Ecological Archives E090-026-A1

Kim Murray and Mary M. Conner. 2009. Methods to quantify variable importance: implications for the analysis of noisy ecological data. Ecology 90:348–355.

Appendix A (Table A1). Performance of six measures of variable importance (R2 = 0.35).


Zero-order

Partial

Semipartial

Standardized

Akaike

Independent

True

Correlation

Correlation

Correlation

Coefficient

Weight

Effect

Correlation

Variable

Value

Weight

Value

Weight

Value

Weight

Value

Weight

Value

Weight

Value

Weight

Value

Weight


Four uncorrelated explanatory variables

x1

0.035

10%

0.051

11%

0.035

10%

0.035

10%

1.000

25%

0.035

10%

0.035

10%

x2

0.070

20%

0.098

21%

0.070

20%

0.070

20%

1.000

25%

0.070

20%

0.070

20%

x3

0.123

35%

0.160

34%

0.123

35%

0.123

35%

1.000

25%

0.123

35%

0.123

35%

x4

0.123

35%

0.160

34%

0.123

35%

0.123

35%

1.000

25%

0.123

35%

0.123

35%

Total

0.351

100%

0.469

100%

0.351

100%

0.351

100%

4.000

100%

0.351

100%

0.351

100%


Two independent and two correlated explanatory variables (rx2x4= 0.40).

x1

0.035

10%

0.048

15%

0.035

14%

0.035

13%

1.000

25%

0.035

12%

0.035

12%

x2

0.070

20%

0.026

8%

0.019

8%

0.022

8%

1.000

25%

0.044

15%

0.044

15%

x3

0.123

35%

0.150

47%

0.123

50%

0.123

46%

1.000

25%

0.123

41%

0.123

41%

x4

0.123

35%

0.093

29%

0.071

29%

0.085

32%

1.000

25%

0.097

32%

0.097

32%

Total

0.351

100%

0.317

99%

0.248

101%

0.265

99%

4.000

100%

0.299

100%

0.299

100%


Four uncorrelated explanatory variables and a spurious variable.

x1

0.035

10%

0.063

6%

0.035

5%

0.035

4%

1.000

20%

0.035

7%

0.035

10%

x2

0.070

20%

0.244

24%

0.168

24%

0.225

25%

1.000

20%

0.106

22%

0.070

20%

x3

0.123

35%

0.192

19%

0.123

18%

0.123

13%

1.000

20%

0.123

26%

0.123

35%

x4

0.123

35%

0.311

31%

0.234

34%

0.315

34%

1.000

20%

0.166

35%

0.123

35%

x5

0.000

0%

0.199

20%

0.129

19%

0.217

24%

1.000

20%

0.051

11%

0.000

0%

Total

0.351

100%

1.009

100%

0.689

100%

0.915

100%

5.000

100%

0.481

101%

0.351

100%


Two independent variables,  two correlated variables (rx2x4= 0.40) and a spurious variable.

x1

0.035

10%

0.051

10%

0.035

10%

0.035

8%

1.000

20%

0.035

10%

0.035

12%

x2

0.070

20%

0.062

13%

0.042

12%

0.057

13%

1.000

20%

0.055

15%

0.044

15%

x3

0.123

35%

0.160

32%

0.123

34%

0.123

28%

1.000

20%

0.123

35%

0.123

41%

x4

0.123

35%

0.144

29%

0.109

30%

0.145

33%

1.000

20%

0.115

32%

0.097

32%

x5

0.000

0%

0.079

16%

0.055

15%

0.078

18%

1.000

20%

0.027

8%

0.000

0%

Total

0.351

100%

0.496

100%

0.364

101%

0.438

100%

5.000

100%

0.355

100%

0.299

100%


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