Package {ModalNet}

Type:	Package
Title:	Regularized Parametric Modal Regression: Lasso, Elastic Net and Ridge
Version:	0.3.0
Description:	Variable selection and estimation for parametric modal regression with continuous positive responses (Gamma, Weibull and Lognormal families) under Lasso, elastic-net, ridge and adaptive-Lasso penalties. The conditional mode is linked to a linear predictor through a logarithmic link using the mode reparameterization of Galarza and Lachos (2026) <doi:10.48550/arXiv.2603.07099>. The penalized log-likelihood is maximized with a proximal Newton algorithm (iteratively reweighted penalized least squares): at each iteration the modal log-likelihood is replaced by a local quadratic surrogate in the linear predictor, which yields a pseudo-response and a working weight in closed form, and the resulting weighted penalized least-squares subproblem is solved by the coordinate-descent solver of 'glmnet' (Friedman, Hastie and Tibshirani, 2010, <doi:10.18637/jss.v033.i01>). The regularization parameter is chosen along a warm-started path by the extended Bayesian information criterion of Chen and Chen (2008) <doi:10.1093/biomet/asn034>.
License:	GPL-3
Encoding:	UTF-8
Depends:	R (≥ 4.1.0)
Imports:	glmnet, stats, graphics
Suggests:	survival
LazyData:	true
URL:	https://github.com/chedgala/ModalNet
BugReports:	https://github.com/chedgala/ModalNet/issues
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2026-10-22 04:36:04 UTC; chedgala
Author:	Christian E. Galarza [aut, cre, cph] (affiliation: Escuela Superior Politécnica del Litoral, Guayaquil, Ecuador), Víctor H. Lachos [aut] (affiliation: University of Connecticut, Storrs, CT, USA), Dashun Liu [aut] (affiliation: University of Connecticut, Storrs, CT, USA)
Maintainer:	Christian E. Galarza <chedgala@espol.edu.ec>
Repository:	CRAN
Date/Publication:	2026-11-04 09:40:02 UTC

Methods for ModalNet fits

Description

Print, summarize and extract the components of a model fitted by modal_net.

Usage

## S3 method for class 'ModalNet'
print(x, digits = 4, ...)

## S3 method for class 'ModalNet'
summary(object, digits = 4, ...)

## S3 method for class 'summary.ModalNet'
print(x, digits = 4, ...)

## S3 method for class 'ModalNet'
coef(object, s = NULL, ...)

## S3 method for class 'ModalNet'
fitted(object, ...)

## S3 method for class 'ModalNet'
logLik(object, ...)

Arguments

Value

print.ModalNet and print.summary.ModalNet return their argument invisibly. summary.ModalNet returns an object of class "summary.ModalNet", a list with the coefficient table of the selected covariates (estimates on the log-mode scale and their exponentials), the dispersion, the selected penalty, the log-likelihood, EBIC and degrees of freedom, the names of the selected covariates, the mode-mean constant c(\hat\phi) with the implied mean-scale intercept, and a data frame summarizing the path. coef.ModalNet returns the named coefficient vector (intercept first), fitted.ModalNet the fitted conditional modes, and logLik.ModalNet an object of class "logLik".

Examples

set.seed(2)
X <- matrix(rnorm(150 * 10), 150, 10)
dat <- generate_modal_data(X, c(0.5, 0.8, -0.6, rep(0, 8)), phi = 0.2,
                           family = "weibull")
fit <- modal_net(dat$y, X, family = "weibull")
print(fit)
s <- summary(fit)
s$coefficients
coef(fit)
head(fitted(fit))
logLik(fit)

Simulate data from a modal regression model

Description

Generates positive responses whose conditional mode is M_i = \exp(\gamma_0 + x_i^\top\gamma) under the Gamma, Weibull or Lognormal mode reparameterization used by modal_net.

Usage

generate_modal_data(X, gamma, phi, family = c("gamma", "weibull", "lognormal"))

Arguments

Value

A list with y, mode and mean.

