# rho_M1Y: Approximate Correlation between Continuous Mixture Variable... In SimCorrMix: Simulation of Correlated Data with Multiple Variable Types Including Continuous and Count Mixture Distributions

## Description

This function approximates the expected correlation between a continuous mixture variables M1 and another random variable Y based on the mixing proportions, component means, and component standard deviations of M1 and correlations between components of M1 and Y. The equations can be found in the Expected Cumulants and Correlations for Continuous Mixture Variables vignette. This function can be used to see what combination of correlations between components of M1 and Y gives a desired correlation between M1 and Y.

## Usage

 `1` ```rho_M1Y(mix_pis = NULL, mix_mus = NULL, mix_sigmas = NULL, p_M1Y = NULL) ```

## Arguments

 `mix_pis` a vector of mixing probabilities that sum to 1 for component distributions of M1 `mix_mus` a vector of means for component distributions of M1 `mix_sigmas` a vector of standard deviations for component distributions of M1 `p_M1Y` a vector of correlations between the components of M1 and Y; i.e., `p_M1Y[1]` is the correlation between the 1st component of M1 and Y

## Value

the expected correlation between M1 and Y

## References

Please see references for `rho_M1M2`.

`rho_M1Y`
 ```1 2 3``` ```# M1 is mixture of N(-2, 1) and N(2, 1); pairwise correlation set to 0.35 rho_M1Y(mix_pis = c(0.4, 0.6), mix_mus = c(-2, 2), mix_sigmas = c(1, 1), p_M1Y = c(0.35, 0.35)) ```