Estimated means in growth models
Message/Author
 Julia posted on Tuesday, January 17, 2017 - 7:05 pm
I have a latent basis growth model with six time points. The Tech4 output shows that means of intercept and slope were 5.432 and 2.830. The Residual output shows the estimated means of each time point are 5.376(T1), 5.927(T2), 6.034(T3), 7.071(T4), 7.772(T5) and 7.954(T6).
At the same time, I can calculate the scores of each time point by the regression model y= a+bx. Since intercept is 5.432 and slope 2.830. I assume the regression should be y=5.432+2.830x. The unstandardized coefficients for each time point are 0.197,0.238,0.646, 0.937 and 1. Using this regression model, I get the scores of each time point are the following.
T1: intercept = 5.432;
T2: 5.432+2.830*0.197=5.989;
T3: 5.432+2.830*0.238=6.10554;
T4: 5.432+2.830*0.646=7.26018;
T5: 5.432+2.830*0.937=8.0837;
T6: 5.432+2.830*1 =8.262;

Why are the scores of each time point different by using the two calculation methods? Which one should I report and why? Thanks.
 Bengt O. Muthen posted on Wednesday, January 18, 2017 - 11:16 am
 Julia posted on Wednesday, January 18, 2017 - 7:36 pm
Thanks. I figured it out yesterday. My latent basis growth model uses censored data because of ceiling effect. When I remove "censored are T1 T2 T3 T4 T5 T6(a)", the two results of estimated means are the same!

By the way, when I use the censored growth model, I should report estimated means calculated by myself according to the regression model or just use those in Residual output? I think I should just use Residual output.

 Bengt O. Muthen posted on Thursday, January 19, 2017 - 5:54 pm
Right.
 Julia posted on Monday, January 23, 2017 - 7:15 pm
Thank you very much for your fast reply. I have two more questions. Why I cannot use the regression model y=ax+b to calculate the estimated means in the censored growth models?(I know I can use it in a regular linear growth model) What formula should I use then?

like I mentioned, in the Residual output, the estimated mean for T1 is 5.376. The intercept is 5.432 in the censored growth model. Why the estimated mean of T1 is not the value of intercept? I am curious about the interpretation of the latent variable of intercept in the censored growth models.

Thank you very much in advance.
 Bengt O. Muthen posted on Tuesday, January 24, 2017 - 6:34 am
Our new book describes how to evaluate means for censored variables.