Build Implied Correlation Matrices for Observed Path Models

Usage

c_mat_ft(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 containing the directed-effects matrix, residual covariance matrix, implied correlation matrix, multiple-\(R^2\) values, number of free parameters, and model degrees of freedom.

Details

This helper builds the RAM-style matrices used by observed-variable path models. Directed paths are stored in A_mat; residual variances and exogenous covariances are stored in S_mat; and the implied correlation matrix is computed as \((I - A)^{-1} S (I - A)^{-T}\).

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 "

c_mat_ft(model, Br)
#> $model_input
#> [1] "## Regression paths\nPerformance ~  Self_confidence  + Cognitive  + Somatic\nSelf_confidence ~ Cognitive + Somatic "
#> 
#> $A_mat
#>                 Performance Self_confidence   Cognitive    Somatic
#> Performance               0      0.08316153 -0.09261001  0.3162950
#> Self_confidence           0      0.00000000  0.42870532 -0.2457839
#> Cognitive                 0      0.00000000  0.00000000  0.0000000
#> Somatic                   0      0.00000000  0.00000000  0.0000000
#> 
#> $S_mat
#>                 Performance Self_confidence  Cognitive    Somatic
#> Performance       0.8910782       0.0000000  0.0000000  0.0000000
#> Self_confidence   0.0000000       0.6713626  0.0000000  0.0000000
#> Cognitive         0.0000000       0.0000000  1.0000000 -0.4006848
#> Somatic           0.0000000       0.0000000 -0.4006848  1.0000000
#> 
#> $F_mat
#>                 Performance Self_confidence Cognitive Somatic
#> Performance               1               0         0       0
#> Self_confidence           0               1         0       0
#> Cognitive                 0               0         1       0
#> Somatic                   0               0         0       1
#> 
#> $C_mat
#>                 Performance Self_confidence  Cognitive    Somatic
#> Performance      1.00000000     -0.09773331 -0.1755029  0.3186775
#> Self_confidence -0.09773331      1.00000000  0.5271872 -0.4175596
#> Cognitive       -0.17550292      0.52718720  1.0000000 -0.4006848
#> Somatic          0.31867753     -0.41755963 -0.4006848  1.0000000
#> 
#> $Mul_R2
#>     Performance Self_confidence 
#>       0.1089218       0.3286374 
#> 
#> $num_freePar
#> [1] 8
#> 
#> $df
#> [1] 2
#>