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 bmuthen posted on Friday, May 17, 2002 - 3:15 pm
Every individual-level variable can in principle be decomposed into variance and covariance components for two orthogonal parts: the within- and the between-parts. Mplus automatically generates both parts. This is different from conventional multilevel programs, where the user has to create a variable containing the cluster-specific mean of an individual-level variable for use on the between level. This mean is the between part of what Mplus automatically generates. So, with Mplus the user should not create cluster-specific mean variables, unless he/she wants to use the individual-level variable in cluster-mean form only in the between part of the model.

Because of this, individual-level variables have a between covariance matrix part in Mplus when using the MUML approach. If you don't want the between parts of individual-level variables to be predictors on the between level, one fixes the between regression coefficients at zero. But one still needs to capture the between-level covariances among those predictors so the program includes that part automatically.

The new FIML approach makes things a little easier in this regard. The individual-level variables that you do not want to use as predictors on the between level can be specified on the Within = list and they will then be excluded from the between part of the model automatically. So with FIML, one doesn't have to fix those between-level regression coefficients to zero.
 Feiming Li posted on Tuesday, April 26, 2005 - 7:29 am
Does the new FIML approach refer to MLM and MLMV?
What's the difference between MLM and MLMV?
Where I can find a paper or some fomula about them? Thanks a lot!
 Linda K. Muthen posted on Tuesday, April 26, 2005 - 11:06 am
The new FIML approach refers to ML, MLR, and MLF. See the technical appendices on our website. See Chapter 15 under Estimator for a brief description of the estimators and also for a table that shows which estimators are available for various analyses.
 Feiming Li posted on Wednesday, April 27, 2005 - 1:50 pm
I checked the techincal appendices and the table you mentioned, I want to make sure my understanding about MLM, MLMV and MUML.
1. these three are all quasi-likelihood estimator, so they belong to LIML, right?
2. these three all can be used to estimate the multilevel model with unbalanced group sizes. But the difference is:
MLM is ML parameter estimates with robust standard errors and a mean-adjusted chi-square test statistic;
MLMV is ML parameter estimates with robust standard errors and a mean- and variance-ajusted chi-square test statistic;
And what's the difference between MUML and these above two? Is it also with robust standard errors and chi-square?
When we have the multilevel data with unbiased group size, which one is better to use?
I'm so confused by these three method, could you correct my understanding and clarify the difference between them.
Thank you so much!!!!
 Linda K. Muthen posted on Wednesday, April 27, 2005 - 5:56 pm
With balanced data MUML is full-information maximum likelihood. With unbalanced data, it is limited information. It is not robust. MLM and MLMV are not limited information.

You must be using Version 2 because in Version 3 the estimator choices are ML, MLR, and MLF. I would recommend MLR.
 Michael J. Zyphur posted on Saturday, July 16, 2005 - 5:16 pm
Hi Bengt,
Using FIML, I am getting fit statistics for a model with 6 indicator variables, for which a single factor is specifies at both within and between levels. I was under the impression that only MUML would return fit statistics because it's the only estimator which allows for a logical saturated model.

I am guessing, now, that FIML will give fit statistics in the cases that a logical saturated can be computed. Can you please tell me if I am right and, if so, under what circumstances logical saturated models exist (e.g., without random coefficients, etc.). For example, if there are variables included at between or within levels that are not specified at the other level, will I still get fit statistics, etc.

Is there any publication I can read about this issue?

Thanks!
 bmuthen posted on Monday, July 18, 2005 - 5:10 pm
Mplus does not give fit indices for models with random slopes, but does give them if the model has only random intercepts. Random slope models have variances for dependent variables that vary with the values of the covariates that have the random slope, so the usual SEM test against a single covariance matrix is less well motivated. This hasn't been written about I think, nor do I know of anybody doing research on overall fit indices for random slope latent variable models - could be useful (dissertation anyone?).
 Michael J. Zyphur posted on Sunday, July 24, 2005 - 6:53 pm
Hi Bengt,
If I understand FIML correctly, a different covariance structure is computed for each set of groups with a similar size, with "d" many sets of groups. If this is true, then one should be unable to recover a single covariance matrix at the between-group level when one models groups with "d" many different sizes.(?)

I have such a model (without random coefficients) and I am getting a single covariance matrix at the between-group level when I use the SAMPSTAT option. Can you please tell me why?

Also, when getting fit statistics for this model, are these fit statistics based on the single covariance matrix provided by Mplus, or are the fit statistics based on comparisons of a saturated model for each set of groups with a similar size? I.e., are the FIML fit statistics for the between model representing a kind of multi-group model with "d" many groups?

