SEM warning message "WARNING: some estimated lv variances are negative" (Latent growth curve model) When running a quadratic latent growth curve model (model_6 below) I get the following warning message: "lavaan WARNING: some estimated lv variances are negative".
What does this mean, am I getting the warning because the quadratic model is not a good fit for the data?
For context: I am using latent growth curve models to model cognitive scores over 4 timepoints. I am in the process of deciding if a linear or quadratic fitted line is most appropriate.
I have included my linear (model_4) and quadratic (model_6) models below. The RMSEA for the linear model is 0.055, whereas the RMSEA for the quadratic model is 0.039.

model_4 = '
    # Intercept     
    i =~ 1*Score.baseline + 1*Score.wave1 + 1*Score.wave2 + 1*Score.wave3
    
    # Slope
    s =~ 0*Score.baseline + 1*Score.wave1 + 2*Score.wave2 + 3*Score.wave3
  
    # Set the residual variances to all the same 
    Score.baseline ~~ r*Score.baseline    
    Score.wave1 ~~ r*Score.wave1
    Score.wave2 ~~ r*Score.wave2
    Score.wave3 ~~ r*Score.wave3
'

lgcm_model_4 <- growth(model_4, data=Data_wide, missing = "fiml")



model_6 <- '
    # Intercept
    i =~ 1*Score.baseline + 1*Score.wave1 + 1*Score.wave2 + 1*Score.wave3

    # Slope 1
    s1 =~ 0*Score.baseline + 1*Score.wave1 + 2*Score.wave2 + 3*Score.wave3

    # Slope 2
    s2 =~ 0*Score.baseline + 1*Score.wave1 + 4*Score.wave2 + 9*Score.wave3
'

lgcm_model_6 <- growth(model_6, data=Data_wide, missing = "fiml")


Below I've also included two plots. The first shows the mean score across the 4 timepoints (waves).

The second plot shows the fitted lines for the linear model (red) and the quadratic model (blue).


This warning means that your model is wrong.
The parameter estimates that are most consistent with the data require negative variances, which cannot exist.
Another way to think of it: There's not enough covariance between the measured variables to provide enough variance for three latent variables.
