Negative variances in Autoregressive Latent Trajectory Model w

[Kinga Bierwiaczonek]

Dear all, 

I am trying to fit an autoregressive latent trajectory model with structured residuals on a 3-wave dataset. I used the lavaan code for two waves from Mund, & Nestler (2017) and I adapted it to three waves. I am getting close fit and large negative variances for both intercepts and slopes. The issue does not seem to be with the data; I assume it's some mistake I made when adapting the code, but I cannot find it. 

Thanks in advance for any help. 

Best, 

Kinga 

altsr <- '

# Define intercept and growth factors

ix =~ 1*x1+1*x2+1*x3

iy1 =~ 1*y1.1+1*y1.2+1*y1.3

iy2 =~ 1*y2.1+1*y2.2+1*y2.3

sx =~ 0*x1+1*x2+2*x3

sy1 =~ 0*y1.1+1*y1.2+2*y1.3

sy2 =~ 0*y2.1+1*y2.2+2*y2.3

# Define phantom latent variables

etax1 =~ 1*x1

etax2 =~ 1*x2

etax3 =~ 1*x3

etay1.1 =~ 1*y1.1

etay1.2 =~ 1*y1.2

etay1.3 =~ 1*y1.3

etay2.1 =~ 1*y2.1

etay2.2 =~ 1*y2.2

etay2.3 =~ 1*y2.3

# Autoregressive effects

etax2 ~ a1*etax1

etax3 ~ a1*etax2

etay1.2 ~ a2*etay1.1

etay1.3 ~ a2*etay1.2

etay2.2 ~ a3*etay2.1

etay2.3 ~ a3*etay2.2

# Crosslagged effects

etay1.2 ~ c1*etax1

etay1.3 ~ c1*etax2

etax2 ~ c2*etay1.1

etax3 ~ c2*etay1.2

etay2.2 ~ c3*etax1

etay2.3 ~ c3*etax2

etax2 ~ c4*etay2.1

etax3 ~ c4*etay2.2

etay2.2 ~ c5*etay1.1

etay2.3 ~ c5*etay1.2

etay1.2 ~ c6*etay2.1

etay1.3 ~ c6*etay2.2

#  Set error variances of the observed variables to zero

x1 ~~ 0*x1

x2 ~~ 0*x2

x3 ~~ 0*x3

y1.1 ~~ 0*y1.1

y1.2 ~~ 0*y1.2

y1.3 ~~ 0*y1.3

y2.1 ~~ 0*y2.1

y2.2 ~~ 0*y2.2

y2.3 ~~ 0*y2.3

# Estimate the variance of the latent variables

etax1 ~~ varx1*etax1

etax2 ~~ varx2*etax2

etax3 ~~ varx3*etax3

etay1.1 ~~ vary1.1*etay1.1

etay1.2 ~~ vary1.2*etay1.2

etay1.3 ~~ vary1.3*etay1.3

etay2.1 ~~ vary2.1*etay2.1

etay2.2 ~~ vary2.2*etay2.2

etay2.3 ~~ vary2.3*etay2.3

# Estimate intercept factor variances, the slope variances and covariances

ix ~~ varix*ix

iy1 ~~ variy1*iy1

iy2 ~~ variy2*iy2

sx ~~ varsx*sx

sy1 ~~ varsy1*sy1

sy2 ~~ varsy2*sy2

ix ~~ covi1*iy1

ix ~~ covi2*iy2

ix ~~ covixsx*sx

ix ~~ covixsy1*sy1

ix ~~ covixsy2*sy2

sx ~~ covsxsy1*sy1

sx ~~ covsxsy2*sy2

iy1 ~~ coviy1iy2*iy2

iy1 ~~ coviy1sx*sx

iy1 ~~ coviy1sy1*sy1

iy1 ~~ coviy1sy2*sy2

sy1 ~~ covsy1sy2*sy2

iy2 ~~ coviy2sx*sx

iy2 ~~ coviy2sy1*sy1

iy2 ~~ coviy2sy2*sy2

# Covariance between the intercepts and

#    the slopes and the latents of the first time point set to zero

etax1 ~~ 0*ix

etay1.1 ~~ 0*ix

etay2.1 ~~ 0*ix

etax1 ~~ 0*sx

etay1.1 ~~ 0*sx

etay2.1 ~~ 0*sx

etax1 ~~ 0*iy1

etay1.1 ~~ 0*iy1

etay2.1 ~~ 0*iy1

etax1 ~~ 0*sy1

etay1.1 ~~ 0*sy1

etay2.1 ~~ 0*sy1

etax1 ~~ 0*iy2

etay1.1 ~~ 0*iy2

etay2.1 ~~ 0*iy2

etax1 ~~ 0*sy2

etay1.1 ~~ 0*sy2

etay2.1 ~~ 0*sy2

# Covariance between the latents of x and y

etax1 ~~ cov1*etay1.1

etax2 ~~ e1*etay1.2

etax3 ~~ e1*etay1.3

etax1 ~~ cov2*etay2.1

etax2 ~~ e2*etay2.2

etax3 ~~ e2*etay2.3

etay1.1 ~~ cov3*etay2.1

etay1.2 ~~ e3*etay2.2

etay1.3 ~~ e3*etay2.3

# Mean structure

x1 ~ 0*1

x2 ~ 0*1

x3 ~ 0*1

y1.1 ~ 0*1

y1.2 ~ 0*1

y1.3 ~ 0*1

y2.1 ~ 0*1

y2.2 ~ 0*1

y2.3 ~ 0*1

etax1 ~ 0*1

etax2 ~ 0*1

etax3 ~ 0*1

etay1.1 ~ 0*1

etay1.2 ~ 0*1

etay1.3 ~ 0*1

etay2.1 ~ 0*1

etay2.2 ~ 0*1

etay2.3 ~ 0*1

ix ~ 1

iy1 ~ 1

iy2 ~ 1

sx ~ 1

sy1 ~ 1

sy2 ~ 1

'

Output: 

Variances:

                   Estimate  Std.Err  z-value   P(>|z|)

   .x1                0.000                            

   .x2                0.000                            

   .x3                0.000                            

   .y1.1              0.000                            

   .y1.2              0.000                            

   .y1.3              0.000                            

   .y2.1              0.000                            

   .y2.2              0.000                            

   .y2.3              0.000                            

    etax1   (vrx1)  210.773    0.090  2348.260    0.000

   .etax2   (vrx2)    3.334    0.185    18.051    0.000

   .etax3   (vrx3)    3.242    0.204    15.919    0.000

    etay1.1 (v1.1)   60.928    0.159   382.545    0.000

   .etay1.2 (v1.2)    0.882    0.373     2.362    0.018

   .etay1.3 (v1.3)    0.664    0.442     1.501    0.133

    etay2.1 (v2.1)  217.734    0.071  3063.569    0.000

   .etay2.2 (v2.2)    1.375    0.077    17.790    0.000

   .etay2.3 (v2.3)    1.423    0.086    16.462    0.000

    ix      (varx) -206.781    0.105 -1970.834    0.000

    iy1     (vry1)  -54.890    0.332  -165.183    0.000

    iy2     (vry2) -214.591    0.096 -2235.964    0.000

    sx      (vrsx)   -1.915    0.163   -11.781    0.000

    sy1     (vrs1)    0.040    0.184     0.219    0.827

    sy2     (vrs2)   -0.756    0.084    -9.003    0.000