elastic_net_var_select: Elastic net for variable selection in IMLEGIT model
In AlexiaJM/LEGIT: Latent Environmental & Genetic InTeraction (LEGIT) Model

Description Usage Arguments Format Value References Examples

[Fast and accurate, highly recommended] Apply Elastic Net (from the glmnet package) with IMLEGIT to obtain the order of variable removal that makes the most sense. The output shows the information criterion at every step, so you can decide which variable to retain. It is significantly faster (seconds/minutes instead of hours) than all other variable selection approaches (except for stepwise) and it is very accurate. Note that, as opposed to LEGIT/IMLEGIT, the parameters of variables inside the latent variables are not L1-normalized; instead, its the main model parameters which are L1-normalized. This is needed to make elastic net works. It doesn't matter in the end, because we only care about which variables were removed and we only output the IMLEGIT models without elastic net penalization.

1	elastic_net_var_select

`data`	data.frame of the dataset to be used.
`latent_var`	list of data.frame. The elements of the list are the datasets used to construct each latent variable. For interpretability and proper convergence, not using the same variable in more than one latent variable is highly recommended. It is recommended to set names to the list elements to prevent confusion because otherwise, the latent variables will be named L1, L2, ... (See examples below for more details)
`formula`	Model formula. The names of `latent_var` can be used in the formula to represent the latent variables. If names(`latent_var`) is NULL, then L1, L2, ... can be used in the formula to represent the latent variables. Do not manually code interactions, write them in the formula instead (ex: GE1E2 or G:E1:E2).
`latent_var_searched`	Optional If not null, you must specify a vector containing all indexes of the latent variables you want to use elastic net on. Ex: If latent_var=list(G=genes, E=env), specifying latent_var_search=c(1,2) will use both, latent_var_search=1 will only do it for G, and latent_var_search=2 will only do it for E.
`cross_validation`	(Optional) If TRUE, will return cross-validation criterion (slower, but very good criterion).
`alpha`	The elasticnet mixing parameter (between 0 and 1). 1 leads to lasso, 0 leads to ridge. See glmnet package manual for more information. We recommend somewhere betwen .50 and 1.
`standardize`	If TRUE, standardize all variables inside every latent_var component during training (but we still output LEGIT models with unstandardized variables). Note that if FALSE, glmnet will still standardize and unstandardize, but it will do so for each model (i.e., when at the step of estimating the parameters of latent variable G it standardize them, apply glmnet, then unstandardize them). This means that fixed parameters in the alternating steps are not standardized when standardize=FALSE. In practice, we found that standardize=FALSE leads to weird paths that do not always make sense. In the end, we only care about the order of the variable removal from the glmnet. We highly recommend standardize=TRUE for best results.
`lambda_path`	Optional vector of all lambda (penalty term for elastic net, see glmnet package manual). By default, we automatically determine it.
`lambda_mult`	scalar which multiplies the maximum lambda (penalty term for elastic net, see glmnet package manual) from the lambda path determined automatically. Sometimes, the maximum lambda found automatically is too big or too small and you may not want to spend the effort to manually set your own lambda path. This is where this comes in, you can simply scale lambda max up or down. (Default = 1)
`lambda_min`	minimum lambda (penalty term for elastic net, see glmnet package manual) from the lambda path. (Default = .0001)
`n_lambda`	Number of lambda (penalty term for elastic net, see glmnet package manual) in lambda path. Make lower for faster training, or higher for more precision. If you have many variables, make it bigger than 100 (Default = 100).
`start_latent_var`	Optional list of starting points for each latent variable (The list must have the same length as the number of latent variables and each element of the list must have the same length as the number of variables of the corresponding latent variable).
`eps`	Threshold for convergence (.01 for quick batch simulations, .0001 for accurate results).
`maxiter`	Maximum number of iterations.
`family`	Outcome distribution and link function (Default = gaussian).
`ylim`	Optional vector containing the known min and max of the outcome variable. Even if your outcome is known to be in [a,b], if you assume a Gaussian distribution, predict() could return values outside this range. This parameter ensures that this never happens. This is not necessary with a distribution that already assumes the proper range (ex: [0,1] with binomial distribution).
`cv_iter`	Number of cross-validation iterations (Default = 5).
`cv_folds`	Number of cross-validation folds (Default = 10). Using `cv_folds=NROW(data)` will lead to leave-one-out cross-validation.
`folds`	Optional list of vectors containing the fold number for each observation. Bypass cv_iter and cv_folds. Setting your own folds could be important for certain data types like time series or longitudinal data.
`classification`	Set to TRUE if you are doing classification (binary outcome).
`Huber_p`	Parameter controlling the Huber cross-validation error (Default = 1.345).
`print`	If FALSE, nothing except warnings will be printed. (Default = TRUE).
`get_main_reg`	If TRUE, we also return the fits which have the L1-normalized main models. Normally, LEGIT L1-normalize (enforce that the absolute value of the weights of the parameters) the weights of the G and E models, but not the main effect model. For Elastic net, we do it for the main effect model, but at the very end of training, we convert back the models to only L1-normalize the G and E models. This option gives the L1-normalized main effect models. It can be useful. (Default = FALSE).

An object of class function of length 1.

Returns an object of the class "elastic_net_var_select" which is list containing, in the following order: the criterion at each lambda, the coefficients of the latent variables at each lambda, the fits of each IMLEGIT models for each variable retained at each lambda, and the vector of lambda used.

Alexia Jolicoeur-Martineau, Ashley Wazana, Eszter Szekely, Meir Steiner, Alison S. Fleming, James L. Kennedy, Michael J. Meaney, Celia M.T. Greenwood and the MAVAN team. Alternating optimization for GxE modelling with weighted genetic and environmental scores: examples from the MAVAN study (2017). arXiv:1703.08111.

## Not run: 
N = 1000
train = example_3way(N, sigma=1, logit=FALSE, seed=7)
g1_bad = rbinom(N,1,.30)
g2_bad = rbinom(N,1,.30)
g3_bad = rbinom(N,1,.30)
g4_bad = rbinom(N,1,.30)
g5_bad = rbinom(N,1,.30)
train$G = cbind(train$G, g1_bad, g2_bad, g3_bad, g4_bad, g5_bad)
lv = list(G=train$G, E=train$E)
fit = elastic_net_var_select(train$data, lv, y ~ G*E)
summary(fit)
best_model(fit, criterion="BIC")
 # Instead of taking the best, if you want the model with "Model index"=17 from summary, do
plot(fit)
# With Cross-validation
fit = elastic_net_var_select(train$data, lv, y ~ G*E, cross_validation=TRUE, cv_iter=1, cv_folds=5)
best_model(fit, criterion="cv_R2")
# Elastic net only applied on G
fit = elastic_net_var_select(train$data, lv, y ~ G*E, c(1))
# Elastic net only applied on E
fit = elastic_net_var_select(train$data, lv, y ~ G*E, c(2))
# Most E variables not removed, use lambda_mult > 1 to remove more
fit = elastic_net_var_select(train$data, lv, y ~ G*E, c(2), lambda_mult=5)
# Lasso (only L1 regularization)
fit = elastic_net_var_select(train$data, lv, y ~ G*E, alpha=1)
# Want more lambdas (useful if # of variables is large)
fit = elastic_net_var_select(train$data, lv, y ~ G*E, n_lambda = 200)

## End(Not run)