Hi All

I am conducting an MLM and am unsure if I have specified my analysis correctly and whether I am thinking correctly about my model specification, output and postestimation commands. I am hoping you all can help me to think clearly about this. I am particularly unsure about what to with my sampling weights and likelihood-ratio tests to compare model fit.

Specifically, I have 3-Wave panel data on a nationally representative survey. At Wave 1, I have 3 IVs (IV1, IV2, IV3) and 2 covariates (CV1, CV2). My dependent variable (DV) was assessed 3 times-- at Wave 1 (DVW1), Wave 2 (DVW2), and Wave 3 (DVW3).

To test my hypotheses, I want to estimate the relationship between the IVs (while controlling for the CVs) and change in the DVs across the 3-Waves. For this, I want to measure the repeated observations on the DV as multilevel data.

First, I reshaped my data into long form:


Code:
gen ID=_n
reshape long DVW, i(ID) j(group)
Next, my ML Model 1:

Code:
 mixed DVW c.CV1 i.CV2 i.group c.IV1 c.IV2 c.IV  || ID:  c.IV1 c.IV2 c.IV,
Alternatively, my ML Model 2, which is the same as Model 1 but includes an interaction term for my "Wave" variable (i.e., group):
Code:
 mixed DVW c.CV1 i.CV2 i.group c.IV1##i.group c.IV2##i.group c.IV##i.group || ID:  c.IV1 c.IV2 c.IV,
Questions:

1) Is Model 1 specified correctly? Do I need the fixed effect term for group?

2) Is Model 2 correctly if my intention is to test for non-linearity of my IVs? If the interaction terms are non-significant, should I drop the interactions from the final model?


3) I want to compare models, whether that is models with or without an interaction term as a fixed effect for my "Wave" variable or comparing models with or without a Random Intercept or Random Slopes. For that, lrtest is recommended. Is there a way to do this with sample weights?

4) Regarding sample weights, I have sample weights for my Level 1 variables but do not have it for my Level 2 variables. Here is my code for the sample weights.

ML Model 1:
Code:
 mixed DVW c.CV1 i.CV2 i.group c.IV1 c.IV2 c.IV [pw=weight3]  || ID:  c.IV1 c.IV2 c.IV, pwscale(size)
ML Model 2:
Code:
 mixed DVW c.CV1 i.CV2 i.group c.IV1##i.group c.IV2##i.group c.IV##i.group [pw=weight3] || ID:  c.IV1 c.IV2 c.IV,    pwscale(size)
I applied sample weights at Level 1, but am not sure what's appropriate for Level 2 given my repeated measures design. Should I not specify Level 2 weights and just add a rescale command (e.g., pwscale(size))? Is pwscale(size) needed here?

5) When using sample weights, the LR test is not possible. Would it be appropriate to conduct these tests without sample weights to determine the most parsimonious model. And then apply the sample weights to this model to get the most valid estimates? Or, is there an alternative approach that people recommend? I know the Wald test is possible but it doesn't allow me to compare different models.

Any help is appreciated. I am using STATA 17. Thanks!!