干旱区生态环境知识资源中心(Arid): Explaining the Shortcomings of Log-Transforming the Dependent Variable in Regression Models and Recommending a Better Alternative: Evidence From Soil CO2 Emission Studies

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DOI	10.1029/2021JG006238
	Explaining the Shortcomings of Log-Transforming the Dependent Variable in Regression Models and Recommending a Better Alternative: Evidence From Soil CO2 Emission Studies
	Liaw, Kao-Lee; Khomik, Myroslava; Arain, M. Altaf
通讯作者	Khomik, M (corresponding author), McMaster Univ, Sch Earth Environm & Soc, McMaster Ctr Climate Change, Hamilton, ON, Canada. ; Khomik, M (corresponding author), Univ Waterloo, Dept Geog & Environm Management, Hydrometeorol Res Grp, Waterloo, ON, Canada.
来源期刊	JOURNAL OF GEOPHYSICAL RESEARCH-BIOGEOSCIENCES
ISSN	2169-8953
EISSN	2169-8961
出版年	2021
卷号	126 期号:5
英文摘要	Log-transforming the dependent variable of a regression model, though convenient and frequently used, is accompanied by an under-prediction problem. We found that this underprediction can reach up to 20%, which is significant in studies that aim to estimate annual budgets. The fundamental reason for this problem is simply that the log-function is concave, and it has nothing to do with whether the dependent variable has a log-normal distribution or not. Using field-observed data of soil CO2 emission, soil temperature and soil moisture in a saturated-specification of a regression model for predicting emissions, we revealed that the under-predictions of the log-transformed approach were pervasive and systematically biased. The key determinant of the problem's severity was the coefficient of variation in the dependent variable that differed among different combinations of the values of the explanatory factors. By applying a parsimonious (Gaussian-Gamma) specification of the regression model to data from four different ecosystems, we found that this under-prediction problem was serious to various extents, and that for a relatively weak explanatory factor, the log-transformed approach is prone to yield a physically nonsensical estimated coefficient. Finally, we showed and concluded that the problem can be avoided by switching to the nonlinear approach, which does not require the assumption of homoscedasticity for the error term in computing the standard errors of the estimated coefficients. Plain Language Summary The goal of this study is to persuade empirical researchers to switch from a conventional practice of log-transforming the dependent variable in a regression model to a nonlinear approach, because the conventional practice has a pervasive and systematically biased underprediction problem that can be quite serious. For many decades, this problem was mistakenly assumed to result from the dependent variable being log-normally distributed and hence could not be properly corrected by an adjustment factor derived from this assumption. Using the examples of predicting soil CO2 emission from soil temperature and soil moisture in four ecosystems, we showed (1) that the fundamental reason for this problem is the concavity of the log-function, (2) that the under-predictions by the conventional practice were indeed pervasive and systematically biased, and (3) that the under-prediction problem was quite serious, but could be avoided by switching to a nonlinear approach.
英文关键词	carbon cycle desert forest Gaussian-Gamma model grassland log-transforming dependent variable marsh Mediterranean climate nonlinear estimation method soil CO2 emissions soil respiration soil temperature soil water content temperate climate under-prediction wetland
类型	Article
语种	英语
收录类别	SCI-E
WOS记录号	WOS:000655232300006
WOS关键词	RESPIRATION ; TEMPERATURE ; EFFLUX ; BIAS ; MOISTURE ; FOREST
WOS类目	Environmental Sciences ; Geosciences, Multidisciplinary
WOS研究方向	Environmental Sciences & Ecology ; Geology
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/350841
作者单位	[Liaw, Kao-Lee; Khomik, Myroslava; Arain, M. Altaf] McMaster Univ, Sch Earth Environm & Soc, McMaster Ctr Climate Change, Hamilton, ON, Canada; [Khomik, Myroslava] Univ Waterloo, Dept Geog & Environm Management, Hydrometeorol Res Grp, Waterloo, ON, Canada
推荐引用方式 GB/T 7714	Liaw, Kao-Lee,Khomik, Myroslava,Arain, M. Altaf. Explaining the Shortcomings of Log-Transforming the Dependent Variable in Regression Models and Recommending a Better Alternative: Evidence From Soil CO2 Emission Studies[J],2021,126(5).
APA	Liaw, Kao-Lee,Khomik, Myroslava,&Arain, M. Altaf.(2021).Explaining the Shortcomings of Log-Transforming the Dependent Variable in Regression Models and Recommending a Better Alternative: Evidence From Soil CO2 Emission Studies.JOURNAL OF GEOPHYSICAL RESEARCH-BIOGEOSCIENCES,126(5).
MLA	Liaw, Kao-Lee,et al."Explaining the Shortcomings of Log-Transforming the Dependent Variable in Regression Models and Recommending a Better Alternative: Evidence From Soil CO2 Emission Studies".JOURNAL OF GEOPHYSICAL RESEARCH-BIOGEOSCIENCES 126.5(2021).