Characterizing the Domain of a Regression Model

Brooks, Daniel G.; Carroll, Steven S.; Verdini, William A.

doi:10.1080/00031305.1988.10475559

Cited by 23 publications

(6 citation statements)

References 3 publications

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“…However, it has been suggested (e.g., Jungers, 1988;Aiello, 1992;Ruff, 1998) that RMA should be used if the prediction involves an extrapolation. The precise cut-off separating interpolation from extrapolation can be difficult to define (Brooks et al, 1988;Konigsberg et al, 1998), but a first useful approximation is that extrapolation occurs when the case to be predicted falls outside of the domain of the regression, i.e., outside of the range of observed values of the predictor variable (Brooks et al, 1988). Even ignoring statistical problems of increasing uncertainty as inferences are made at the extremes of a distribution, extrapolation always is of concern because it raises uncertainty about a fundamental assumption of the prediction process; namely, that the case to be predicted is a member of the same population as the sample used to calculate the equation.…”

Section: Indications For Rma and Olsmentioning

confidence: 99%

Use and misuse of the reduced major axis for line‐fitting

Smith

2009

American J Phys Anthropol

638

565

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Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate.

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Section: Indications For Rma and Olsmentioning

confidence: 99%

Use and misuse of the reduced major axis for line‐fitting

Smith

2009

American J Phys Anthropol

638

565

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“…One of the difficulties of predicting response variables is the extrapolation of results to areas where the environmental conditions of the initial dataset (used to estimate the structural equation models) are not covered. Attempting to use predictive equations to estimate areas that differ considerably from the original dataset can lead to unreliable predictions (Brooks et al., 1988). Although this is still a current topic of research interest in multidimensional statistical analysis (Ebert et al., 2014), we propose to use the Mahalanobis distance to identify outliers with regard to the centre of the observed distribution given by the 231 points present in our dataset.…”

Section: Methodsmentioning

confidence: 99%

Global projections of the soil microbiome in the Anthropocene

Guerra

Delgado‐Baquerizo

Duarte

et al. 2021

Global Ecol. Biogeogr.

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Aim Soil microbes are essential for maintenance of life‐supporting ecosystem services, but projections of how these microbes will be affected by global change scenarios are lacking. Therefore, our aim was to provide projections of future soil microbial distribution using several scenarios of global change. Location Global. Time period 1950–2090. Major taxa studied Bacteria and fungi. Methods We used a global database of soil microbial communities across six continents to estimate past and future trends of the soil microbiome. To do so, we used structural equation models to include the direct and indirect effects of changes in climate and land use in our predictions, using current climate (temperature and precipitation) and land‐use projections between 1950 and 2090. Results Local bacterial richness will increase in all scenarios of change in climate and land use considered, although this increase will be followed by a generalized community homogenization process affecting > 85% of terrestrial ecosystems. Changes in the relative abundance of functional genes associated with the increases in bacterial richness are also expected. Based on an ecological cluster analysis, our results suggest that phylotypes such as Geodermatophilus spp. (typical desert bacteria), Mycobacterium sp. (which are known to include important human pathogens), Streptomyces mirabilis (major producers of antibiotic resistance genes) or potential fungal soil‐borne plant pathogens belonging to Ascomycota fungi (Venturia spp., Devriesia spp.) will become more abundant in their communities. Main conclusions Our results provide evidence that climate change has a stronger influence on soil microbial communities than change in land use (often including deforestation and agricultural expansion), although most of the effects of climate are indirect, through other environmental variables (e.g., changes in soil pH). The same was found for microbial functions such as the prevalence of phosphate transport genes. We provide reliable predictions about the changes in the global distribution of microbial communities, showing an increase in alpha diversity and a homogenization of soil microbial communities in the Anthropocene.

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“…(6)- (13). The use of a convex hull can be seen in Brooks et al [49] and in Mitra et al [50]. The convex hull ensures a more tight regression domain which increases the validity of the model in its boundaries [51].…”

Section: Practical Challenges Of the Case Studymentioning

confidence: 96%

“…surge, choke, and minimum and maximum Inlet Guide Vane opening. Instead, this feasible operational window of the compressor is defined from the domain of the regression model [49]. The regression domain is a part of the actual operational window.…”

Section: Practical Challenges Of the Case Studymentioning

confidence: 99%