Estimate Regression Coefficients from a Correlation Matrix

Usage

find_B(model_input, R)

Arguments

model_input: Model input as a character string. Multiple models need to be on their own line. Regression syntax uses a lavaan-like outcome ~ predictor1 + predictor2 form.
R: A named correlation matrix, typically the pooled correlation matrix extracted from a fitted mars object.

Value

A list of named vectors of standardized regression coefficients, one element per regression equation in model_input.

Details

Each regression line is parsed independently. For a statement such as y ~ x1 + x2, find_B() reorders R into predictor and outcome blocks and computes the standardized least-squares coefficients as \(R_{xx}^{-1} R_{xy}\). Blank lines and comment lines are ignored by the lower-level model parser.

Examples

Br <-  matrix(c(1.00000000, -0.09773331, -0.1755029,  0.3186775,
-0.09773331,  1.00000000,  0.5271873, -0.4175596,
-0.17550292,  0.5271872,  1.0000000, -0.4006848,
0.31867753, -0.41755963, -0.4006848,  1.0000000),
nrow = 4, byrow = TRUE)

colnames(Br) <- c("Performance",  "Self_confidence",  "Cognitive", "Somatic" )

rownames(Br) <- colnames(Br)

## Proposed path model
model <- "## Regression paths
Performance ~  Self_confidence  + Cognitive  + Somatic
Self_confidence ~ Cognitive + Somatic "

find_B(model, Br)
#> [[1]]
#> Self_confidence -> Performance       Cognitive -> Performance 
#>                     0.08316153                    -0.09261001 
#>         Somatic -> Performance 
#>                     0.31629500 
#> 
#> [[2]]
#> Cognitive -> Self_confidence   Somatic -> Self_confidence 
#>                    0.4287053                   -0.2457839 
#>