# EBelasticNet.Gaussian: The EB Elastic Net Algorithm for Gaussian Model In EBEN: Empirical Bayesian Elastic Net

## Description

General linear regression, normal-Gamma (NG) hierarchical prior for regression coefficients

## Usage

 `1` ```EBelasticNet.Gaussian(BASIS, Target, lambda, alpha,Epis = "no",verbose = 0) ```

## Arguments

 `BASIS` sample matrix; rows correspond to samples, columns correspond to features `Target` Response each individual `lambda` Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; lambda>0 `alpha` Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; 0

## Details

If Epis="yes", the program adds two-way interaction of K*(K-1)/2 more columns to BASIS

## Value

 `weight` the none-zero regression coefficients: col1,col2 are the indices of the bases(main if equal); col3: coefficent value; col4: posterior variance; col5: t-value; col6: p-value `WaldScore` Wald Score `Intercept` Intercept `lambda` the hyperparameter; same as input lambda `alpha` the hyperparameter; same as input alpha

## Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

## References

Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```library(EBEN) data(BASIS) data(y) n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; Blup = EBelasticNet.Gaussian(BASIS, y,lambda = 0.0072,alpha = 0.95, Epis = "no",verbose = 0) betas = Blup\$weight betas ```

### Example output

```                                        t    pvalue
[1,]  5  5  1.3254046 1.2046611 1.2075804 0.2330053
[2,] 16 16  0.7289649 0.9098397 0.7642302 0.4483948
[3,] 26 26 -2.0675308 4.7593678 0.9477141 0.3479257
[4,] 27 27 -2.0346988 4.1608860 0.9974869 0.3234288
[5,] 85 85 -0.2057527 0.2836561 0.3863220 0.7009307
[6,] 86 86 -1.3611349 1.3043131 1.1918188 0.2390728
[7,] 88 88 -0.5463346 0.7211937 0.6433284 0.5230106
```

EBEN documentation built on May 2, 2019, 6:15 a.m.