Nonlinear relationship - covariates a...
Message/Author
 Michael Lap posted on Wednesday, March 21, 2018 - 2:42 pm
In a linear regression, the relationship between the predictor and the outcome is quadratic (looks like a curve and a quadratic coefficient is strongly significant).

1) If I use this predictor as a covariate and the outcome variable as a variable to form class trajectories in LCGA, would the quadratic relationship between them be a problem? In other words, does LCGA require linearity b/w covariates and predicted class trajectories?

All other covariates are nominal (binary).

2) If non-linearity is a problem, we can split the continuous covariate into categories if needed.

Thank you!
 Bengt O. Muthen posted on Wednesday, March 21, 2018 - 3:04 pm
Is the covariate a time-varying covariate or not? Is the growth linear or quadratic?
 Michael Lap posted on Wednesday, March 21, 2018 - 3:54 pm
Bengt,

the covariate is actually time-varying but it is strongly correlated with the outcome at each time point (we have 4 timepoints). So they correlate at T1, T2, T3, and T4 at .7-.8

Therefore, we included just the T1 covariate as one of predictors of time trajectories.

The trajectories are more non-linear than linear but we struggle to model the quadratic pattern. So we have a linear trend T1-T3 and then a slight increase from T3 to T4.
 Bengt O. Muthen posted on Thursday, March 22, 2018 - 3:47 pm
So you can have a regular multinomial logistic regression model

C on T1;

and have a piece-wise linear for the growth part. The quadratic effect of T1 on the outcomes could then be reflected by say high T1 values making a C class with high second-piece slope more likely.
 Michael Lap posted on Thursday, March 22, 2018 - 4:07 pm
Thank you, Brent!

the quadratic part now works, I figured it out. The quadratic slope is significant in 2 out of 3 class trajectories.

So If I include the quadratic or piecewise part, then the quadratic relationship b/w the covariate measured at T1 only and the latent trajectories will be reflected in the "high T1 values making a C class with high second-piece slope more likely", right?
 Michael Lap posted on Thursday, March 22, 2018 - 4:13 pm
Bengt,

C on T1 (and other covariates) is reflected in the multinomial part of the output, right?
Just want to make sure I understand you correctly.
 Bengt O. Muthen posted on Thursday, March 22, 2018 - 4:26 pm
Right on both posts.
 Michael Lap posted on Thursday, March 22, 2018 - 4:36 pm
Thank you, Bengt!