Examples

X <- matrix(rnorm(100 * 5), 100, 5)
d <- generate_modal_data(X, c(1, 0.5, -0.5, 0, 0, 0), phi = 0.3, family = "weibull")
str(d)

Alias of modal_net kept for compatibility

Description

modal_lasso() was the main function of the package when it was called ModalLasso. It calls modal_net with the same arguments, so existing code keeps working. New code should use modal_net().

Usage

modal_lasso(...)

Arguments

Value

The same object as modal_net.

Penalized parametric modal regression for positive responses

Description

Fits the modal regression model \log M_i = \gamma_0 + x_i^\top\gamma, where M_i is the conditional mode of a positive response, by maximizing the penalized log-likelihood

\ell_p(\gamma,\phi) = \ell(\gamma,\phi)/n - \lambda\,\Psi(\gamma),

with \Psi the Lasso, elastic-net, ridge or adaptive-Lasso penalty on the slopes (the intercept is never penalized). The Gamma, Weibull and Lognormal families are available, each written in terms of its mode through the reparameterization of Galarza and Lachos (2026).

Usage

modal_net(
  y,
  X,
  family = c("gamma", "weibull", "lognormal"),
  lambda = NULL,
  nlambda = 50,
  lambda.min.ratio = NULL,
  alpha = 1,
  penalty.factor = NULL,
  gamma_ebic = 0.5,
  dfmax = NULL,
  line_search = TRUE,
  standardize = TRUE,
  tol = 1e-06,
  maxit = 200,
  verbose = FALSE
)

Arguments

Details

The estimator is computed by a proximal Newton algorithm, equivalently an iteratively reweighted penalized least-squares (IRPLS) scheme. At each iteration the modal log-likelihood is replaced by its second-order expansion in the linear predictor \eta_i, which yields a pseudo-response z_i and a working weight w_i in closed form:

• Gamma: w_i = y_i/(\phi M_i), z_i = \eta_i + 1 - (1+\phi)M_i/y_i;

• Weibull: w_i = k^2 (y_i/\lambda_i)^k, z_i = \eta_i + \{1 - (\lambda_i/y_i)^k\}/k;

• Lognormal: w_i = 1/\phi, z_i = \log y_i - \phi (the surrogate is exact).

The update of \gamma is then the weighted penalized least-squares problem \min_\gamma \tfrac12\sum_i w_i (z_i - x_i^\top\gamma)^2 + \lambda\Psi(\gamma), solved exactly by the cyclical coordinate descent of glmnet with observation weights, so that variable selection is performed by the optimizer itself (exact zeros, no thresholding). An optional backtracking line search keeps the penalized objective monotone. The dispersion \phi is then updated by maximizing the profile log-likelihood (closed form for the Lognormal family, one-dimensional optimization otherwise).

The regularization parameter is chosen by path following: a decreasing grid \lambda_1 > \cdots > \lambda_L is built once from the initial pseudo-response, the algorithm is run to convergence at each grid point with a warm start at the previous solution, and the extended BIC

\mathrm{EBIC}(\lambda) = -2\ell + \mathrm{df}\log n + 2\gamma_{\mathrm{EBIC}}\,\mathrm{df}\log p, \qquad \mathrm{df} = |\hat S_\lambda| + 2,

is evaluated across the converged fits. The initialization uses a lightly penalized Gaussian Lasso of \log y on X, which stays well defined when p > n.

The penalty is \lambda\Psi(\gamma) = \lambda\sum_j v_j\{\alpha|\gamma_j| + (1-\alpha)\gamma_j^2/2\} on the standardized columns (v_j given by penalty.factor), and \lambda is expressed on the scale used by glmnet, whose weights are rescaled to sum to n. For the Lasso this makes the Lognormal fit at penalty \lambda coincide with the Gaussian Lasso of \log y at the same \lambda (slopes identical, intercepts differing by exactly \phi). For alpha < 1, glmnet divides its ridge term by the standard deviation of the response it receives; the inner call compensates for this, so the penalty above holds exactly for every alpha.

Value

An object of class "ModalNet", a list with components

plus family, n, p, gamma_ebic, call.

References

Galarza, C. E. and Lachos, V. H. (2026). A proximal Newton algorithm for penalized modal regression with high-dimensional positive responses.

