knitr::opts_chunk$set( comment = "#>", collapse = TRUE, dpi = 300, fig.retina = 2, fig.width = 6, fig.height = 6, fig.align = "center", out.width = "65%" )
The msaenet package implemented the multi-step adaptive elastic-net method introduced in @xiao2015msaenet for feature selection in high-dimensional regressions.
First, we generate some simulated data under a setting often used for testing
high-dimensional linear models, with the function msaenet.sim.gaussian()
:
library("msaenet")
dat <- msaenet.sim.gaussian( n = 150, p = 500, rho = 0.5, coef = rep(1, 10), snr = 5, p.train = 0.7, seed = 1001 )
The parameter rho
controls the degree of correlation among the variables.
coef
sets the coefficients of the "true" variables, and in this case,
the first 10 variables will have coefficient 1 while the other 490 variables
will have coefficient 0. snr
represents the designated signal-to-noise ratio
(SNR) in the simulated data. The parameter p.train
decides the proportion of
the training set (relative to the total number of observations n
).
To generate simulation data for the other types of generalized linear models
supported by msaenet, simply use msaenet.sim.binomial()
(logistic regression),
msaenet.sim.cox()
(Cox regression), or msaenet.sim.poisson()
(Poisson regression).
The returned object dat
contains both the training and test set. We will only
use the training set to do the modeling (parameter tuning and model fitting),
and then evaluate the model's performance on the test set independently.
msaenet.fit <- msaenet( dat$x.tr, dat$y.tr, alphas = seq(0.1, 0.9, 0.1), nsteps = 10L, tune.nsteps = "ebic", seed = 1005 )
The parameter alphas
sets the alpha tuning grid for elastic-net in all
adaptive estimation steps. nsteps
indicates how many adaptive estimation steps
should be used.
By default, the internal parameter tuning is done by k-fold cross-validation,
and the parameters which produce the minimum prediction errors will be selected.
You could also set parallel = TRUE
and run
library("doParallel") registerDoParallel(detectCores())
before calling this function to make the parameter tuning run in parallel.
This will probably save some time if the alphas
grid is denser and the
data size is larger.
To select the optimal model in each estimation step with a different criterion,
use the argument tune
. Options include "cv"
(k-fold cross-validation, default),
"aic"
(AIC), "bic"
(BIC), and "ebic"
(Extended BIC).
Similarly, use tune.nsteps
to specify the criterion for selecting the optimal
estimation step (the optimal model from all steps), options include
"max"
(select the final-step, default), "aic"
, "bic"
, and "ebic"
.
Let's inspect the fitted model, by looking into the best step and the selected variables (variables with non-zero coefficients), and the number of false positive selections/true positive selections:
msaenet.fit$best.step msaenet.nzv(msaenet.fit) msaenet.nzv.all(msaenet.fit) msaenet.fp(msaenet.fit, 1:10) msaenet.tp(msaenet.fit, 1:10)
Next, we make predictions on the test set using the fitted model, and compute some evaluation metrics, such as RMSE and MAE:
msaenet.pred <- predict(msaenet.fit, dat$x.te) msaenet.rmse(dat$y.te, msaenet.pred) msaenet.mae(dat$y.te, msaenet.pred)
A coefficient plot that shows the coefficient changes of all the variables across every adaptive estimation step:
#| fig-coef-path plot(msaenet.fit, label = TRUE, label.cex = 0.5)
The y-axis in the plot represents the relative effect size estimations (standardized into [0, 1]) of the variables.
You can customize the graphical details through additional arguments in the
plot method, especially the variable label appearance. For example, specifying
meaningful label text for the non-zero variables via label.vars
.
For all available options, see ?plot.msaenet
for details.
Now, we plot the change of the information criterion (EBIC here) used to select the optimal step:
#| fig-criterion plot(msaenet.fit, type = "criterion")
Create a dot plot for the model coefficients at the optimal step:
#| fig-dotplot plot(msaenet.fit, type = "dotplot", label = TRUE, label.cex = 1)
To plot the absolute values of the coefficients instead of the raw coefficients,
use abs = TRUE
.
The vanilla adaptive elastic-net [@zou2009aenet] is implemented by the function
aenet()
. For multi-step adaptive estimation based on MCP-net or SCAD-net,
see ?amnet
, ?asnet
, ?msamnet
, and ?msasnet
for details.
All the analyses above apply to the models fitted by these functions as well.
If you find msaenet useful for your research, please feel free to cite our paper [@xiao2015msaenet] in your publications. If you have any questions or have a bug to report, please create an issue on GitHub.
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