# The main function of the LD LASSO method

### Description

The LD LASSO uses the correlation of SNP genotypes in a penalized least squares regression framework. The estimator is the solution to a convex optimization problem, and here we use the solution from the package quadprog.

### Usage

1 2 |

### Arguments

`block.obj` |
An object of class gwaa.data from GenABEL. |

`block.cood` |
A vector of length p+1, where p is the number of SNPs. block.cood is an indicator vector that indicates block boundaries at all p+1 SNP bounded intervals. Use find.bounds to create this vector. |

`Xa` |
If block.obj is NA then a genotype matrix must be provided. Xa is a matrix of genotype values codes as 0, 1 or 2 for homozygous major, heterozygous, or homozygous minor, respectively. |

`Y` |
If block.obj is NA then a phenotype vector Y must be provided. Y is a vector of diagnoses, where 0 is non-diseased and 1 is diseased. |

`s1` |
The LASSO constraint parameter – the sum of the magnitude of the estimates is bounded by s1. |

`s2` |
The LD LASSO constraint parameter – the absolute difference of SNP pair estimates is bounded by s2 times the log of r-squared |

`r2.cut` |
Only SNP pairs with correlation greater than r2.cut are bounded by the LD LASSO constraint. |

`delta` |
Included so that optimization is numerically feasible in cases when r-squared = 1 |

`form` |
Form of constraint matrix. form is either 1, 2 or 3: |

`ytype` |
If ytype is 1 then Y is a vector of binary disease phenotypes, 0 for non-disease, 1 for diseased. If ytype is 2 then Y is the normalized log OR. |

`solve` |
logical variable indicating whether or not to solve regression problem. Useful when ld_lasso is used to construct constraint matrix, and the solution is not necessary, as in the selction of the r2 cutoff. |

### Details

This function performs the ld lasso regression with parameters s1, s2 and r2.cut on block.obj with haplotype block boundaries defined by block.cood.

### Value

`qp` |
List from the function solve.QP in the package quadprog. This object contains the solutions for c( beta, beta+, beta- ) and so the LD LASSO estimates are the first p elements, or qp$solution[1:p] |

`y` |
A vector of normalized log OR |

`A` |
The constraint matrix |

`r2` |
The vector of r-squared values used to define constraint matrix. Elements in this vector are the correlation estimates for all inter-block SNP pairs. |

`b0` |
The vector of ld lasso constraints with length 3p |

`OR` |
A vector of odds ratios |

### Author(s)

Samuel G. Younkin

### References

D. Goldfarb and A. Idnani, "A numerically stable dual method for solving strictly convex quadratic programs," Mathematical Programming, vol. 27, pp. 1-33, 1983.

### See Also

ld_lasso_method, quadprog, solve.QP

### Examples

1 2 | ```
data("ldlasso_example")
ldlasso.test <- ld_lasso( block.obj, block.cood, s1 = 1, s2 = 0.5 )
``` |

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