Thanks for your time,

Michael Zyphur
 bmuthen posted on Monday, July 25, 2005 - 5:31 pm
I think you are referring to the FIML approach of using "d"-specific sample covariance matrices S_Bd in the old multiple-group approach for random intercepts (not random slopes) models (this was described in my tech report Muthén, B. (1990). Mean and covariance structure analysis of hierarchical data. Paper presented at the Psychometric Society meeting in Princeton, NJ, June 1990. UCLA Statistics Series 62. (#32)). But one needs to make a distinction between sample and population - note that even though there are several S_Bd, there is still only one Sigma_B matrix. Also, note that the more general FIML approach does not compute such "d"-specific covariance matrices when doing modeling, but works with raw data.

SAMPSTAT computes an ML estimate of the unrestricted (H1) within and between covariance matrix, so one estimated Sigma_B.

The fit statistics for the model (H0) are based on a comparison between the H0-estimated Sigma_B and the H1-estimated Sigma_B (and the same for within of course).
 Michael J. Zyphur posted on Saturday, July 30, 2005 - 3:16 pm
Interesting. So, when using FIML with many different group sizes (without random coefficients), the parameter estimates should be more accurate than under MUML because the individual-level data are used. However, in such a case, if the model fit statistics are based on a single Sigma_B, then shouldn't these fit statistics be as problematic as when using MUML?

In other words, fit statistics will always be based on a single Sigma_B matrix, so these fit statistics will suffer when, for example, ICCs are low, the between-group sample size is small, and there are groups of widely variant sizes.
 bmuthen posted on Sunday, July 31, 2005 - 10:46 am
First a quick and to the point answer which is that model fitting that considers a single Sigma_B is appropriate even if we use cluster-size specific S_Bd sample covariance matrices.

It is good to disentangle this. (1) Your 2nd sentence talks about the virtue of using more information than the 2 sample covariance matrices S_B and S_PW used by MUML. (2) Your 3rd sentence talks about model testing focusing on estimating the population matrix Sigma_B. So in (1) the issues are sample information and estimation - how to use sample information for parameter estimation, while in (2) the issues are model testing and population structures - how to test the model for Sigma_B. (1) is not directly related to (2).

Another way of answering is to note that, yes MUML uses limited information and is only equal to ML when cluster sizes are the same - but does give good estimates and tests of fit also with unequal cluster sizes. FIML can be seen as using several S_Bd sample matrices and S_PW (although this is a correct view only if we don't have random slopes), but this doesn't mean that we have a different Sigma_B model for each cluster size.

So, fit statistics based on a single Sigma_B don't "suffer" in the cases you mention last. It's a lot to keep track of in this area and rather little pedagogical material is available so far unfortunately. But there is always our annual course in November.
 Marco posted on Thursday, November 24, 2005 - 8:18 am
The Muthén-paper (1994) says that the sample between-cov matrix could be obtained by a standard statistic software. I guess that this is simple, but I still don´t know how to do that? There seems to be no special option (in SPSS), so is there a general procedure to "compute" the S-B?

Thanks for your help!
 Bmuthen posted on Friday, November 25, 2005 - 8:21 am
To compute S_B you first create cluster means. The cluster means are the values on a variable (z, say) that has as many observations as there are clusters (C say). Then you simply use any program to create a regular sample covariance matrix for the variable z with n = C.
 Judith C. Baer posted on Tuesday, May 09, 2006 - 5:31 pm
The discussion board talks about using FIML (full-info-max liklihood) but I can't make it run on Mplus. Also there are some other techniques (without weights) to dtermine percenatges of covariance structures explained by the missing patterns etc. Can you help?
 Linda K. Muthen posted on Tuesday, May 09, 2006 - 5:47 pm
Please send input, data, output, and license number to support@statmodel.com so I can see why you are having a problem.
 Judith C. Baer posted on Wednesday, May 10, 2006 - 8:42 am
Dear Linda

These are the details of what I am trying to accomplish:
-I have N (a subpopulation)= 5964
-I have weights= gweights, stratum, PSU

When I run a model in SEM (shown in the attached output), I find that I am missing a large portion of data (N=3464) and they are MAR. My concern is that listwise deletion will not be appropriate. These are the things I need to do (as per your notes on the web): run a FIML (“Saying Analysis type = missing implies using all available data. With FIML this is the standard "MAR" approach to missingness” from your notes)

These are the commands I have been trying to use :
- subpop option
- Type= Missing
- Type=complex
- Estimator=FIML (or equivalent)
- The dependent variable(HIVT) is categorical (0/1).
- independent vars are: slhc ,doc5, urb ,zedu ,zinc, mcare

However I cannot run TYPE= Complex, Missing both at the same time. I also cannot use the subpop option with Type=missing. Is there anyway to accomplish all this at the same time?
Thanks for your reply-
Judy BaerMplus VERSION 4.0
MUTHEN & MUTHEN
05/03/2006 2:10 PM

