[R] specifying a structural equation model with sem

[David Villegas Ríos]

Hi all,
I'm new to sem package and sem analyses, so this is probably very basic,
although I was not able to solve it myself reading some other similar
posts. I was trying to specify a structural equation model using a
correlation matrix of three variables. The correlation matrix comes from a
mixed model in which repeated measures of each variable were analysed as a
function of some fixed and random effects. All the correlations are really
high:

                   mirror          novel       shelter
mirror  1.0000000 0.8360787  0.9107897
novel   0.8360787 1.0000000  0.8745305
shelter 0.9107897 0.8745305  1.0000000

I want to test two models using sem:

1. Independence model: the three variables are independent
2. Syndrome model: all the variables linked through a common latent variable

So my code is:

*# independence model*

model.0=specifyModel()
mirror<->mirror, e1, NA
novel<->novel, e2, NA
shelter<->shelter, e3, NA

*# syndrome model; L represents the latent variable*

model.1=specifyModel()
L->mirror,a1,NA
L->novel,a2,NA
L->shelter,a3,NA
L<->L,NA,1
mirror<->mirror,e1,NA
novel<->novel,e2,NA
shelter<->shelter,e3,NA

*Sem function:*

output0.b=sem(model.0,b,N=235)
output1.b=sem(model.1,b,N=235)

*And my outputs are:*

> summary(output0.b)

 Model Chisquare =  761.9988   Df =  3 Pr(>Chisq) = 7.543238e-165
 AIC =  767.9988
 BIC =  745.62

 Normalized Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.000   0.000  12.790   8.911  13.380  13.930

 Parameter Estimates
   Estimate Std Error  z value  Pr(>|z|)
e1 1        0.09245003 10.81665 2.870676e-27 mirror <--> mirror
e2 1        0.09245003 10.81665 2.870676e-27 novel <--> novel
e3 1        0.09245003 10.81665 2.870676e-27 shelter <--> shelter

 Iterations =  0


> summary(output1.b)

 Model Chisquare =  3.117506e-13   Df =  0 Pr(>Chisq) = NA
 AIC =  12
 BIC =  3.117506e-13

 Normalized Residuals
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
1.107e-07 1.627e-07 1.701e-07 1.696e-07 1.753e-07 2.457e-07

 R-square for Endogenous Variables
 mirror   novel shelter
 0.8707  0.8028  0.9527

 Parameter Estimates
   Estimate   Std Error  z value   Pr(>|z|)
a1 0.93313643 0.04964952 18.794470 8.381262e-79 mirror <--- L
a2 0.89598763 0.05105094 17.550855 5.859107e-69 novel <--- L
a3 0.97605200 0.04790520 20.374657 2.806748e-92 shelter <--- L
e1 0.12925637 0.01801049  7.176726 7.140033e-13 mirror <--> mirror
e2 0.19720615 0.02206224  8.938628 3.940334e-19 novel <--> novel
e3 0.04732249 0.01537861  3.077164 2.089805e-03 shelter <--> shelter

 Iterations =  23

*My questions are:*

1) Are the models properly specyfied? I followed some examples in the
literature, specifically Broomer et al., 2014 Behav
Ecol, doi:10.1093/beheco/aru057

2) The outputs look pretty strange to me...first, all the paths seems
(highly!) significant. But looking at the model fit, and which model fits
the data better, I guess that the AIC value of the syndrome model is not
correct, and that the Df=0...so I guess that particular model is not
properly specified (unidentified model?). Also, in the independence model,
all the Z values are the same (?)

3) I specifyied N=235 since the original data consist of 235 rows for one
of the variables (5 repeated measures of 47 individuals). But for the two
other variables, I only have 94 rows (2 repeated measures of the same 47
individuals). So I'm not sure which N I should specify in the sem model.
Maybe something like N=c(94,94,235)? Or N=47 because in the end everything
is based on 47 individuals?

Any advise at this point would be greatly appreciated, I'm a bit at loss.

David

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