Description Details Author(s) References

Fast Empirical Bayesian Lasso (EBlasso) and Elastic Net (EBEN) are generalized linear regression methods for variable selections and effect estimations.
Similar as `lasso`

and `elastic net`

implemented in the package glmnet, EBglmnet features
the capabilities of handling *p>>n* data, where `p`

is the number of variables and `n`

is
the number of samples in the regression model, and inferring a sparse solution such that irrelevant variables
will have exactly zero value on their regression coefficients. Additionally, there are several unique features in EBglmnet:

1) Both `EBlasso`

and `EBEN`

can select more than `n`

nonzero effects.

2) EBglmnet also performs hypothesis testing for the significance of nonzero estimates.

3) EBglmnet includes built-in functions for epistasis analysis.

There are three sets of hierarchical prior distributions implemented in EBglmnet:

1) EBlasso-NE is a two-level prior with (normal + exponential) distributions for the regression coefficients.

2) EBlasso-NEG is a three-level hierarchical prior with (normal + exponential + gamma) distributions.

3) EBEN implements a normal and generalized gamma hierarchical prior.

While those sets of priors are all "peak zero and flat tails", `EBlasso-NE`

assigns more probability mass to the tails, resulting in more nonzero estimates having large *p*-values. In contrast, `EBlasso-NEG`

has a third level constraint on the `lasso`

prior, which results in higher probability mass around zero, thus more sparse results in the final outcome. Meanwhile, `EBEN`

encourages a grouping effect such that highly correlated variables can be selected as a group.
Similar as the relationship between `elastic net`

and `lasso`

, there are two parameters *(α, λ)* required for `EBEN`

, and it is reduced to `EBlasso-NE`

when parameter *α = 1*. We recommend using EBlasso-NEG when there are a large number of candidate effects, using EBlasso-NE when effect sizes are relatively small, and using EBEN when groups of highly correlated variables such as co-regulated gene expressions are of interest.

Two models are available for both methods: linear regression model and logistic regression model. Other features in this package includes:

* 1 * epistasis (two-way interactions) can be included for all models/priors;

* 2 * model implemented with memory efficient `C`

code;

* 3 * LAPACK/BLAS are used for most linear algebra computations.

Several simulation and real data analysis in the reference papers demonstrated that EBglmnet enjoys better performance than `lasso`

and `elastic net`

methods in terms of power of detection,
false discover rate, as well as encouraging grouping effect when applicable.

Key Algorithms are described in the following paper:

1. EBlasso-NEG: (Cai X., Huang A., and Xu S., 2011), (Huang A., Xu S., and Cai X., 2013)

2. EBlasso-NE: (Huang A., Xu S., and Cai X., 2013)

3. group EBlasso: (Huang A., Martin E., et al. 2014)

4. EBEN: (Huang A., Xu S., and Cai X., 2015)

5. Whole-genome QTL mapping: (Huang A., Xu S., and Cai X., 2014)

Package: | EBglmnet |

Type: | Package |

Version: | 4.1 |

Date: | 2016-01-15 |

License: | gpl |

Anhui Huang, Dianting Liu

Maintainer: Anhui Huang <a.huang1@umiami.edu>

Huang, A., Xu, S., and Cai, X. (2015). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 114(1): 107-115.

Huang, A., E. Martin, et al. (2014). "Detecting genetic interactions in pathway-based genome-wide association studies." Genet Epidemiol 38(4): 300-309.

Huang, A., S. Xu, et al. (2014). "Whole-genome quantitative trait locus mapping reveals major role of epistasis on yield of rice." PLoS ONE 9(1): e87330.

Huang, A. (2014). "Sparse model learning for inferring genotype and phenotype associations." Ph.D Dissertation. University of Miami(1186).

Huang A, Xu S, Cai X. (2013). Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 14(1):5.

Cai, X., Huang, A., and Xu, S. (2011). Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping. BMC Bioinformatics 12, 211.

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