Dataset Information

Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term.

ABSTRACT: In multiple regression Y ~ ?0 + ?1X1 + ?2X2 + ?3X1 X2 + ?., the interaction term is quantified as the product of X1 and X2. We developed fractional-power interaction regression (FPIR), using ?X1 M X2 N as the interaction term. The rationale of FPIR is that the slopes of Y-X1 regression along the X2 gradient are modeled using the nonlinear function (Slope = ?1 + ?3MX1 M-1 X2 N), instead of the linear function (Slope = ?1 + ?3X2) that regular regressions normally implement. The ranges of M and N are from -56 to 56 with 550 candidate values, respectively. We applied FPIR using a well-studied dataset, nest sites of the crested ibis (Nipponia nippon).We further tested FPIR by other 4692 regression models. FPIRs have lower AIC values (-302 ± 5003.5) than regular regressions (-168.4 ± 4561.6), and the effect size of AIC values between FPIR and regular regression is 0.07 (95% CI: 0.04-0.10). We also compared FPIR with complex models such as polynomial regression, generalized additive model, and random forest. FPIR is flexible and interpretable, using a minimum number of degrees of freedom to maximize variance explained. We have provided a new R package, interactionFPIR, to estimate the values of M and N, and suggest using FPIR whenever the interaction term is likely to be significant. • Introduced fractional-power interaction regression (FPIR) as Y ~ ?0 + ?1X1 + ?2X2 + ?3X1 M X2 N + ? to replace the current regression model Y ~ ?0 + ?1X1 + ?2X2 + ?3X1 X2 + ?; • Clarified the rationale of FPIR, and compared it with regular regression model, polynomial regression, generalized additive model, and random forest using regression models for 4692 species; • Provided an R package, interactionFPIR, to calculate the values of M and N, and other model parameters.

SUBMITTER: Li X

PROVIDER: S-EPMC7549115 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term.

Li Xinhai X Li Baidu B Wang Guiming G Zhan Xiangjiang X Holyoak Marcel M

MethodsX 20200916

In multiple regression Y ~ β0 + β1X1 + β2X2 + β3X1 X2 + ɛ., the interaction term is quantified as the product of X1 and X2. We developed fractional-power interaction regression (FPIR), using βX1 M X2 N as the interaction term. The rationale of FPIR is that the slopes of Y-X1 regression along the X2 gradient are modeled usi ...[more]

PMID: 33072528

Similar Datasets

Project description:MotivationSystems immunology leverages recent technological advancements that enable broad profiling of the immune system to better understand the response to infection and vaccination, as well as the dysregulation that occurs in disease. An increasingly common approach to gain insights from these large-scale profiling experiments involves the application of statistical learning methods to predict disease states or the immune response to perturbations. However, the goal of many systems studies is not to maximize accuracy, but rather to gain biological insights. The predictors identified using current approaches can be biologically uninterpretable or present only one of many equally predictive models, leading to a narrow understanding of the underlying biology.ResultsHere we show that incorporating prior biological knowledge within a logistic modeling framework by using network-level constraints on transcriptional profiling data significantly improves interpretability. Moreover, incorporating different types of biological knowledge produces models that highlight distinct aspects of the underlying biology, while maintaining predictive accuracy. We propose a new framework, Logistic Multiple Network-constrained Regression (LogMiNeR), and apply it to understand the mechanisms underlying differential responses to influenza vaccination. Although standard logistic regression approaches were predictive, they were minimally interpretable. Incorporating prior knowledge using LogMiNeR led to models that were equally predictive yet highly interpretable. In this context, B cell-specific genes and mTOR signaling were associated with an effective vaccination response in young adults. Overall, our results demonstrate a new paradigm for analyzing high-dimensional immune profiling data in which multiple networks encoding prior knowledge are incorporated to improve model interpretability.Availability and implementationThe R source code described in this article is publicly available at https://bitbucket.org/kleinstein/logminer .Contactsteven.kleinstein@yale.edu or stefan.avey@yale.edu.Supplementary informationSupplementary data are available at Bioinformatics online.

Dataset Information

Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term.

Publications

Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets