I am testing for significant random slope variance on a within person main effect. I am predicting a count variable with a continuous predictor. I am using count = CIG_AM_2 (nb); for the count variable distribution.
When using bayes, MLF, and MLR estimators I get equal effect sizes but different p-values. How do I know which estimator to use?
I would go by the confidence intervals. The MLF and MLR CIs are symmetric (and the p-values are based on this assumption) while your application may need non-symmetric CIs. Non-symm CIs are obtained by ML with bootstrap and Bayes.
Thank you. I initially was using MLR (which is the default I believe), but was getting a saddle point error. Using the MLF resolved this issue. MLF also works for running my indirect effect model constraints.
If my confidence intervals are symmetric, MLF should be appropriate then?
The key is if the sampling distribution is symmetric - then a symmetric CI is suitable. Bayes is a good way to check that by looking at the posterior distribution of the estimate. You can also use ML with bootstrap to see if the resulting CI is symmetric (you can use ML with BS either way).
I see, you have a count DV. Bayes is not implemented for counts yet in Mplus. So check out bootstrapping.
It is not the DV distribution non-symmetry that is the key (although it plays a role), it is the distribution of an estimate when you take several independent samples. The count estimates are in a log(mean) scale so they are close to normally distributed, but if you consider exp(b) which is common in count modeling, the distribution of such estimates is no symmetric/normal.
Thanks for all the help, I believe I have resolved the estimator issue. Another quick question. In the below syntax I am testing a 1-1-1 mediation with within person day level x/m variables predicting a day level count DV. I've been reading through several posts/articles on centering and am I little unclear as to what defining a variable as within does. Do I need to group mean center my within person variables, or is this done by defining them as within? In other words, if I do not include the centering command am I still testing for day level indirect effects?
Thank you! I've been battling with this question. Should my DV be group mean centered as well since it is also collected as a day level variable within person? I don't believe I can center a count variable however.
It's a good question not often explained. Your DV is implicitly (latent variable) group-mean centered by the fact that it has a random intercept. Think of the decomposition into between-level and wihin-level parts of the observed DV y,
y_ij = y(b)_j + y(w)_ij.
For a random intercept model, y(b)_j is the between-level random intercept that varies across level-2 units. What is left, y(w)_ij, is then the group-mean centered y:
y(w)_ij = y_ij - y(b)_j.
In other words, y(b)_j plays the (latent) role of the (observed) cluster/group mean x-bar_j. It is y(w)_ij that is regressed on other variables on the Within level.
Q1: Not quite. The product a_j * b_j is the within indirect effect for cluster j. The average of that is not [aw]*[bw] because the expected value of a product is not the product of expected values.
Q2: That latent variance breakdown should indeed also be applied to x and m but this is hard algorithmically with ML - you can however use Bayes for it in the current Mplus Version 8.1. This is why the approximation of using the cluster sample mean of x and m is used.
A just accepted (somewhat technical) paper for the SEM journal which discusses this can be found under Recent Papers on our website:
Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and time-series models. Technical Report, Version 2. August 5, 2018. (Download scripts).
Great! That is a great way to think about why x/m are group mean centered. I'll make that paper some light evening reading.
Just to confirm, in the above syntax, the model constraint can be interpreted as an indirect effect with random slopes? If I were to run a fixed slope mediation, I would create model constraints based on
%WITHIN% na_AM_1 on wfc_AM_1 (a); CIG_AM_2 on na_AM_1 (b); CIG_AM_2 on wfc_AM_1 (c);