# GE_scoreeq_sim.R

### Description

Here we perform simulation to verify that we have solved for the correct alpha values in GE_bias_norm_squaredmis(). Make the same assumptions as in GE_bias_norm_squaredmis().

### Usage

1 2 | ```
GE_scoreeq_sim(num_sims = 5000, num_sub = 2000, beta_list, prob_G, rho_list,
cov_Z = NULL, cov_W = NULL)
``` |

### Arguments

`num_sims` |
The number of simulations to run, we suggest 5000. |

`num_sub` |
The number of subjects to generate in every simulation, we suggest 2000. |

`beta_list` |
A list of the effect sizes in the true model. Use the order beta_0, beta_G, beta_E, beta_I, beta_Z, beta_M. If Z or M is a vector, then beta_Z and beta_M should be vectors. |

`prob_G` |
Probability that each allele is equal to 1. Since each SNP has two alleles, the expectation of G is 2*prob_G. |

`rho_list` |
A list of the 6 pairwise covariances between the covariates. These should be in the order (1) cov_GE (2) cov_GZ (3) cov_EZ (4) cov_GW (5) cov_EW (6) cov_ZW. Again if Z or W are vectors then terms like cov_GZ should be vectors (in the order cov(G,Z_1),...,cov(G,Z_p)) where Z is of dimension p, and similarly for W. If Z or M are vectors, then cov_ZW should be a vector in the order (cov(Z_1,W_1),...,cov(Z_1,W_q), cov(Z_2,W_1),........,cov(Z_p,W_q) where Z is a vector of length p and W is a vector of length q. |

`cov_Z` |
Only used if Z is a vector, gives the covariance matrix of Z (remember by assumption Z has mean 0 and variance 1). The (i,j) element of the matrix should be the (i-1)(i-2)/2+j element of the vector. |

`cov_W` |
Only used if W is a vector, gives the covariance matrix of W (remember by assumption W has mean 0 and variance 1). The (i,j) element of the matrix should be the (i-1)(i-2)/2+j element of the vector. |

### Value

A list of the fitted values alpha

### Examples

1 2 |