coef.ggmncv {GGMncv}

Regression Coefficients from ggmncv Objects

Description

There is a direct correspondence between the inverse covariance matrix and multiple regression (Stephens 1998; Kwan 2014). This readily allows for converting the off diagonal elements to regression coefficients, resulting in noncovex penalization for multiple regression modeling.

Usage

## S3 method for class 'ggmncv'
coef(object, ...)

Arguments

object

An Object of class ggmncv.

...

Currently ignored.

Value

A matrix of regression coefficients.

Note

The coefficients can be accessed via coefs[1,], which provides the estimates for predicting the first node.

Further, the estimates are essentially computed with both the outcome and predictors scaled to have mean 0 and standard deviation 1.

References

Kwan CC (2014). “A regression-based interpretation of the inverse of the sample covariance matrix.” Spreadsheets in Education, 7(1), 4613.

Stephens G (1998). “On the Inverse of the Covariance Matrix in Portfolio Analysis.” The Journal of Finance, 53(5), 1821–1827.

Examples

# data
Y <- GGMncv::ptsd[,1:5]

# correlations
S <- cor(Y)

# fit model
fit <- ggmncv(R = S, n = nrow(Y), progress = FALSE)

# regression
coefs <- coef(fit)

coefs


# no regularization, resulting in OLS

# data
# note: scaled for lm()
Y <- scale(GGMncv::ptsd[,1:5])

# correlations
S <- cor(Y)

# fit model
# note: non reg
fit <- ggmncv(R = S, n = nrow(Y), progress = FALSE, lambda = 0)

# regression
coefs <- coef(fit)

# fit lm
fit_lm <- lm(Y[,1] ~ 0 + Y[,-1])

# ggmncv
coefs[1,]

# lm
as.numeric(coef(fit_lm))