# 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).

• Were the variances estimated with the Cramer-Rao bound? If so, what is the condition number of your Fisher information matrix? Nov 29, 2021 at 16:37
• What optimization strategy did you use? Nov 29, 2021 at 16:46
• Why have you manually set some of the parameters? Example: 9 * Score.wave3. Nov 29, 2021 at 19:25