# Mixed effects Score Test for continuous outcomes

### Description

Test for association between a set of SNPS/genes and continuous outcomes by including variant characteristic information and using score statistics.

### Usage

1 | ```
linear.test(y, X, G, Z, method = "liu")
``` |

### Arguments

`y` |
a numeric vector of the continuous outcome variables. Missing values are not allowed. |

`X` |
a numeric matrix of covariates with rows for individuals and columns for covariates. |

`G` |
a numeric genotype matrix with rows for individuals and columns for SNPs. Each SNP should be coded as 0, 1, and 2 for AA, Aa, aa, where A is a major allele and a is a minor allele. Missing genotypes are not allowed. |

`Z` |
a numeric matrix of second level covariates for variant characteristics. Each row corresponds to a variant and each column corresponds to a variant characteristic. If there is no second level covariates, a vector of 1 should be used. |

`method` |
a method to compute the p-value and the default value is "liu". Method "davies" represents an exact method that computes the p-value by inverting the characteristic function of the mixture chisq. Method "liu" represents an approximation method that matches the first 3 moments. |

### Value

`S.tau ` |
score statistic for the variant hetergenous effect. |

`S.pi ` |
score statistic for the variant mean effect. |

`p.value.S.tau` |
p-value for testing the variant hetergenous effect. |

`p.value.S.pi` |
p-value for testing the variant mean effect. |

`p.value.overall` |
overall p-value for testing the association between the set of SNPS/genes and outcomes. It combines p.value.S.pi and p.value.S.tau by using Fisher's procedure. |

### Author(s)

Jianping Sun, Yingye Zheng, and Li Hsu.

### References

Sun, J., Zheng, Y., and Hsu, L. (2013) A Unified Mixed-Effects Model for Rare-Variant Association in Sequencing Studies. Genet Epidemiol. 2013 Mar 9. doi: 10.1002/gepi.21717

H. Liu, Y. Tang, H.H. Zhang (2009) A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables, Computational Statistics and Data Analysis, 53, 853-856.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
data(MiST.data)
attach(MiST.data)
##########################################################################
# Test the association between a set of SNPs and continuous outcomes
# - without information about SNP characteristics. Z is a vector of 1's.
out <- linear.test(y.con, X, G, Z)
##########################################################################
# Test the association between a set of SNPs and continuous outcomes
# - including SNP characteristics
out <- linear.test(y.con, X, G, Z.func)
``` |