文章基本信息

标题：Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term
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作者：Xinhai Li ; Baidu Li ; Guiming Wang 等
期刊名称：MethodsX
印刷版ISSN：2215-0161
电子版ISSN：2215-0161
出版年度：2020
卷号：7
页码：1-12
DOI：10.1016/j.mex.2020.101067
语种：English
出版社：Elsevier
摘要：AbstractIn multiple regression Y ~ β0 + β1X1 + β2X2 + β3X1X2 + ɛ., the interaction term is quantified as the product of X1and X2. We developed fractional-power interaction regression (FPIR), using βX1MX2Nas the interaction term. The rationale of FPIR is that the slopes of Y-X1regression along the X2gradient are modeled using the nonlinear function (Slope = β1 + β3MX1M-1X2N), instead of the linear function (Slope = β1 + β3X2) that regular regressions normally implement. The ranges ofMandNare 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 ofMandN, and suggest using FPIR whenever the interaction term is likely to be significant.• Introduced fractional-power interaction regression (FPIR) as Y ~ β0 + β1X1 + β2X2 + β3X1MX2N + ɛ to replace the current regression model Y ~ β0 + β1X1 + β2X2 + β3X1X2 + ɛ;• 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 ofMandN, and other model parameters.Graphical abstractDisplay Omitted
关键词：Fractional-power interaction regression (FPIR);Multiple linear regression;Nonlinearity;InteractionFPIR;R package