gic.DMR

Computes values of Generalized Information Criterion for the entire sequence of models from a <code>DMR</code> object.

Model selection algorithms for regression and classification, where the predictors can be continuous or categorical and the number of regressors may exceed the number of observations. The selected model consists of a subset of numerical regressors and partitions of levels of factors. Szymon Nowakowski, Piotr Pokarowski, Wojciech Rejchel and Agnieszka Sołtys, 2023. Improving Group Lasso for High-Dimensional Categorical Data. In: Computational Science – ICCS 2023. Lecture Notes in Computer Science, vol 14074, p. 455-470. Springer, Cham. <doi:10.1007/978-3-031-36021-3_47>. Aleksandra Maj-Kańska, Piotr Pokarowski and Agnieszka Prochenka, 2015. Delete or merge regressors for linear model selection. Electronic Journal of Statistics 9(2): 1749-1778. <doi:10.1214/15-EJS1050>. Piotr Pokarowski and Jan Mielniczuk, 2015. Combined l1 and greedy l0 penalized least squares for linear model selection. Journal of Machine Learning Research 16(29): 961-992. <https://www.jmlr.org/papers/volume16/pokarowski15a/pokarowski15a.pdf>. Piotr Pokarowski, Wojciech Rejchel, Agnieszka Sołtys, Michał Frej and Jan Mielniczuk, 2022. Improving Lasso for model selection and prediction. Scandinavian Journal of Statistics, 49(2): 831–863. <doi:10.1111/sjos.12546>.

Szymon Nowakowski

DMRnet

Delete or Merge Regressors Algorithms for Linear and Logistic
Model Selection and High-Dimensional Data

Agnieszka Prochenka-Sołtys

Piotr Pokarowski

gic.DMR function

<dl><dt>x</dt>
<dd>Fitted <code>DMR</code> object.</dd>
<dt>c</dt>
<dd>Parameter controlling amount of penalization for complexity of the model in the generalized information criterion (GIC). For linear regression GIC for model M is defined as $$GIC_M = RSS_M + df_M*c* log{p}*s^2,$$ where $RSS_M$ is the residual sum of squares and $df_M$ is the number of parameters in the model M; $s^2$ is an estimator of $sigma^2$ based on the model in the <code>DMR</code> object with the largest number of parameters. For logistic regression GIC for model M is defined as $$GIC_M = -2*loglik_M + |M|*c* log{p},$$ where $loglik_M$ is the logarithm of the likelihood function and $df_M$ is the number of parameters in the model M. Recommended values are <code>c=2.5</code> for linear regression and <code>c=2</code> for logistic regression.</dd></dl>

Arguments

gic.DMR — gic.DMR

<dl>

<dt>x</dt>
<dd>Fitted <code>DMR</code> object.</dd>


<dt>c</dt>
<dd>Parameter controlling amount of penalization for complexity of the model in the generalized information criterion (GIC). For linear regression GIC for model M is defined as $$GIC_M = RSS_M + df_M*c* log{p}*s^2,$$ where $RSS_M$ is the residual sum of squares and $df_M$ is the number of parameters in the model M; $s^2$ is an estimator of $sigma^2$ based on the model in the <code>DMR</code> object with the largest number of parameters. For logistic regression GIC for model M is defined as $$GIC_M = -2*loglik_M + |M|*c* log{p},$$ where $loglik_M$ is the logarithm of the likelihood function and $df_M$ is the number of parameters in the model M. Recommended values are <code>c=2.5</code> for linear regression and <code>c=2</code> for logistic regression.</dd>

</dl>

gic.DMR: gic.DMR

Description

Usage

Value

Arguments

See Also

Examples