Understanding Society User Support

Dear User Support Team,
I hope you are well. I am planning to run a multi-level model to longitudinally analyse data from waves 1, 3, 6, and 9 of Understanding Society. Following the advice on Understanding Society MLM Analysis guidance page (https://www.understandingsociety.ac.uk/documentation/mainstage/user-guides/main-survey-user-guide/analysis-guidance-for-weights-when-fitting-multilevel-models/), I am going to use a two level model. An ICC indicated that about 50% of variation in the outcome (GHQ) is at the respondent level rather than at the response (aka wave) level. So, I am going to use the levels of wave and respondent, and I will also set standard errors to be robust to PSU clustering using the “mixed” command in Stata.
Please could you advise me on which weights to use for a two-level multilevel model where level 1 = wave and level 2 = respondent?

I have organised my data so that each respondent has up to three rows. Each row contains an outcome variable from one wave (i.e., outcomes were measured in waves 3, 6, or 9) and predictors that were measured two or three waves before the outcome (i.e., predictors were measured in waves 1, 3, and 6 respectively). I have attached an example of the data structure in case that is helpful.

I created a variable called “w_indscus_lw” using the indscus_lw weight for the outcome wave for each row.

Based on https://www.understandingsociety.ac.uk/documentation/mainstage/user-guides/main-survey-user-guide/analysis-guidance-for-weights-when-fitting-multilevel-models/, I think the correct stata syntax would be:
mixed outcome predictors [pw= 𝑤ᵢ|ⱼ] || pidp:, mle pweight(𝑤ⱼ) vce(cluster psu) pwscale (gk)

Please could you let me know which weighting variables would be appropriate to use as 𝑤ⱼ, and 𝑤ᵢⱼ or 𝑤ᵢ|ⱼ?

Could “w_indscus_lw” be used as 𝑤ᵢⱼ?
If so, could I use “c_indscus_lw” as 𝑤ⱼ ?
And then could 𝑤ᵢ|ⱼ be “c_indscus_lw”/ “w_indscus_lw”?

Or should I use an earlier variable as 𝑤ⱼ? Such as a_indinus_xw?

Many thanks,

Benedict Hignell