Hi Navio

Maybe you could initially set the models up as latent class growth models which have the variance of the intercept, slope, and in this case the quadratic, latent variables fixed at zero. These models do not have the convergence/improper solution problems that more general LGM can sometimes exhibit. This may give you a clearer idea about whether the quadratic term is actually necessary or not. Alternatively you could try a model with unspecified trajectory by freeing some factor loadings on the slope factor, or try a piecewise growth model if you roughly know the non-linear shape of the trajectory.

I was having some problems with a growth curve model recently and chatted with a colleague about it, and he wisely told me to go back to the data and engage in some serious EDA and let the sample means be your friend in deciding a modelling strategy.

Best wishes

Mark

I believe you inspect significant differnces in variances when examinng hierarchical models under GLM.

Hope this helps,

Matt

Thank you, Matthew Kerry and Mark Shevlin for your responses!

Navio,

1. The parameter tests are known to have low power. So, rather than testing the significance of the mean and variance parameters of the latent slope factors, you may compare models (e.g. linear vs quadratic latent growth) based on chi-squared difference test or even better, based on likelihood-based fit indices, such as AIC and BIC, in order to determine whether you need a latent quadratic slope factor.

2. "Having a statistically non-significant mean but significant variance for the latent quadratic slope factor" does not suggest that the overall shape of the trajectories is linear (or non-linear) because there is no "overall" shape of the trajectories in Latent Growth Modeling. You are interested in modeling the individual trajectories and that is why you are using LGM instead of Repeated Measures Anova/GLM.

3. Assuming the model is correct, the pattern you ended up with (i.e. significant variance but non-significant mean for the quadratic slope factor) indicates that there is significant variability in individuals’ quadratic growth rates (i.e. the amount of acceleration/deceleration in the rate of change). Non-significant mean only suggests that the estimated quadratic slope coefficient is probably negative for some individuals and positive for others but they cancel out and their mean is not significantly different than zero. If the models fit indices also indicate a better fit for the quadratic growth model, the statistically significant variance can be interpreted as an additional proof that there is a need for the quadratics growth model because individuals seem to grow at the different quadratic rates.

Dear Serkan Dolma, many thanks for providing this great explanation of cancelling-out effects (your point #3) in the context of LGMs. I am currently having a similar situation with one of my LGMs and was wondering whether you had a specific reference for your point? That is, beyond the more general LGM literature's interpretation what the slope growth factor is compared to its variance? This would be much appreciated!

Best,

Jakob