Multitrait-multistate model: negative variances

[Simon Columbus]

Hi all,

I am trying to specify a multitrait-multistate model (two states, six item-specific traits) in lavaan; I've attached a diagram for illustration. Unfortunately, I am running into problems with negative ov and lv variances (i.e., warning messages "some estimated ov/lv variances are negative"), which I have not been able to resolve. The model looks as follows (I've included code to simulate a data set. This does not always yield usable data; I have attached a data frame that yields the relevant error):

# GENERATE DATA

df.i <- as.data.frame(matrix(NA,3000,12))
t <- rep(rnorm(6, 0, 1),times=2)
s <- rep(rnorm(2, 0, 1),times=6)
for (i in 1:12){
  df.i[,i] <- rnorm(3000,0,1)+t[i]+s[i]
}


names(df.i) <- paste("y", rep(1:6, times=2), rep(1:2, each=6), sep="")


# MODEL


model.sis <- '
# latent variables
## latent states
s1 =~ 1*y11 + la211*y21 + la311*y31 + la411*y41 + la511*y51 + la611*y61
s2 =~ 1*y12 + la221*y22 + la321*y32 + la421*y42 + la521*y52 + la621*y62


## latent traits
t1 =~ 1*y11 + la122*y12
t2 =~ 1*y21 + la222*y22
t3 =~ 1*y31 + la322*y32
t4 =~ 1*y41 + la422*y42
t5 =~ 1*y51 + la522*y52
t6 =~ 1*y61 + la622*y62


# (co)variances
## variances of states s
s1 ~~ vars1*s1
s2 ~~ vars2*s2


## variances of traits t
t1 ~~ vart1*t1
t2 ~~ vart2*t2
t3 ~~ vart3*t3
t4 ~~ vart4*t4
t5 ~~ vart5*t5
t6 ~~ vart6*t6


## variances of indicators
y11 ~~ vary11*y11
y21 ~~ vary21*y21
y31 ~~ vary31*y31
y41 ~~ vary41*y41
y51 ~~ vary51*y51
y61 ~~ vary61*y61
y12 ~~ vary12*y12
y22 ~~ vary22*y22
y32 ~~ vary32*y32
y42 ~~ vary42*y42
y52 ~~ vary52*y52
y62 ~~ vary62*y62


## covariances
s1 + s2 ~~ 0*t1 + 0*t2 + 0*t3 + 0*t4 + 0*t5 + 0*t6 # covariances of states and traits set to 0
s1 ~~ 0*s2 # covariances of states set to 0
t1 ~~ cov12*t2 + cov13*t3 + cov14*t4 + cov15*t5 + cov16*t6
t2 ~~ cov23*t3 + cov24*t4 + cov25*t5 + cov26*t6
t3 ~~ cov34*t4 + cov35*t5 + cov36*t6
t4 ~~ cov45*t5 + cov46*t6
t5 ~~ cov56*t6


# invariances


vars1 == vars2
'

# FIT CFA

fit <- cfa(model.sis, data=df.i)

I have tried to resolve this problem by specifying additional invariances between the factor loadings for the latent trait factors:

la211 == la221
la311 == la321
la411 == la421
la511 == la521
la611 == la621

However, this does not resolve the issue. At the moment, I am puzzled as to why the CFA leads to negative variances; so I'd appreciate any pointers.

Kind regards,

Simon

[Terrence Jorgensen]

Doesn't sound like lavaan is the problem.  Perhaps you could post you question on SEMNET to see if anyone can offer advice.

www2.gsu.edu/~mkteer/semnet.html

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen