[R] structural equation modeling in sem, error, The model has negative degrees of freedom = -3, and The model is almost surely misspecified...

[Alex Anderson]

Hi all,
I am attempting to learn my way through the sem package by constructing 
a simple structural model for some of my data on bird diversity, 
abundance, and primary productivity.

I have constructed a covariance matrix between these variables as per 
the following:

 >S_matrix = matrix(c(
 >+ 0.003083259, 0,             0,
 >+ 0.143870284, 89.7648490,      0,
 >+ 0.276950919, 81.3484101, 215.3570157
 > ), ncol = 3, byrow = T)
 >rownames(S_matrix) = colnames(S_matrix) = c("dec_mean_EVI", "density", 
"ALL_Jack1")

I then construct a model using a symbolic ram specification as follows

 >tmodel <- specify.model()
 >dec_mean_EVI     -> density, gam1,  NA
 >density          -> ALL_Jack1, gam2,  NA
 >dec_mean_EVI  -> ALL_Jack1, gam3,  NA
 >dec_mean_EVI <-> dec_mean_EVI, ps1,   NA
 >density <-> density, ps2,   NA
 >ALL_Jack1 <-> ALL_Jack1, theta1,   NA
 >dec_mean_EVI <-> density, theta2, NA
 >dec_mean_EVI <-> ALL_Jack1, theta2, NA
 >density <-> ALL_Jack1,  theta3, NA

I then try to run the sem analysis using the matrix and model.

 >sem_1 <- sem(ram = tmodel, S = S_matrix, N = 88, fixed.x = 
c("dec_mean_EVI"))
 >summary(sem_1)

However, I only get the following error message:

"Error in sem.default(ram = ram, S = S, N = N, param.names = pars, 
var.names = vars,  :
   The model has negative degrees of freedom = -3
In addition: Warning message:
In sem.default(ram = ram, S = S, N = N, param.names = pars, var.names = 
vars,  :
   The following variables have no variance or error-variance parameter 
(double-headed arrow):
  density, ALL_Jack1, dec_mean_EVI    , density    , density        , 
ALL_Jack1
The model is almost surely misspecified; check also for missing 
covariances."

It must be obvious to those experienced with sem, but I can't yet see 
where I have gone wrong in constructing my matrix or model, any thoughts 
would be much appreciated.
thanks in advance,
Alex