Description Usage Arguments Value References See Also Examples

This function calculates the expected correlation matrix between Outcomes (Y) and Covariates (X) in a correlated system of continuous variables.
This system is generated with `nonnormsys`

using the techniques of Headrick and Beasley (doi: 10.1081/SAC-120028431).
These correlations are determined based on the beta (slope) coefficients calculated with `calc_betas`

, the correlations
between independent variables *X_{(pj)}* for a given outcome *Y_p*, for `p = 1, ..., M`

, and the
variances. The result can be used to compare the simulated correlation matrix to the theoretical correlation matrix.
If there are continuous mixture variables and the betas are specified in terms of non-mixture and mixture variables, then the correlations in
`corr.x`

will be calculated in terms of non-mixture and mixture variables using
`rho_M1M2`

and `rho_M1Y`

. In this case, the dimensions of the matrices in `corr.x`

should not
match the number of columns of `betas`

. The function result will be in terms of non-mixture and mixture variables. Otherwise,
the result will be in terms of non-mixture and components of mixture variables. The vignette **Theory and Equations for
Correlated Systems of Continuous Variables** gives the equations, and the vignette **Correlated Systems of Statistical Equations
with Non-Mixture and Mixture Continuous Variables** gives examples. There are also vignettes in `SimCorrMix`

which provide more details on continuous
non-mixture and mixture variables.

1 2 3 |

`betas` |
a matrix of the slope coefficients calculated with |

`corr.x` |
list of length |

`vars` |
a list of same length as |

`mix_pis` |
a list of same length as |

`mix_mus` |
a list of same length as |

`mix_sigmas` |
a list of same length as |

`error_type` |
"non_mix" if all error terms have continuous non-mixture distributions, "mix" if all error terms have continuous mixture distributions, defaults to "non_mix" |

`corr.yx`

a list of length `M`

, where `corr.yx[[p]]`

is matrix of correlations
between *Y* (rows) and *X_p* (columns); if the dimensions of `betas`

match the dimensions of the matrices in
`corr.x`

, then the correlations will be in terms of non-mixture and components of mixture variables; otherwise, `mix_pis`

,
`mix_mus`

, and `mix_sigmas`

must be provided and the correlations will be in terms of non-mixture and mixture variables

Headrick TC, Beasley TM (2004). A Method for Simulating Correlated Non-Normal Systems of Linear Statistical Equations. Communications in Statistics - Simulation and Computation, 33(1). doi: 10.1081/SAC-120028431

`nonnormsys`

, `calc_betas`

, `rho_M1M2`

, `rho_M1Y`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
# Example: system of three equations for 2 independent variables, where each
# error term has unit variance, from Headrick & Beasley (2002)
corr.yx <- list(matrix(c(0.4, 0.4), 1), matrix(c(0.5, 0.5), 1),
matrix(c(0.6, 0.6), 1))
corr.x <- list()
corr.x[[1]] <- corr.x[[2]] <- corr.x[[3]] <- list()
corr.x[[1]][[1]] <- matrix(c(1, 0.1, 0.1, 1), 2, 2)
corr.x[[1]][[2]] <- matrix(c(0.1974318, 0.1859656, 0.1879483, 0.1858601),
2, 2, byrow = TRUE)
corr.x[[1]][[3]] <- matrix(c(0.2873190, 0.2589830, 0.2682057, 0.2589542),
2, 2, byrow = TRUE)
corr.x[[2]][[1]] <- t(corr.x[[1]][[2]])
corr.x[[2]][[2]] <- matrix(c(1, 0.35, 0.35, 1), 2, 2)
corr.x[[2]][[3]] <- matrix(c(0.5723303, 0.4883054, 0.5004441, 0.4841808),
2, 2, byrow = TRUE)
corr.x[[3]][[1]] <- t(corr.x[[1]][[3]])
corr.x[[3]][[2]] <- t(corr.x[[2]][[3]])
corr.x[[3]][[3]] <- matrix(c(1, 0.7, 0.7, 1), 2, 2)
corr.e <- matrix(0.4, nrow = 3, ncol = 3)
diag(corr.e) <- 1
vars <- list(rep(1, 3), rep(1, 3), rep(1, 3))
betas <- calc_betas(corr.yx, corr.x, vars)
calc_corr_yx(betas, corr.x, vars)
``` |

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