Modelling change in 2 repeated meausres
Message/Author
 Xu, Man posted on Sunday, April 24, 2011 - 8:41 am
Dear Dr. Muthen,

I have two repeated measures of math achievement. Is it possible to see if a person level variable gender, could predict the growth of Maths over the two time point?

As there are only two data points per person, the model would not converge unless I set the residual variance of the slope of time to be 0. Do you think the cross level interaction between gender and time would be interpretable this way?

Or what do you think is the best for me to do?

Thanks!

Xu Man
 Linda K. Muthen posted on Monday, April 25, 2011 - 8:23 am
With two time points, this is the best you can do.
 Xu, Man posted on Monday, April 25, 2011 - 2:19 pm
Thank you very much for your reply! Then how the interpretation of the corss product term between gender and time would differ, compared to when it is in a model where the effect of time is made random (provided there are three time points)?
 Bengt O. Muthen posted on Monday, April 25, 2011 - 6:03 pm
You can still regress s on gender, even if the residual variance of s is fixed at zero. It just implies that the s mean is different for the two genders.
 Xu, Man posted on Tuesday, April 26, 2011 - 1:15 am
Thank you very much for your reply. I think indeed I have seen many papers estimting a cross level interaction without even making the slope to be random. I guess it is acceptable. Here I am little confused (but much clearer now) because the growth modelling textbook always refers "at least three genuine repeated measure" as a rule of thumb for growth type of analysis.

Could I ask a follow up question please? If there are indeed variance in S, would constraining the variance of s to be zero bias the effect of gender on s (provided I have more time points to allow the variance of s to be estimated)?
 Bengt O. Muthen posted on Tuesday, April 26, 2011 - 6:10 pm
Growth modeling does indeed require more than 2 time points. Preferrably at least 4. What you are forced to do is making simplifying assumptions which may or may not be true, so you are not doing true growth modeling.

In your last question I think you mean residual variance of s, not the variance of s. I think you run the risk of biasing the effect.
 Xu, Man posted on Wednesday, April 27, 2011 - 12:31 am
Thank you very much for your kind replies and advice. Now I undrestand my data and this issue much better.
 Xu, Man posted on Wednesday, September 21, 2011 - 3:01 am
Dear Dr. Muthen,

Now that I have another go at this question, I thought maybe it's more sensible to make the slope random and the residual at time level to be constrained to be 0. This way the gender can be used to predict the variances in slope. What do you think?

Thanks!

Kate
 Bengt O. Muthen posted on Wednesday, September 21, 2011 - 6:19 am
I think neither approach is really satisfactory - you need more time points.
 Xu, Man posted on Wednesday, September 21, 2011 - 6:37 am
Thanks. But what do you think about the latent change score approach (if it is not just an alternative parameterisation of the same model)? For instance in experimental designs, the change from pre measure to post is predicted by treament group.
 Bengt O. Muthen posted on Wednesday, September 21, 2011 - 7:50 am
But then you are no longer focused on a growth model. I think framing it in a growth model context is misleading with only two time points in that it can give the impression that you have learned about development - when not all growth parameters can be identified, you haven't.
 Xu, Man posted on Wednesday, September 21, 2011 - 8:31 am
I see. do you mean it is better to present the model as in latent change scores such as this (note X is the person level predictor)?

Y1 by i11
i12 i13 (1-2);

Y2 by i21
i22 i23 (1-2);

[i11 i21](3);
[i12 i22](4);
[i13 i23](5);

i11 with i21;
i12 with i22;
i13 with i23;

Y2 ON Y1@1;
LC by Y2@1;
Y2@0;
LC*;
[LC*];

LC WITH Y1;

LC Y1 ON X;

I found the below growth context syntax gives the same results as the above syntax:

i s | Y1@0 Y2@0;
Y1@0;
Y2@0;
 Xu, Man posted on Wednesday, September 21, 2011 - 8:43 am
sorry, forgot one more line to the growth syntax. It should be:

i s | Y1@0 Y2@0;
Y1@0;
Y2@0;
i s ON X;

If my syntax are correct, then I thought latent change model and the "growth" model is the same thing. But I agree with you that the later is conceptually misleading. I was more used to the growth context because some papers I want to replicate adopted the growth idea with only two wave of time points.
 M. Howland posted on Thursday, March 09, 2017 - 1:22 pm
Hi,

I am looking at change from T1 to T2 on a measure with ceiling effects. Is it possible fit a latent change score model with censored data?