[R] Fitting Structural Equation Model with sem package and Summary issues

[Guillaume Souchay]

Hi all,

I am trying to analyse bird data to investigate carry-over effect
using structural equation model.
I failed to run properly a big model with several latent variables
with both L -> M block and M -> L block.
Rather than trying again and again with the huge model, I am now
looking to a subset of the model.

Due to previous error message (singularity in the matrix), I scaled
all the variables.
Here is a subset of the data:
> dataE[1:15,]
   Fledgling_date_t Total_Output_t Breed_nb.clutch_t.1 Breed_Egg_t.1
Breed_Total_Output_t.1
1        1.09397971     1.19657515           0.4696909   -0.69784742
           1.2558119
2        0.62564592     0.37786584           0.4696909    0.02046473
          -0.1762543
3        1.51548013     1.19657515          -1.0568046    0.89840181
          -1.8947338
4        0.15731212     1.60592981          -1.0568046   -1.49597204
          -1.3219073
5        0.48514578    -0.44084348           0.4696909   -0.69784742
           0.6829854
6        1.93698054    -0.03148882           0.4696909    0.02046473
           0.9693987
7       -1.66918968    -0.85019813          -1.0568046    0.97821428
          -0.4626676
8        0.01681198     0.78722049           0.4696909   -0.53822250
           1.2558119
9        0.34464564     1.60592981          -1.0568046   -0.13916019
          -1.8947338
10       1.23447985     1.19657515          -1.0568046    1.93596382
          -0.7490808
11      -0.12368816    -0.85019813           0.4696909    1.93596382
           0.1101589
12      -0.17052154     0.78722049          -1.0568046   -0.45841004
          -0.1762543
13      -1.52868954    -0.44084348          -1.0568046    1.37727658
          -0.4626676
14       0.15731212    -1.25955279          -1.0568046    1.61671397
          -0.4626676
15      -0.17052154    -0.85019813          -1.0568046    0.97821428
          -1.6083205

Library(sem)
# the covariance matrix for scaled data
S.covE <- readMoments(diag=T,names=c("Fledgling_date_t","Total_Output_t","Breed_nb.clutch_t.1","Breed_Egg_t.1","Breed_Total_Output_t.1"))
1.0000000
0.350170246 1.0000000
-0.075832501 -0.099929893 1.0000000
-0.15439341 -0.091334987 -0.131698418 1.0000000
-0.191457491 -0.227843749 0.510666663 -0.386711653 1.0000000

# specification of the model - I also provided a diagram of the model
in the attached PDF.
modelE <- specifyModel()
EndBreed -> Fledgling_date_t,                       lambda1,   NA
EndBreed -> Total_Output_t,                         lambda1,   NA
Fledgling_date_t <-> Fledgling_date_t,              delta1,    NA
Total_Output_t <-> Total_Output_t,                  delta2,    NA
Fledgling_date_t <-> Total_Output_t,                theta1,    NA
EndBreed -> BreedSucc,                              gamma1,    NA
EndBreed <-> EndBreed,                              phi1,      NA
BreedSucc -> Breed_Egg_t.1,                         lamdae,    NA
BreedSucc -> Breed_Total_Output_t.1,                lamdae,    NA
BreedSucc -> Breed_nb.clutch_t.1,                   lamdae,    NA
Breed_nb.clutch_t.1 <-> Breed_nb.clutch_t.1,        eps1,      NA
Breed_Egg_t.1 <-> Breed_Egg_t.1,                    eps2,      NA
Breed_Total_Output_t.1 <-> Breed_Total_Output_t.1,  eps3,      NA
Breed_nb.clutch_t.1 <-> Breed_Egg_t.1,              psie12,    NA
Breed_Egg_t.1 <-> Breed_Total_Output_t.1,           psie23,    NA
Breed_nb.clutch_t.1 <-> Breed_Total_Output_t.1,     psie13,    NA
BreedSucc <-> BreedSucc,                            zetae,     NA

# estimation of the model
semE <- sem(modelE,S.covE,N=39,debug=T)

To this point, everything seemed fine, the parameter were estimated
after 129 iterations with all data.
However, the problem arised when I asked for a summary of the model:

> summary(semE)
Error in summary.objectiveML(semE) :
  coefficient covariances cannot be computed

But the model seemed to work well :

> semE

 Model Chisquare =  0.9876903   Df =  1

   lambda1     delta1     delta2     theta1     gamma1       phi1
lamdae       eps1       eps2
 0.8251654  0.3302009  0.3418300 -0.3138143  0.4122545  0.9752364
-0.4671335  0.8020365  0.7857964
      eps3     psie12     psie23     psie13      zetae
 0.7461566 -0.3377820 -0.6207350  0.2847632  0.8828395

 Iterations =  75
> semE$convergence
[1] TRUE

I also tried with using SpecifyEquations() instead of SpecifyModel() :
# specification of the model using specifyEquations
modelEe <- specifyEquations()
Fledgling_date_t = lambda1*EndBreed
Total_Output_t = lambda1*EndBreed
c(Fledgling_date_t,Total_Output_t) = theta1
Breed_nb.clutch_t.1 = lamdae*BreedSucc
Breed_Egg_t.1 = lamdae*BreedSucc
Breed_Total_Output_t.1 = lamdae*BreedSucc
c(Breed_nb.clutch_t.1,Breed_Egg_t.1) = psi12
c(Breed_nb.clutch_t.1,Breed_Total_Output_t.1) = psi13
c(Breed_Egg_t.1,Breed_Total_Output_t.1) = psi23
BreedSucc = gamma1*EndBreed
v(EndBreed) = phi1
v(BreedSucc) = zeta1
v(Fledgling_date_t) = delta1
v(Total_Output_t) = delta2
v(Breed_nb.clutch_t.1) = eps1
v(Breed_Egg_t.1) = eps2
v(Breed_Total_Output_t.1) = eps3

# estimation of the model
semEe <- sem(modelEe,covE,N=39,debug=T)

> semEe

 Model Chisquare =  0.9876903   Df =  1

   lambda1     theta1     lamdae      psi12      psi13      psi23
gamma1       phi1      zeta1
 0.8220182 -0.3346606  0.5034442 -0.3550646  0.2674806 -0.6380177
-0.3694630  1.0135693  0.8326144
    delta1     delta2       eps1       eps2       eps3
 0.3093554  0.3209828  0.7847537  0.7685137  0.7288741

 Iterations =  79
> summary(semEe)
Error in summary.objectiveML(semEe) :
  coefficient covariances cannot be computed

I also tried to set one loading to 1 instead of setting equality among
loadings, but the results were the same.

Could it be possible that the low number of data (N=39 but no NA
inside) may be the cause of the error?
In the model, the df is 1, thus all the parameters should be identifiable.

Hoping you will have enough information to help a bit.

Thanks in advance.

Cheers,

Guillaume

-- 

Guillaume SOUCHAY, Ph.D

Post-doctoral fellow in population dynamics

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"There is no true model" Anderson & Burhnam 1999

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