Galarza, C. E. and Lachos, V. H. (2026). Parametric modal regression for right-censored positive responses. arXiv preprint doi:10.48550/arXiv.2603.07099.

Friedman, J., Hastie, T. and Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. doi:10.18637/jss.v033.i01.

Chen, J. and Chen, Z. (2008). Extended Bayesian information criteria for model selection with large model spaces. Biometrika, 95, 759–771. doi:10.1093/biomet/asn034.

Examples

set.seed(1)
n <- 200; p <- 30
X <- matrix(rnorm(n * p), n, p)
gamma_true <- c(1, 0.6, -0.5, 0.4, rep(0, p - 3))
dat <- generate_modal_data(X, gamma_true, phi = 0.3, family = "gamma")
fit <- modal_net(dat$y, X, family = "gamma")
fit
summary(fit)
plot(fit)

Plot the EBIC curve and the coefficient path of a ModalNet fit

Description

Plot the EBIC curve and the coefficient path of a ModalNet fit

Usage

## S3 method for class 'ModalNet'
plot(x, which = c(1, 2), ...)

Arguments

Value

The "ModalNet" object, invisibly. Called for its side effect: the EBIC against \log\lambda, with the selected value marked, and the coefficient paths on the log-mode scale.

Examples

set.seed(4)
X <- matrix(rnorm(150 * 10), 150, 10)
dat <- generate_modal_data(X, c(1, 0.6, -0.4, rep(0, 8)), phi = 0.3,
                           family = "lognormal")
fit <- modal_net(dat$y, X, family = "lognormal")
plot(fit)
plot(fit, which = 2)

Predict conditional modes (or means) from a fitted ModalNet model

Description

Predict conditional modes (or means) from a fitted ModalNet model

Usage

## S3 method for class 'ModalNet'
predict(object, newdata, type = c("mode", "link", "mean"), ...)

Arguments

Value

A numeric vector with one prediction per row of newdata (or of the training matrix), on the scale chosen by type.

Examples

set.seed(3)
X <- matrix(rnorm(120 * 8), 120, 8)
dat <- generate_modal_data(X, c(1, 0.7, -0.5, rep(0, 6)), phi = 0.3,
                           family = "gamma")
fit <- modal_net(dat$y[1:100], X[1:100, ], family = "gamma")
new <- X[101:120, ]
cbind(mode = predict(fit, new), mean = predict(fit, new, type = "mean"))[1:5, ]

Riboflavin production in Bacillus subtilis (100 most variable genes)

Description

Riboflavin (vitamin B2) production rate of Bacillus subtilis together with the expression levels of the 100 genes with the largest empirical variance, for n = 71 fermentation runs. This is the riboflavinV100 subset used by Schelldorfer et al. (2011) and in Galarza and Lachos (2026), derived from the riboflavin data of Bühlmann, Kalisch and Meier (2014) distributed with the hdi package.

Usage

riboflavinV100

Format

A list with two components:

y

numeric vector of length 71: riboflavin production rate on the original (positive) scale, obtained as exp() of the log-production rate of the hdi data.

x

numeric matrix 71 \times 100 of log gene expression levels (column names are the gene identifiers).

Details

The 71 runs are repeated measurements on 28 strains; the analyses in the literature, and the one in the package examples, treat them as independent. The model is scale equivariant, so y may be rescaled (for instance divided by its mean) for numerical convenience without changing the selected set or the slopes.

Source

Bühlmann, P., Kalisch, M. and Meier, L. (2014). High-dimensional statistics with a view towards applications in biology. Annual Review of Statistics and Its Application, 1, 255–278. doi:10.1146/annurev-statistics-022513-115545. Data from the R package hdi (GPL).

References

Schelldorfer, J., Bühlmann, P. and van de Geer, S. (2011). Estimation for high-dimensional linear mixed-effects models using L1-penalization. Scandinavian Journal of Statistics, 38, 197–214. doi:10.1111/j.1467-9469.2011.00740.x.

Examples

data(riboflavinV100)
y <- riboflavinV100$y / mean(riboflavinV100$y)
fit <- modal_net(y, riboflavinV100$x, family = "gamma")
colnames(riboflavinV100$x)[fit$selected]