About the formative measurement model in SEM

[Jie Tang]

Dear Lavaan users,

'm trying to build a structural equation model using both reflective and formative specifications of latent variables. I use the sem function in the lavaan package for estimation, but get warning message. Below are my model and the warning message.

fit.mod1<-'

## Measurement model

F1=~ x1+x2+x3+x4+x5+x6+x7
F2=~ x8+x9+x10+x11+x12+x13+x14+x15+x16
F3=~ x17+x18+x19+x20+x21+x22+x23
F4=~ x24+x25+x26+x27+x28+x29
F5=~ x30+x31+x32+x33

pb =~ x34+x35+x36
ses =~ x37+x38+x39
IMG<~ F1+ F2+ F3+ F3+ F4

## Structural  model
pbi ~ o1*x
ses ~ o2*x
ur ~ o3*x

F1 ~ i1*x+i11*pbi+i12*ses+i13*ur
F2 ~ i2*x+i21*pbi+i22*ses+i23*ur
F3 ~ i3*x+i31*pbi+i32*ses+i33*ur
F4 ~ i4*x+i41*pbi+i42*ses+i43*ur
F5 ~ i5*x+i51*pbi+i52*ses+i53*ur
IMG ~ i6*x+i61*pbi+i62*ses+i63*ur

y ~ b1*x+t11*pbi+t12*ses+t13*ur+ t14*IMG

##  Variance Co-variance

IMG ~~ 0*IMG

'

fit.mod1 <- sem(mod1, data=alldata,std.lv=TRUE,meanstructure=TRUE,fixed.x =FALSE,missing='ml')

Warning message:
In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :
  lavaan WARNING:
    Could not compute standard errors! The information matrix could
    not be inverted. This may be a symptom that the model is not
    identified.

And the error when use modificationindices function:

Error in modificationindices(fit.mod1) :
  lavaan ERROR: could not compute modification indices; information matrix is singular

 Is there anything wrong with my model?

Would be very appreciative if could get these bugs de!!!

Thanks in advance