curvilinear/ non-linear growth curve model with random slope

[Yuhan HU]

i have the dependent variable observed 4 years, 2011, 2013, 2015, 2018. i would like to observe the change trend during this time period. i first used "graph twoway" and found there is a non-linear growth curve maybe. and then i used "mixed" command to test whether Linear Growth curve model with random slope or curviLinear Growth curve model with random slope is better or not. i begin with unconditional model:

// unconditional model Linear Growth curve model with random slope
mixed depvar i.year|| communityID: || ID2:, covariance(unstructured) nolog
est store linearrandomintercept
// unconditional model curviLinear Growth curve model with random slope
mixed depvar i.year i.year#i.year || communityID:i.year || ID2: i.year, covariance(unstructured) nolog
est store curvilinearrandomintercept

the first model can run successfully, but when i ran the second model, i receive the warning message: "convergence not achieved"

i am new with the growth curve model, could you please tell me whether my code is right and how to fix it to achieve convergence? thanks a lot!!

[Maarten Buis]

i.year adds indicator (dummy) variables for year, so it is as non-linear is is possible. If you want year to be linear you just add year or c.year if you want to be explicit. If you add year linearly, you could add it as a quadratic with c.year##c.year. i.year##i.year is just meaningless. Since you only have 4 years would only compare linear with indicator variables and leave the quadratic out (you only save one degree of freedom)

[Yuhan HU]

Thanks for your reply! If i cannot estimate using non-linear growth curve model, whether using linear growth curve model is not suitable also. Because according to the scatter graph, there may exist a u-shaped trend. Are there other solutions?

[Maarten Buis]

You can, and you already did, estimate a non-linear growth curve model by using i.year instead of c.year. The only mistake you made was thinking that it was a linear growth curve model, while in reality it is the most non-linear model possible. This is also why you could not add the interaction term between i.year and itself: you cannot be more non-linear than the most non-linear relationship possible.

You can use c.year##c.year, but i would not do so in your case. The point of adding a quadratic is to find a sweet spot between allowing enough non-linearity and not using too many degrees of freedom. The quadratic is more flexible than a linear, but is still quite limiting. If you many years than this may be an ok trade-off, but with only 4 years you are better of just using i.year.

[Yuhan HU]

got it! thank you so much!