory graph analysis

Arguments for

`EGA.type`

can be added (see links for details on specific function arguments)- plot.itemStability
Boolean (length = 1). Should the plot be produced for

`item.replication`

? Defaults to`TRUE`

- typicalStructure
Boolean (length = 1). If

`TRUE`

, returns the median (`"glasso"`

or`"BGGM"`

) or mean (`"TMFG"`

) network structure and estimates its dimensions (see**Details**for more information). Defaults to`FALSE`

- plot.typicalStructure
Boolean (length = 1). If

`TRUE`

, returns a plot of the typical network structure. Defaults to`FALSE`

- seed
Numeric (length = 1). Defaults to

`NULL`

or random results. Set for reproducible results. See Reproducibility and PRNG for more details on random number generation in`EGAnet`

- verbose
Boolean (length = 1). Should progress be displayed? Defaults to

`TRUE`

. Set to`FALSE`

to not display progress- ...
Additional arguments that can be passed on to

`auto.correlate`

,`network.estimation`

,`community.detection`

,`community.consensus`

,`EGA`

,`EGA.fit`

,`hierEGA`

, and`riEGA`

## Value

Returns a list containing:

- iter
Number of replica samples in bootstrap

- bootGraphs
A list containing the networks of each replica sample

- boot.wc
A matrix of membership assignments for each replica network with variables down the columns and replicas across the rows

- boot.ndim
Number of dimensions identified in each replica sample

- summary.table
A data frame containing number of replica samples, median, standard deviation, standard error, 95% confidence intervals, and quantiles (lower = 2.5% and upper = 97.5%)

- frequency
A data frame containing the proportion of times the number of dimensions was identified (e.g., .85 of 1,000 = 850 times that specific number of dimensions was found)

- TEFI
`tefi`

value for each replica sample- type
Type of bootstrap used

- EGA
Output of the empirical EGA results (output will vary based on

`EGA.type`

)- EGA.type
Type of

`*EGA`

function used- typicalGraph
A list containing:

`graph`

— Network matrix of the median network structure`typical.dim.variables`

— An ordered matrix of item allocation`wc`

— Membership assignments of the median network

- plot.typical.ega
Plot output if

`plot.typicalStructure = TRUE`

## Details

The typical network structure is derived from the median (or mean) value of each pairwise relationship. These values tend to reflect the "typical" value taken by an edge across the bootstrap networks. Afterward, the same community detection algorithm is applied to the typical network as the bootstrap networks.

Because the community detection algorithm is applied to the typical network structure,
there is a possibility that the community algorithm determines
a different number of dimensions than the median number derived from the bootstraps.
The typical network structure (and number of dimensions) may *not*
match the empirical `EGA`

number of dimensions or
the median number of dimensions from the bootstrap. This result is known
and *not* a bug.

## References

**Original implementation of bootEGA**

Christensen, A. P., & Golino, H. (2021).
Estimating the stability of the number of factors via Bootstrap Exploratory Graph Analysis: A tutorial.
*Psych*, *3*(3), 479-500.

## See also

`itemStability`

to estimate the stability of
the variables in the empirical dimensions and
`dimensionStability`

to estimate the stability of
the dimensions (structural consistency)

## Author

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <alexpaulchristensen@gmail.com>

## Examples

```
# Load data
wmt <- wmt2[,7:24]
if (FALSE) { # \dontrun{
# Standard EGA parametric example
boot.wmt <- bootEGA(
data = wmt, iter = 500,
type = "parametric", ncores = 2
)
# Standard resampling example
boot.wmt <- bootEGA(
data = wmt, iter = 500,
type = "resampling", ncores = 2
)
# Example using {igraph} `cluster_*` function
boot.wmt.spinglass <- bootEGA(
data = wmt, iter = 500,
algorithm = igraph::cluster_spinglass,
# use any function from {igraph}
type = "parametric", ncores = 2
)
# EGA fit example
boot.wmt.fit <- bootEGA(
data = wmt, iter = 500,
EGA.type = "EGA.fit",
type = "parametric", ncores = 2
)
# Hierarchical EGA example
boot.wmt.hier <- bootEGA(
data = wmt, iter = 500,
EGA.type = "hierEGA",
type = "parametric", ncores = 2
)
# Random-intercept EGA example
boot.wmt.ri <- bootEGA(
data = wmt, iter = 500,
EGA.type = "riEGA",
type = "parametric", ncores = 2
)} # }
```