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GLASSO with Non-convex Penalties

Source: R/network.nonconvex.R
network.nonconvex.Rd

The graphical least absolute shrinkage and selection operator with a non-convex regularization penalties

Usage

network.nonconvex(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  penalty = c("iPOT", "LGP", "POP", "SPOT"),
  gamma = NULL,
  lambda = NULL,
  nlambda = 50,
  lambda.min.ratio = 0.01,
  penalize.diagonal = TRUE,
  optimize.over = c("none", "lambda", "both"),
  ic = c("AIC", "AICc", "BIC", "EBIC"),
  ebic.gamma = 0.5,
  fast = TRUE,
  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 must be provided 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

  • "cosine" — Uses cosine to compute cosine similarity

  • "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

penalty

Character (length = 1). Available options:

  • "iPOT" — Inverse power of two

  • "LGP" — Lambda-gamma power

  • "POP" — Plus one Pareto

  • "SPOT" — Sigmoid power of two (default)

gamma

Numeric (length = 1). Adjusts the shape of the penalty. Defaults:

  • "iPOT" = 5

  • "LGP" = 5

  • "POP" = 4

  • "SPOT" = 3

lambda

Numeric (length = 1). Adjusts the initial penalty provided to the non-convex penalty function

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 0.01

penalize.diagonal

Boolean (length = 1). Should the diagonal be penalized? Defaults to FALSE

optimize.over

Character (length = 1). Whether optimization of lambda, gamma, both, or no hyperparamters should be performed. Defaults to "none" or no optimization

ic

Character (length = 1). What information criterion should be used for model selection? Available options include:

  • "AIC" — Akaike's information criterion: \(-2L + 2E\)

  • "AICc" — AIC corrected: \(AIC + \frac{2E^2 + 2E}{n - E - 1}\)

  • "BIC" — Bayesian information criterion: \(-2L + E \cdot \log{(n)}\)

  • "EBIC" — Extended BIC: \(BIC + 4E \cdot \gamma \cdot \log{(E)}\)

Term definitions:

  • \(n\) — sample size

  • \(p\) — number of variables

  • \(E\) — edges

  • \(S\) — empirical correlation matrix

  • \(K\) — estimated inverse covariance matrix (network)

  • \(L = \frac{n}{2} \cdot \log \text{det} K - \sum_{i=1}^p (SK)_{ii}\)

Defaults to "BIC"

ebic.gamma

Numeric (length = 1) Value to set gamma parameter in EBIC (see above). Defaults to 0.50

Only used if ic = "EBIC"

fast

Boolean (length = 1). Whether the glassoFast version should be used to estimate the GLASSO. Defaults to TRUE.

The fast results may differ by less than floating point of the original GLASSO implemented by glasso and should not impact reproducibility much (set to FALSE if concerned)

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

...

Additional arguments to be passed on to auto.correlate

Value

A network matrix

Author

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

Examples

# Obtain data
wmt <- wmt2[,7:24]

# Obtain network
awe_network <- network.nonconvex(data = wmt)