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.

# S3 method for 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


# \donttest{

# 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
#> Estimates:
#> 
#> node.1
#>  node.2 node.3 node.4 node.5
#>   0.275      0  0.374  0.144
#> ---
#> 
#> node.2
#>  node.1 node.3 node.4 node.5
#>    0.24  0.561      0      0
#> ---
#> 
#> node.3
#>  node.1 node.2 node.4 node.5
#>       0  0.502  0.193  0.205
#> ---
#> 
#> node.4
#>  node.1 node.2 node.3 node.5
#>   0.324      0  0.215  0.329
#> ---
#> 
#> node.5
#>  node.1 node.2 node.3 node.4
#>   0.142      0   0.26  0.376
#> ---
#> 


# 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,]
#> [1] 0.23883387 0.06552783 0.35127553 0.15686903

# lm
as.numeric(coef(fit_lm))
#> [1] 0.23881439 0.06549431 0.35128376 0.15687468

# }