Complex data set with varying time lags
Message/Author
 Carm  posted on Monday, March 05, 2018 - 6:51 am
Dear Professor Muthén,

I have a complex dataset involving six measurements, organized in pairs. W1 and W2 are one day apart, and so on for W3/W4 and W5/W6.

However, W2-W3 are three weeks apart, same as W4-W5.

My aim is to analyse this data using a random intercept model in order to capture within and between subject differences.

So far, I got to analyse W1,W3,W5 and W2,W4,W6, given that the time between these waves is similar. However, by running two separate models like this, the smaller time differences in W1/W2, W3/W4, W5/W6 are missing.

I was told that it IS possible to create a model with all the six waves, but then input the different time lags between the waves. For instance between W1 and W2, W3 and W4, and W5 and W6 state one day difference, while for the other waves, state three weeks apart.

I'm a bit at odds with a flow of theoretical material when looking how to solve this issue, but at the same time, finding no precise references for which MPlus syntax I could use for this purpose.

I would be most grateful if you could give me any directions for what to write in the syntax, or point to any useful resources.

 Bengt O. Muthen posted on Monday, March 05, 2018 - 11:01 am
So you have essentially 3 different measurement periods. One question is if those periods share the same parameter values. For instance, if there is trend - do they follow the same trend? Is the level (intercept random effect) the same? If the answer is yes, you can simply give them different time scores that reflect the timings.
 Carm  posted on Thursday, March 15, 2018 - 4:18 am
Thank you for your answer prof. Muthén. Indeed, there is a trend in the data. One of the creators of RI-CLPM suggested to constrain the lagged parameters between W1/W2, W3/W4, and W5/W6 to be equal, and separately constrain the lagged parameters between W2/W3 and W4/W5 to be equal. This seems like an elegant solution.

In the MPlus manual: parameters are constrained to be equal by 'placing the same number or list of numbers in parentheses following the parameters that are to be held equal', as you know: y1 ON x1(1); y2 ON x2(2); y3 ON x3(1); y4 ON x4(2).

Supposing that CA1, CA2, CA3, CA4, CA5 and CA6 are the lagged within-person parameters for variable 1, and BA1, BA2, BA3, BA4, BA5 and BA6 are the lagged within-person parameters for variable 2, is this correct:
cA2 ON cA1(1);
cA3 ON cA2(2);
cA4 ON cA3(1);
cA5 ON cA4(2);
cA6 ON cA5(1);
cB2 ON cB1(1);
cB3 ON cB2(2);
cB4 ON cB3(1);
cB5 ON cB4(2);
cB6 ON cB5(1);

The lagged parameters with a one-day difference would then be equal(1), however different than the parameters from the waves which are more apart in time(2).
Further, I let the cross-lagged parameters (for instance cB5 on CA4) to be freely estimated. Is this code and solution correct? Thank you in advance!
 Bengt O. Muthen posted on Friday, March 16, 2018 - 6:33 am
I don't know why you have equalities across processes.
 Carm  posted on Friday, March 16, 2018 - 9:44 am
Dear Professor, the equalities are to signal that the timings between certain waves is equal(one day), as opposed to other time frames when the timing between the waves is longer (but still equal to one another, three weeks).

Further, could you please share how you would give parameters 'different time scores which reflect the timings?'
 Bengt O. Muthen posted on Friday, March 16, 2018 - 1:53 pm
Different processes - CA versus CB - can't be expected to have the same slopes even if they have the same time difference between measurements. I think you can drop all equality labels.

"Different time scores that reflect the timings" would be relevant if you have a growth model with a trend, not in a random intercept only model.

See also the paper by Hamaker et al 2015 in Psych Methods.
 Carm  posted on Tuesday, March 20, 2018 - 4:28 am
I understand. It was actually professor Hamaker who suggested the equality constraints. But, I just learned that it had to be done in another way. Thank you for your answer and for sending in the reference.