This function uses the `glasso`

package
(Friedman, Hastie and Tibshirani, 2011) to compute a
sparse gaussian graphical model with the graphical lasso
(Friedman, Hastie & Tibshirani, 2008).
The tuning parameter is chosen using the Extended Bayesian Information criterion
(EBIC) described by Foygel & Drton (2010).

## Usage

```
EBICglasso.qgraph(
data,
n = NULL,
corr = c("auto", "cor_auto", "pearson", "spearman"),
na.data = c("pairwise", "listwise"),
gamma = 0.5,
penalize.diagonal = FALSE,
nlambda = 100,
lambda.min.ratio = 0.1,
returnAllResults = FALSE,
penalizeMatrix,
countDiagonal = FALSE,
refit = FALSE,
model.selection = c("EBIC", "JSD"),
verbose = FALSE,
...
)
```

## 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

- 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

- gamma
Numeric (length = 1) EBIC tuning parameter. Defaults to

`0.50`

and is generally a good choice. Setting to`0`

will cause regular BIC to be used- penalize.diagonal
Boolean (length = 1). Should the diagonal be penalized? Defaults to

`FALSE`

- nlambda
Numeric (length = 1). Number of lambda values to test. Defaults to

`100`

- lambda.min.ratio
Numeric (length = 1). Ratio of lowest lambda value compared to maximal lambda. Defaults to

`0.1`

.**NOTE**`qgraph`

sets the default to`0.01`

- returnAllResults
Boolean (length = 1). Whether all results should be returned. Defaults to

`FALSE`

(network only). Set to`TRUE`

to access`glassopath`

output- penalizeMatrix
Boolean matrix. Optional logical matrix to indicate which elements are penalized

- countDiagonal
Boolean (length = 1). Should diagonal be counted in EBIC computation? Defaults to

`FALSE`

. Set to`TRUE`

to mimic`qgraph`

< 1.3 behavior (not recommended!)- refit
Boolean (length = 1). Should the optimal graph be refitted without LASSO regularization? Defaults to

`FALSE`

- model.selection
Character (length = 1). How lambda should be selected within GLASSO. Defaults to

`"EBIC"`

.`"JSD"`

is experimental and should not be used otherwise- verbose
Boolean (length = 1). Whether messages and (insignificant) warnings should be output. Defaults to

`FALSE`

(silent calls). Set to`TRUE`

to see all messages and warnings for every function call- ...
Arguments sent to

`glasso`

## Details

The glasso is run for 100 values of the tuning parameter logarithmically
spaced between the maximal value of the tuning parameter at which all edges are zero,
lambda_max, and lambda_max/100. For each of these graphs the EBIC is computed and
the graph with the best EBIC is selected. The partial correlation matrix
is computed using `wi2net`

and returned.

## References

**Instantiation of GLASSO**

Friedman, J., Hastie, T., & Tibshirani, R. (2008).
Sparse inverse covariance estimation with the graphical lasso.
*Biostatistics*, *9*, 432-441.

**glasso + EBIC**

Foygel, R., & Drton, M. (2010).
Extended Bayesian information criteria for Gaussian graphical models.
*In Advances in neural information processing systems* (pp. 604-612).

**glasso package**

Friedman, J., Hastie, T., & Tibshirani, R. (2011).
glasso: Graphical lasso-estimation of Gaussian graphical models.
R package version 1.7.

**Tutorial on EBICglasso**

Epskamp, S., & Fried, E. I. (2018).
A tutorial on regularized partial correlation networks.
*Psychological Methods*, *23*(4), 617–634.