An algorithm to identify whether data were generated from a factor or network model using factor and network loadings. The algorithm uses heuristics based on theory and simulation. These heuristics were then submitted to several deep learning neural networks with 240,000 samples per model with varying parameters.

## Arguments

- data
Matrix or data frame. Should consist only of variables to be used in the analysis. Can be raw data or a correlation matrix

- 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 replicate samples to be drawn from a multivariate normal distribution (uses

`MASS::mvrnorm`

). Defaults to`100`

(recommended)- 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`

, and`EGA`

## Value

Returns a list containing:

- empirical
Prediction of model based on empirical dataset only

- bootstrap
Prediction of model based on means of the loadings across the bootstrap replicate samples

- proportion
Proportions of models suggested across bootstraps

## References

**Model training and validation**

Christensen, A. P., & Golino, H. (2021).
Factor or network model? Predictions from neural networks.
*Journal of Behavioral Data Science*, *1*(1), 85-126.

## Author

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

## Examples

```
# Get data
data <- psych::bfi[,1:25]
if (FALSE) # Compute LCT
## Factor model
LCT(data) # \dontrun{}
```