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 Greg Thrasher posted on Thursday, August 02, 2018 - 1:46 pm
Hello,

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?

Your help is much appreciated.
 Bengt O. Muthen posted on Thursday, August 02, 2018 - 2:07 pm
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.
 Greg Thrasher posted on Thursday, August 02, 2018 - 2:24 pm
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?
 Bengt O. Muthen posted on Thursday, August 02, 2018 - 2:44 pm
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).
 Greg Thrasher posted on Thursday, August 02, 2018 - 2:53 pm
We're using

count = CIG_AM_2 (nb);

to account for the distribution of alcohol frequency , so the distribution is skewed. Would the binomial regression account for that asymmetry? I'll run the Bayes to check the CIs.

Thanks again!
 Bengt O. Muthen posted on Thursday, August 02, 2018 - 3:18 pm
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.
 Greg Thrasher posted on Monday, August 06, 2018 - 10:19 am
This makes sense, but I get an error that bootstrapping is unavailable in two level models.

We have daily alcohol frequency within individuals predicted by continuous survey measures. What would be the best way to test for the symmetry of CIs in this case?
 Bengt O. Muthen posted on Monday, August 06, 2018 - 3:32 pm
Hmm - you are up against current Mplus not having Bayes for counts or bootstrapping for twolevel. I don't have a good suggestion.
 Greg Thrasher posted on Thursday, August 09, 2018 - 2:52 pm
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?

count = CIG_AM_2 (nb);

cluster is ID;

BETWEEN = ;

WITHIN = wfc_AM_1 na_AM_1;

Missing are all (999);

USEOBSERVATIONS are CIG_AM_2 < 24;

Define: Center wfc_AM_1 na_AM_1 (Groupmean);

Analysis:

TYPE = twolevel random;
ESTIMATOR = MLF;
Algorithm = Integration;
Integration = MONTECARLO;

MODEL:

%WITHIN%
aw | na_AM_1 on wfc_AM_1;
bw | CIG_AM_2 on na_AM_1;
cw | CIG_AM_2 on wfc_AM_1;

%BETWEEN%
[aw] (a);
[bw] (b);
[cw] (cp);

aw with bw (covab);
aw with cw;
bw with cw;

MODEL CONSTRAINT:
new (ind);
ind = a*b + covab;

OUTPUT: Sampstat TECH1 Residual TECH8 CINTERVAL Stand(stdyx) MODINDICES;
 Bengt O. Muthen posted on Thursday, August 09, 2018 - 3:20 pm
Yes, you should group-mean center the 2 predictor variables as you have done. This is not done automatically by defining them as Within. Your setup looks correct.

Putting a variable on the Within list implies that we don't model any variation for this variable on the Between level.
 Greg Thrasher posted on Thursday, August 09, 2018 - 3:25 pm
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.
 Bengt O. Muthen posted on Thursday, August 09, 2018 - 5:38 pm
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.
 Greg Thrasher posted on Thursday, August 09, 2018 - 7:37 pm
So interpreting the a, b, and c paths is basically saying a*b is the within indirect effect, accounting for the between variance on y?

May be a silly question, but why does that that variance breakdown not apply to the x and m within variables. Daily data on attitude/affect variables should will have some between variance, right?

for example, wouldn't

x(b)_j = the between level intercept and yxw)_ij = the group mean centered x variable?

It makes sense to run the x and m as within and group mean centered...just curious.

All of this is extremely helpful. Thanks again.
 Bengt O. Muthen posted on Friday, August 10, 2018 - 2:24 pm
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).
 Greg Thrasher posted on Friday, August 10, 2018 - 6:12 pm
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);

%BETWEEN%
CIG_AM_2;

MODEL CONSTRAINT:
new (ind);
ind = a*b;
 Bengt O. Muthen posted on Saturday, August 11, 2018 - 3:35 pm
Q1: Yes.

Q2: Right.
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