TMFG {NetworkToolbox}

Triangulated Maximally Filtered Graph

Description

Applies the Triangulated Maximally Filtered Graph (TMFG) filtering method (Please see and cite Massara et al., 2016). The TMFG method uses a structural constraint that limits the number of zero-order correlations included in the network (3n - 6; where n is the number of variables). The TMFG algorithm begins by identifying four variables which have the largest sum of correlations to all other variables. Then, it iteratively adds each variable with the largest sum of three correlations to nodes already in the network until all variables have been added to the network. This structure can be associated with the inverse correlation matrix (i.e., precision matrix) to be turned into a GGM (i.e., partial correlation network) by using LoGo. See Details for more information on this network estimation method.

Usage

TMFG(
  data,
  normal = TRUE,
  na.data = c("pairwise", "listwise", "fiml", "none"),
  depend = FALSE
)

Arguments

data

Can be a dataset or a correlation matrix

normal

Should data be transformed to a normal distribution? Input must be a dataset. Defaults to TRUE. Computes correlations using the cor_auto function. Set to FALSE for Pearson's correlation

na.data

How should missing data be handled? For "listwise" deletion the na.omit function is applied. Set to "fiml" for Full Information Maximum Likelihood (corFiml). Full Information Maximum Likelihood is recommended but time consuming

depend

Is network a dependency (or directed) network? Defaults to FALSE. Set to TRUE to generate a TMFG-filtered dependency network (output obtained from the depend function)

Details

The TMFG method applies a structural constraint on the network, which restrains the network to retain a certain number of edges (3n-6, where n is the number of nodes; Massara et al., 2016). The network is also composed of 3- and 4-node cliques (i.e., sets of connected nodes; a triangle and tetrahedron, respectively). The TMFG method constructs a network using zero-order correlations and the resulting network can be associated with the inverse covariance matrix (yielding a GGM; Barfuss, Massara, Di Matteo, & Aste, 2016). Notably, the TMFG can use any association measure and thus does not assume the data is multivariate normal.

Construction begins by forming a tetrahedron of the four nodes that have the highest sum of correlations that are greater than the average correlation in the correlation matrix. Next, the algorithm iteratively identifies the node that maximizes its sum of correlations to a connected set of three nodes (triangles) already included in the network and then adds that node to the network. The process is completed once every node is connected in the network. In this process, the network automatically generates what’s called a planar network. A planar network is a network that could be drawn on a sphere with no edges crossing (often, however, the networks are depicted with edges crossing; Tumminello, Aste, Di Matteo, & Mantegna, 2005).

Value

Returns a list containing:

A

The filtered adjacency matrix

separators

The separators (3-cliques) in the network (wrapper output for LoGo)

cliques

The cliques (4-cliques) in the network (wrapper output for LoGo)

Author(s)

Alexander Christensen <[e-mail]>

References

Christensen, A. P., Kenett, Y. N., Aste, T., Silvia, P. J., & Kwapil, T. R. (2018). Network structure of the Wisconsin Schizotypy Scales-Short Forms: Examining psychometric network filtering approaches. Behavior Research Methods, 50, 2531-2550.

Massara, G. P., Di Matteo, T., & Aste, T. (2016). Network filtering for big data: Triangulated maximally filtered graph. Journal of Complex Networks, 5, 161-178.

Examples

# Pearson's correlation only for CRAN checks
A <- TMFG(neoOpen, normal = FALSE)$A