selectnet: Model selection

In netgwas: Network-Based Genome Wide Association Studies

Model selection

Description

Estimate the optimal regularization parameter at EM convergence based on different information criteria .

Usage

selectnet(netgwas.obj, opt.index= NULL, criteria= NULL, ebic.gamma=0.5, 
		   ncores= NULL, verbose= TRUE)

Arguments

netgwas.obj	An object with S3 class "netgwas"
opt.index	The program internally determines an optimal graph using opt.index= NULL. Otherwise, to manually choose an optimal graph from the graph path.
criteria	Model selection criteria. "ebic" and "aic" are available. BIC model selection can be calculated by fixing ebic.gamma = 0. Applicable only if opt.index= NULL.
ebic.gamma	The tuning parameter for ebic. Theebic.gamma = 0 results in bic model selection. The default value is 0.5. Applicable only opt.index= NULL.
ncores	The number of cores to use for the calculations. Using ncores = "all" automatically detects number of available cores and runs the computations in parallel.
verbose	If verbose = FALSE, printing information is disabled. The default value is TRUE. Applicable only opt.index= NULL.

Details

This function computes extended Bayesian information criteria (ebic), Bayesian information criteria, Akaike information criterion (aic) at EM convergence based on observed or joint log-likelihood. The observed log-likelihood can be obtained through

\ell_Y(\widehat{\Theta}_\lambda) = Q(\widehat{\Theta}_\lambda | \widehat{\Theta}^{(m)}) - H (\widehat{\Theta}_\lambda | \widehat{\Theta}^{(m)}),

Where Q can be calculated from netmap, netsnp, netphenogeno function and H function is

H(\widehat{\Theta}_\lambda | \widehat{\Theta}^{(m)}_\lambda) = E_z[\ell_{Z | Y}(\widehat{\Theta}_\lambda) | Y; \widehat{\Theta}_\lambda] = E_z[\log f(z)| Y ;\widehat{\Theta}_\lambda ] - \log p(y).

The "ebic" and "aic" model selection criteria can be obtained as follow

ebic(\lambda) = -2 \ell(\widehat{\Theta}_\lambda) + ( \log n + 4 \gamma \log p) df(\lambda)

aic(\lambda) = -2 \ell(\widehat{\Theta}_\lambda) + 2 df(\lambda)

where df refers to the number of non-zeros offdiagonal elements of \hat{\Theta}_\lambda, and \gamma \in [0, 1]. Typical value for for ebic.gamma is 1/2, but it can also be tuned by experience. Fixing ebic.gamma = 0 results in bic model selection.

Value

An obj with S3 class "selectnet" is returned:

opt.adj	The optimal graph selected from the graph path
opt.theta	The optimal precision matrix from the graph path
opt.sigma	The optimal covariance matrix from the graph path
ebic.scores	Extended BIC scores for regularization parameter selection at the EM convergence. Applicable if opt.index = NULL.
opt.index	The index of optimal regularization parameter.
opt.rho	The selected regularization parameter.
par.cor	A partial correlation matrix.
V.names	Variables name whose are not isolated.

and anything else that is included in the input netgwas.obj.

Author(s)

Pariya Behrouzi and Ernst C.Wit
Maintainer: Pariya Behrouzi [e-mail]

References

1. BBehrouzi, P., and Wit, E. C. (2019). Detecting epistatic selection with partially observed genotype data by using copula graphical models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 68(1), 141-160.
2. Behrouzi, P., Arends, D., and Wit, E. C. (2023). netgwas: An R Package for Network-Based Genome-Wide Association Studies. The R journal, 14(4), 18-37.
3. Ibrahim, Joseph G., Hongtu Zhu, and Niansheng Tang. (2012). Model selection criteria for missing-data problems using the EM algorithm. Journal of the American Statistical Association. 4. D. Witten and J. Friedman. (2011). New insights and faster computations for the graphical lasso. Journal of Computational and Graphical Statistics, to appear.
5. J. Friedman, T. Hastie and R. Tibshirani. (2007). Sparse inverse covariance estimation with the lasso, Biostatistics.
6. Foygel, R. and M. Drton. (2010). Extended bayesian information criteria for Gaussian graphical models. In Advances in Neural Information Processing Systems, pp. 604-612.

See Also

netmap, netsnp, netphenogeno

Examples

	
		   
		#simulate data
		D <- simgeno(p=50, n=100, k= 3, adjacent = 3, alpha = 0.06 , beta = 0.06)
		plot(D)

		#explore intra- and inter-chromosomal interactions
		out  <-  netsnp(D$data, n.rho= 5, ncores= 1)
		plot(out)

		#different graph selection methods
		sel.ebic1 <- selectnet(out, criteria = "ebic")
		plot(sel.ebic1, vis = "CI")

		sel.aic <- selectnet(out, criteria = "aic")
		plot(sel.aic, vis = "CI")

		sel.bic <- selectnet(out, criteria = "ebic", ebic.gamma = 0)
		plot(sel.bic, vis = "CI")
	

netgwas documentation built on Aug. 7, 2023, 5:10 p.m.