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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