# How to Statistically Disentangle the Effects of Environmental Factors and Human Disturbances: A Review

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## Abstract

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## 1. Introduction

^{2}, and the inclusion of random variables in a model [19]. In comparison, the regression of residuals tends to underestimate the effects of the targeted predictor, as the variance explained in the first regression is attributed to the co-variables alone [21]. Subsequently, we select nine approaches that are relatively new, promising but less used, commonly used but controversial, or specifically designed for freshwater studies. We review the concept, applications, potentials-limitations, and related r-packages for each of the approaches.

## 2. Modeling Based on Stratified Randomized Survey

## 3. Structured Equation Model (SEM)

## 4. Propensity Scores (PS)

## 5. Hierarchical Partitioning (HP)

^{2}for linear regression or χ

^{2}for logistic regression. The unique effect is measured as the average increase in model fit across all models that contain the predictor of interest compared with the models without it. If the predictor has a high independent effect, the increase should be substantial, and vice versa. The averaging should alleviate the compounding effects [19]. Three steps are needed to estimate the joint effect. First, one calculates the goodness-of-fit for the model based on a predictor j alone as R

_{j}, based on a subset of other predictors, e.g., l and k as R

_{lk}, and based on all the predictors (j, l, k) as R

_{jlk}. Second, the joint effect of predictor j with the given subset of predictors is calculated as (R

_{j}+ R

_{lk}− R

_{jlk}). Third, the joint effects for predictor j and all possible subsets of other predictors are averaged as the final estimate of predictor j. If a predictor is highly correlated with the response variable as well as with other predictors, the joint effect will be high; however, the unique effect will be low. As a result, the result may not be too informative. Thus, it is critical to reduce multicollinearity by selecting meaningful and relatively independent predictors at the first palce.

^{2}as its value is not comparable among different models. Users should be aware of these criticisms or weaknesses. Nevertheless, when used approperaitely, this approach is a valuable tool for ecologists.

## 6. Commonality Analysis (CA)

^{2}of a GLM based on n predictors and n − 1 predictors (predictor i is removed). The unique effect of predictor i will be the difference in R

^{2}between the two models. The common effect will be estimated as R

^{2}of the full model minus the unique effect of each predictor. Similarly, one can estimate the unique and common effects of any 2, 3, 4… n − 1 predictors. An r-package, yhat [53] can be used to implement this analysis.

## 7. Sums of AIC Weight (SW)

^{2}of a predictor derived from the commonality analysis described earlier. The effectiveness of these three new approaches appears promising but needs to be further tested with both simulation and empirical data.

## 8. Tree-Based Approaches: Random Forest (RF) and Boosted Regression Tree (BRT)

^{2}. The optimal mtry may vary with datasets but is rarely greater than ten and often less than five. The number of trees can be specified by a user, and the default is 500. A higher number (e.g., 2000) may be needed to achieve a stable prediction if the sample size and/or the number of predictors are large.

## 9. Assessing the Observation against the Expectation (O/E)

## 10. Ordination-Based Variance Partitioning for Multivariate Responses

## 11. Summary and Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The paths of SEM show the standardized regression coefficient vs. marginal R

^{2}of individual physical predictors (x/y) for each of the three response variables across 459 stream sites in Illinois. Mussel SR is the ultimate response variable (blue). Fish species richness (SR) and percent agricultural land in the watershed (Agri) are response variables of other environmental factors, as well as the predictors of mussel SR (light blue). All other variables are predictors (blanks) (Down_Order = order of downstream reach, Ponddn_L = distance from downstream pond, see Table 1 for the abbreviations of other predictors). The R

^{2}for the overall model is shown in each of the blue boxes (see [6] for data sources), and its value is symbolized by the width of the arrow (solid line = statistically significant; dotted line = insignificant).

**Table 1.**Pearson correlations among key natural environment, climate, and land-use variables for 459 stream sites at the watershed scale in the State of Illinois, USA. (modified from [6]) with Long = longitude, Lat = latitude, Slope = average slop of the watershed (WT), Agri = percent agricultural land in WT, Forest = percent forests in WT, BG100 = percent WT with bedrock deeper than 100 feet (30.48 m), BR50 = percent WT with a bedrock of <50 feet, Temp = average annual air temperature in WT, Precip = average annual precipitation of WT, and Perm = average soil permeability of WT.

Lat | long | Slope | Agri | Forest | BG100 | BR50 | Temp | Precip | |
---|---|---|---|---|---|---|---|---|---|

Long | 0.09 | ||||||||

Slope | −0.43 | −0.33 | |||||||

Agri | 0.34 | 0.06 | −0.73 | ||||||

Forest | −0.61 | −0.13 | 0.87 | −0.83 | |||||

BG100 | 0.42 | 0.37 | −0.44 | 0.36 | −0.43 | ||||

BR50 | −0.48 | −0.36 | 0.59 | −0.50 | 0.57 | −0.83 | |||

Temp | −0.99 | −0.08 | 0.39 | −0.30 | 0.57 | −0.40 | 0.44 | ||

Precip | −0.90 | 0.08 | 0.57 | −0.52 | 0.74 | −0.40 | 0.50 | 0.87 | |

Perm | 0.28 | 0.16 | −0.09 | 0.05 | −0.11 | 0.17 | −0.20 | −0.28 | −0.16 |

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Cao, Y.; Wang, L.
How to Statistically Disentangle the Effects of Environmental Factors and Human Disturbances: A Review. *Water* **2023**, *15*, 734.
https://doi.org/10.3390/w15040734

**AMA Style**

Cao Y, Wang L.
How to Statistically Disentangle the Effects of Environmental Factors and Human Disturbances: A Review. *Water*. 2023; 15(4):734.
https://doi.org/10.3390/w15040734

**Chicago/Turabian Style**

Cao, Yong, and Lizhu Wang.
2023. "How to Statistically Disentangle the Effects of Environmental Factors and Human Disturbances: A Review" *Water* 15, no. 4: 734.
https://doi.org/10.3390/w15040734