Growth Curve Episode 5: Nonlinear Trajectories

[@majidghasemy7482]

Thanks so much.

[@yingzhang5597]

Oh my! Thank you so much!!! My dissertation runs into the trouble of fitting a close to linear model but actually, it shouldn't - I modeled children's self-regulation in ages 3, 5, 9. The freeloading model definitely fixed my struggle!!!

[@centerstat]

outstanding....I'm so glad this worked out for you. Good luck with your project -- patrick

[@xinrong123]

Omg thank you so much for this video!!! I've been trying to find a model that can best answer my hypotheses, and I wasn't able to understand how journal articles did it until I saw this.

[@centerstat]

Thank you so much for your kind comment. I'm so glad that you found the video to be of some use. Good luck with your work -- patrick

[@sakkariyaibrahim2650]

Great video

[@룰루랄라-e7r]

You are the best!

[@patinator1995]

Great video, thank you so much! I only have one question: Do you know a reference which allows for a deeper discussion of cubic slopes?

[@centerstat]

Thanks for the kind words. I'm not familiar with a single resource that explores the cubic growth model. A good applied example is presented here: Burchinal, M. R., Bailey Jr, D. B., & Snyder, P. (1994). Using growth curve analysis to evaluate child change in longitudinal investigations. Journal of Early Intervention, 18(4), 403-423. Hope that helps -- patrick

[@장동일-b6s]

Thank you for the lecture!

[@johngalt5258]

Thanks much for this video. A question: can you estimate growth functions that are nonlinear in the parameters? Like a negative exponential or a Gompertz?

[@mcClinas1]

Thanks so much for your videos, Dr. Curran! I was hoping you could clarify a few issues raised in this video. When testing a quadratic growth curve, are you testing whether the average trajectory follows a quadratic shape? Does a quadratic growth curve model impose a quadratic shape on all of the person-specific trajectories? What if a person-specific trajectory doesn't follow a quadratic shape? Similarly, if the loadings of the slope factor were freely estimated, is a shape created that reflects the average trajectory? Or are unique shapes created that perfectly reflect the person-specific trajectories (i.e., no deviations from the trajectories)? Thanks so much! -Andrew

[@mcClinas1]

Thank you for your detailed response, Dr. Curran. I understand these issues much better now. You are providing a great service for LCM neophytes like me. THANK YOU!!

[@annan.9000]

@@mcClinas1 Hi. I don't see Dr. Curran's response to your question and I'd love to see it. Would you post it for us to view too? Thank you!

[@nadiramahomed1751]

Hi can you provide some articles that I can reference with regards to non linear models particularly comparing MLM and SEM? Also if I wanted to determine the impact of a set of variables on a "known" curve eg the grief curve would the free loading model be better suited for this? In otherwise I want to determine how resilience impacts the grief curve trajectory and theorise that multiple trajectories may be possible (high, med, low levels of resilience may have different trajectories)

[@centerstat]

Hi Nadira -- there are a variety of text books available that explore these issues in detail: Bollen & Curran (2006), Grimm, Ram & Estabrook (2016), Newsom (2015), and Hoffman (2015). As for the freed loading model, I believe that would be a question of model comparison; that is, which nonlinear formulation optimally reproduces the characteristics of the observed data. Hope that helps -- patrick

[@nadiramahomed1751]

@@centerstat Thanks, I actually just found the Grimm, Ram, Estabrook book today. I will check out the others as well. For model comparison, does this mean I could/should apply different models and compare model fit?

[@centerstat]

@@nadiramahomed1751 that's right -- if models are nested, you can use a likelihood ratio test; if not, you can use information-based criteria like the BIC and AIC.

[@fishycoffe]

Thank you so much for your videos! They finally helped me to understand latent growth curve models. I'm also reading your book ('latent curve models'), which is the best I've found so far. One thing I struggle to understand is this: in a nonlinear curve model with estimated factor loadings the variance of the slope only pertains to the variance in change from time 0 to time 1 (going with the standard coding), right? So if this variance doesn't differ significantly from 0 I can't say individuals don't differ significantly in their trajectory over the whole period I'm looking at, but only that they don't differ in the rate of change from time 0 to time 1 - is this correct?

[@fishycoffe]

Thanks for your quick respond. I've given it some more thought and I think I got it now. With your explanations in the book I actually didn't have great problems with the interpretation of the factor loadings for the clinical data I am analysing. Compared to the interpretation of parameters in higher polynomial trajectories, this interpretation in the free loading and piecewise trajectory approach seems straight forward... Just another kind word concerning your book: I was really glad to have found literature that thoroughly guides through the mathematics of latent growth curve models. Especially the appendices on identification probably will prove very useful for my thesis. Greetings from the department of methodology, Jena (Germany)

[@willysunshine]

I have depression measured at 3 time points. taking the last approach, the estimate of the time point in the middle is 2.6 (so that makes 0 at T1, 2.6 at T2, 1 at T3). Could we interpret that as a bell-shaped change?

[@centerstat]

Hi -- Unfortunately, no. To over-identify a nonlinear trajectory you must have at least four time points. if you have three and freely estimate one factor loading then you have a just-identified model and are perfectly reproducing the observed data. So I'm afraid you are limited to linear trajectories with three repeated measures -- patrick

[@gertlang4316]

is this also the case for a 2nd order linear growth curve model where you have a factor model (lets say with with 3 indicators) for each measurement point?