em.prec {EMgaussian}

EM algorithm for multivariate normal, precision matrix parameterization

Description

EM algorithm for multivariate normal, precision matrix parameterization

Usage

em.prec(
  dat,
  max.iter = 500,
  tol = 1e-05,
  start = c("diag", "pairwise", "listwise", "full"),
  glassoversion = c("none", "glassoFast", "glasso", "glassonostart"),
  debug = 0,
  ...
)

Arguments

dat

Data frame or matrix that contains the raw data.

max.iter

Max number of EM cycles.

tol

Tolerance for change in parameter estimates across EM Cycles. If all changes are less than tol, the algorithm terminates.

start

Starting value method (see details).

glassoversion

Character indicating whether to do regularization (lasso), and if so, using which package. "glasso" uses the glasso function and uses the E-step covariance matrix for starting values, "glassoFast" uses glassoFast{glassoFast} which also penalizes the diagonal of the precision matrix by default (glasso does not), "glassonostart" also uses glasso but no "warm" starting values.

debug

(Experimental) set an integer value > 1 for some information as the algorithm runs.

...

Arguments passed down to any of the glasso functions.

Details

This function computes all means and the precision matrix (inverse of covariance matrix) among a set of variables using the Expectation-Maximization (EM) algorithm to handle missing values, and assuming multivariate normality. The EM code was originally developed based on Stadler and Buhlmann (2012) and for use with the graphical lasso (i.e., glasso). This version allows the possibility of using a lasso by specifying something other than "none" for glassoversion. However, it can also be used without regularization to just estimate the precision matrix.

For starting values for the EM algorithm itself (not at the M-step), the function accepts either a list that has mu and S slots corresponding to the starting mean and covariance matrix. This is useful if the user would like to use custom starting values. Otherwise, a character corresponding to any of the options available in the startvals.cov function will be used to take a guess at starting values.

Value

A list with the following:

• p.est: all parameter estimates as a vector (means followed by unique elements of precision matrix).

• mu: estimated means.

• S: estimated covariance matrix.

• K: estimated precision matrix.

• it: number of EM cycles completed.

• conv: boolean value indicating convergence (TRUE) or not (FALSE).

References

Städler, N., & Bühlmann, P. (2012). Missing values: sparse inverse covariance estimation and an extension to sparse regression. Statistics and Computing, 22, 219–235. doi:10.1007/s11222-010-9219-7

Examples

  library(psych)
  data(bfi)
  test <- em.prec(bfi[,1:25])