Michael H. Graham. 2003. Confronting multicollinearity in ecological multiple regression. Ecology 84:2809–2815.

EQS file creation protocol

1. Program file was created using TITLE/SPECIFICATIONS under BUILD EQS menu. Use default settings with: normal theory estimators set to ML (maximum likelihood), variables set to 5, and cases set to 38.

2. Create equations using EQUATIONS under BUILD EQS menu.

  a. set number of VARIABLES to 5; set NUMBER OF FACTORS to 2

  b. build the following CREATE EQUATIONS box:

  c. use default CREATE VARIANCE/COVARIANCE box

3. Run EQS

Subsequent EQS program file
1	/TITLE
2	EQS model created by EQS 6 for Windows -- c:\eqs6\filename.ess
3	/SPECIFICATIONS
4	DATA='c:\eqs6\filename.ess';
5	VARIABLES=5; CASES=38; GROUPS=1;
6	METHODS=ML;
7	MATRIX=RAW;
8	ANALYSIS=COVARIANCE;
9	/LABELS
10	V1=Response; V2=OD; V3=BD; V4=LTD; V5=W;
11	/EQUATIONS
12	V1 =   + *F1   + 1E1;
13	F1 =   + *F2   + *V4 + *V5 + 1D1;
14	F2 =   + *V2 + *V3 + 1D2;
15	/VARIANCES
16	V2 = *;
17	V3 = *;
18	V4 = *;
19	V5 = *;
20	E1 = *;
21	D1 = *;
22	D2 = *;
23	/COVARIANCES
24	/PRINT
25	FIT=ALL;
26	TABLE=EQUATION;
27	/TECHNICAL
28	ITERATION= 100;
29	EITERATION= 100;
30	AITERATION= 100;
31	HITERATION= 100;
32	/END
Maximum likelihood solution (normal distribution theory)
EQSstandardized solution:
RESPONSE =V1   = 0.860*F1 + 0.510 E1
F1 = 0.917*F2 - 0.065*LTD + 0.393*W + 0.000 D1
F2 = -0.777*OD + 0.049*BD + 0.627 D2
Note: EQS only outputs standardized solutions.   In order to compare among standard, sequential, and pc regression results, eqs standardized regression coefficients were transformed to un-standardized values.   An un-standardized regression coefficient () equaled the standardized regression coefficient (') minus the average value of the variable (ave[x]) divided by the standard deviation of the variable (SD[X]):
EQSun-standardized solution
RESPONSE =V1   = 0.69*F1
F1 = 1.23*F2 - 0.08*LTD + 0.01*W
F2 = -0.20*OD + 0.01*BD