Numerical integration
Message/Author
 Andrew Percy posted on Monday, August 02, 2004 - 1:50 pm
Dr Muthen

I am trying to run a multi-level logistic regression with 8 within predictors (both categorical and continuous) and two between predictors (both categorical). I receive an error message indicating that I have 9 dimensions of integration. I have tried it with fewer predictors (two within, one between) using montecarlo integration. However, when I do this I receive no output. How can I take this forward?

Andrew Percy
 bmuthen posted on Monday, August 02, 2004 - 1:55 pm
It sounds like you are having 9 random coefficients in your model, which could mean that you have not only a random intercept but also a random slope for each of the 8 predictors. This is a very complex analysis. It is likely that most of your predictors do not need random slopes, i.e. do not have significant level 2 variances. I would suggest starting with the random intercept model and then add one random slope at a time to see which slopes have significant variances. If this doesn't help, please send your input, output, and data to support@statmodel.com
 Sally Czaja posted on Friday, January 21, 2005 - 9:02 am
Can you explain what integration points and dimensions of integration are? If a complex model doesn't converge, how does one decide/justify (1) whether to relax the convergence criteria or specify fewer integration points and (2) how much to do so? I would like to test the interaction of a dichotomous level-2 variable with a 4-category level-1 variable represented by 3 dummy variables but run times are very long. Is there another approach?
Thank you.
 BMuthen posted on Saturday, January 22, 2005 - 3:18 pm
Integration is a complex topic. It is described briefly in the Mplus User's Guide. If you are having convergence problems, you probably need more rather than less integration points or a model that fits your data better. You can use the INTEGRATION option to ask for more integration points. An interation between a level 2 and level 1 variables implies that the level 1 variable has a random slope explained by the level 2 variable.
 Anonymous posted on Monday, June 20, 2005 - 3:12 pm
If I'm doing a numerical integration problem in Mplus 3.12 with the TECH8 output option and with STARTS=10 1.

Shouldn't Mplus produce 10 sets of starting values (based on the start values I provide), and then pick the best overall set of start values for the final stage iterations ?

In my current run of Mplus, it appears that Mplus finds two random sets of start values that are superior to the start values I provide (the absolute value of the LLIKELIHOOD for one of the Mplus-perturbed sets of values is smaller than the one I specified).

Yet when the numerical integration module progresses to the final stage iterations, as best I can tell via the TECH8 output, Mplus reverts to the start values I provided.

Since numerical integration can be very computation intensive -- is there a way I can request that Mplus just use the best of the 10 perturbed start values ?

Thanks.
 Linda K. Muthen posted on Tuesday, June 21, 2005 - 1:57 am
If this is the case, then the other ones failed. You can try the OPTSEED option of the ANALYSIS command to request the best seed and then see if it does actually fail. If not, please send your output, data, and license number to support@statmodel.com.
 Anonymous posted on Tuesday, June 21, 2005 - 1:17 pm
Following up on your response -- should better start values give (potentially) better perturbed values; or are the random starts purely random ?
 Linda K. Muthen posted on Wednesday, June 22, 2005 - 12:07 am
The pertubations are based on starting values. The starting values can be the Mplus default values or user specified values. They are never random starting values. If you are not clear on what the start values should be, you should use the defalt starting values.
 shams42 posted on Thursday, October 27, 2005 - 11:23 pm
To follow up Bengt's post from Aug 2, 2004, how does one determine if the variance in a random slope is significant? Obviously the residual variances are printed on the output, along with their standard errors. This, however, only considers the unexplained variance. Is there a way to look at the entire variance for each slope along with its standard error?

My application involves a categorical level-1 dependent variable with two random slopes and a random intercept. I would like to examine additional random slopes, but the computational demands of this are too high.
 Linda K. Muthen posted on Friday, October 28, 2005 - 7:35 am
Any rnadom parameter has both a mean and a variance and both of these parameters have standard errors. If this does not answer your question, please send your output and license number to support@statmodel.com so I can see your model.
 David Bard posted on Thursday, April 13, 2006 - 4:25 pm
I'm trying to run a nonlinear economic 'risk-value' model using Mplus' Multilevel syntax. I'm trying to trick Mplus to do this using a variety of phantom variables, linear and nonlinear constraints, and the algorithm=integration estimator. I'm not sure what's happening exactly, but the program runs for approximately 35 iterations and then closes without explanation or error messages. The output window does not open automatically, but when manually opened contains only the syntax, INPUT READING TERMINATED NORMALLY, and the title of the project. Here is my syntax. Any thoughts?

TITLE: Study1_JDB
JDB Model for Predicting Certainty Equivalency Responses

DATA:

VARIABLE:
NAMES ARE SubId CE MeanOut Exp1 Exp2 Exp3 Exp4 Exp5;

USEV = SubId CE Meanout Exp1 Exp2 Exp4;
Within = Exp1 Exp2 Exp4;

Cluster IS SubId;

ANALYSIS:
TYPE = twolevel random;

Algorithm=Integration;

Model:
%Within%
Enw by meanout@0;
Epw by meanout@0;
Ew by meanout@0;
Enw on Exp1*1.5 (E1)
Exp2*1 (E2);
Epw on Exp4*1.5 (E4)
Exp1*1 (E5);
Ew on Enw*.8 (d)
Epw*.2 (e);
[Epw@0];
[Enw@0];
[Ew@0];
Enw@0;
Epw@0;
Ew@1;

s1 | CE on Ew ;

%Between%
[s1*.5] (s1);

Model Constraint:
New(Thn);
New(Thp);
New(Pha);
E1 = 100**Thn;
E2 = 50**Thn;
E4 = 50**Thp;
E5 = -100**Thp;
s1 = 2.71828**(-Pha);
d = 1 - e;

Output:
Tech1 Tech8;
 Linda K. Muthen posted on Thursday, April 13, 2006 - 5:29 pm
I think you should send your input, data, partial output, and license number to support@statmodel.com so we can see what is happening. It is not possible to tell without this information.
 mpduser1 posted on Monday, January 26, 2009 - 9:39 am
In running multilevel models in Mplus, provided that the dimensions of integration is reasonable -- is it always preferable to go with the default integration option vs. Monte Carlo?

The User's Guide seems to suggest this is the case; but I wanted to make clear. My ad hoc experimentation with Mplus seems to indicate that the default method gives smaller SEs (and is more stable) than MC.

(And, if numerical integration is preferable to MC, would you be able to provide a reference regarding why this is so -- is it because MC convergence is harder to diagnose, for example?).
 Linda K. Muthen posted on Tuesday, January 27, 2009 - 6:18 am
We recommend using the default INTEGRATION setting of STANDARD. We recommend using the setting of MONTECARLO only when it is requrired. Note that numerical integration is used in both cases. It is the type of numerical integration that changes. You want enough integration points for a precise estimate. With Monte Carlo integration, the loglikelihood may not be precise. Offhand I don't know of a reference for this.