Dear all,
# I have the following sub-datasets of soil carbon change at four sites.
There are four treatments at each site.
DltC <- c(-19.237, -14.857, -14.818, -14.815, -11.014, 3.349, 4.332, 3.956,
-7.638, 9.469, 14.189, 13.037, -9.809, 5.459, 8.748, 11.511)
# Soil C fractions at the start of the experiment at the four sites are:
f.BIOM <- c(0.0294, 0.0294, 0.0294, 0.0294, 0.0169, 0.0169, 0.0169,
0.0169,0.0172, 0.0172, 0.0172, 0.0172, 0.0208, 0.0208, 0.0208, 0.0208) #
Four treatments have the same initial soil C fraction
f.FOM <- c(0.183, 0.183, 0.183, 0.183,0.0223, 0.0223, 0.0223, 0.0223,0.0168,
0.0168, 0.0168, 0.0168, 0.00766, 0.00766, 0.00766, 0.00766)
f.Inert_C <- c(0.197, 0.197, 0.197, 0.197,0.466, 0.466, 0.466,
0.4666,0.5336, 0.533, 0.533, 0.533,0.333, 0.333, 0.3333, 0.3333)
f.HUM <- c(0.589, 0.589, 0.589, 0.589,0.494, 0.494, 0.494, 0.494,0.432,
0.432, 0.432, 0.432,0.638, 0.638, 0.638, 0.638)
# Applying multiple regression model to the data:
fit1 <- lm(DltC ~f.BIOM*f.FOM*f.Inert_C*f.HUM)
fit2 <- lm(DltC~f.Inert_C*f.HUM*f.BIOM*f.FOM) # Just change the order of
the four variables
summary(fit1)
summary(fit2)
# Coefficients of fit1:
Coefficients: (9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 206698 54914 3.764 0.00446 **
f.BIOM -4477270 1716046 -2.609 0.02831 *
f.FOM -2227245 794993 -2.802 0.02066 *
f.Inert_C -996522 280627 -3.551 0.00621 **
f.HUM -172647 56211 -3.071 0.01332 *
f.BIOM:f.FOM NA NA NA NA
f.BIOM:f.Inert_C 46171278 12725547 3.628 0.00550 **
f.FOM:f.Inert_C 10074999 3442541 2.927 0.01685 *
f.BIOM:f.HUM NA NA NA NA
f.FOM:f.HUM NA NA NA NA
f.Inert_C:f.HUM NA NA NA NA
f.BIOM:f.FOM:f.Inert_C NA NA NA NA
f.BIOM:f.FOM:f.HUM NA NA NA NA
f.BIOM:f.Inert_C:f.HUM NA NA NA NA
f.FOM:f.Inert_C:f.HUM NA NA NA NA
f.BIOM:f.FOM:f.Inert_C:f.HUM NA NA NA NA
# Coefficients of fit2:
Coefficients: (9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21052 36457 0.577 0.5778
f.Inert_C -54158 112672 -0.481 0.6422
f.HUM -291540 96625 -3.017 0.0145 *
f.BIOM 7364603 4214425 1.747 0.1145
f.FOM -242470 123836 -1.958 0.0819 .
f.Inert_C:f.HUM 603519 206217 2.927 0.0168 *
f.Inert_C:f.BIOM -13939751 10567698 -1.319 0.2197
f.HUM:f.BIOM NA NA NA NA
f.Inert_C:f.FOM NA NA NA NA
f.HUM:f.FOM NA NA NA NA
f.BIOM:f.FOM NA NA NA NA
f.Inert_C:f.HUM:f.BIOM NA NA NA NA
f.Inert_C:f.HUM:f.FOM NA NA NA NA
f.Inert_C:f.BIOM:f.FOM NA NA NA NA
f.HUM:f.BIOM:f.FOM NA NA NA NA
f.Inert_C:f.HUM:f.BIOM:f.FOM NA NA NA NA
# Comparing with fit1, the coefficients in fit2 is quite another, e.g., the
effect of the interaction between f.Inert_C and f.HUM is significant in
fit2, but it is 'NA' in fit 1.
# Do someone have ideas about the difference between fit1 and fit2, and the
meaning of the NAs.
Thanks very much for your time.
Zachary
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