INPUT INSTRUCTIONS

Title: CFA on AOC: 1 groups, !SUBPOP=ANYSX
montecarlo
Data:
File is C:\Ranjana\Thesis\Noidu2.dat ;
Variable:
Names are
race gend stratum swght urb chnA chnS hivt prcv regc doc ons2 age2
schl2 slhc doc4 doc5 age idu peer graf dmgp lie shop run car st50
rob weap slldr st49 rowd fight gang educ inc mcare prcvR curf owfrn
owcl tvA tvP bed owdt eatp zedu zinc msex mrskp msup sxdm2 anysx sxdm
casl alcsx drgsx anal cndm psu aid;


USEVAR= slhc zedu urb zinc mcare doc5 ;!stratum swght psu

CATEGORICAL ARE SLHC urb;

!SUBPOP= anysx EQ 2;



Missing are all (-9999) ;

!these are the weights:
!WEIGHT=swght;
!STRAT= stratum;
!CLUSTER=psu ;
Analysis:
!Type = COMPLEX MISSING;
TYPE=MISSING;
ESTIMATOR=MLR; !WLSM
!INTEGRATION=MONTECARLO;
ITERATIONS=10000;
MODEL:
f1 BY slhc doc5 urb;

f1 ON zedu zinc mcare;



OUTPUT: MODINDICES(0) TECH3 ;



*** WARNING in Output command
MODINDICES option is not available for ALGORITHM=INTEGRATION.
Request for MODINDICES is ignored.
*** WARNING
Data set contains cases with missing on x-variables.
These cases were not included in the analysis.
Number of cases with missing on x-variables: 2418
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



CFA on AOC: 1 groups,
montecarlo

SUMMARY OF ANALYSIS

Number of groups 1
Number of observations 11079

Number of dependent variables 3
Number of independent variables 3
Number of continuous latent variables 1

Observed dependent variables

Continuous
DOC5

Binary and ordered categorical (ordinal)
SLHC URB

Observed independent variables
ZEDU ZINC MCARE

Continuous latent variables
F1


Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 10000
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 1
Adaptive quadrature ON
Link LOGIT
Cholesky OFF

Input data file(s)
C:\Ranjana\Thesis\Noidu2.dat
Input data format FREE


SUMMARY OF DATA

Number of patterns 4


COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value 0.100


PROPORTION OF DATA PRESENT


Covariance Coverage
SLHC URB DOC5 ZEDU ZINC
________ ________ ________ ________ ________
SLHC 0.984
URB 0.982 0.994
DOC5 0.984 0.994 1.000
ZEDU 0.984 0.994 1.000 1.000
ZINC 0.984 0.994 1.000 1.000 1.000
MCARE 0.984 0.994 1.000 1.000 1.000


Covariance Coverage
MCARE
________
MCARE 1.000


PROPORTION OF DATA PRESENT FOR U


Covariance Coverage
SLHC URB
________ ________
SLHC 0.984
URB 0.982 0.994


PROPORTION OF DATA PRESENT FOR Y


Covariance Coverage
DOC5 ZEDU ZINC MCARE
________ ________ ________ ________
DOC5 1.000
ZEDU 1.000 1.000
ZINC 1.000 1.000 1.000
MCARE 1.000 1.000 1.000 1.000


SUMMARY OF CATEGORICAL DATA PROPORTIONS

SLHC
Category 1 0.186
Category 2 0.814
URB
Category 1 0.443
Category 2 0.557


THE LOGLIKELIHOOD DECREASED IN THE LAST EM ITERATION. CHANGE YOUR MODEL,
STARTING VALUES AND/OR THE NUMBER OF INTEGRATION POINTS.



THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE
COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.






MODEL RESULTS

Estimates

F1 BY
SLHC 1.000
DOC5 1.503
URB 2.801

F1 ON
ZEDU -0.005
ZINC -0.001
MCARE -0.001

Intercepts
DOC5 2.383

Thresholds
SLHC$1 -1.572
URB$1 -0.330

Residual Variances
DOC5 0.000
F1 0.321


Beginning Time: 14:10:21
Ending Time: 14:12:23
Elapsed Time: 00:02:02



MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2006 Muthen & Muthen
 Bengt O. Muthen posted on Wednesday, May 10, 2006 - 1:31 pm
It is not possible for me to help you with this problem on Mplus Discussion. It is a support question. Please send your input, data, output, and license number to support@statmodel.com so I can see why you are having a problem.
 Ringo Ho posted on Sunday, December 03, 2006 - 4:22 am
Dear Prof. Muthen

I cannot find the details of the FIML (MLR estimator) for fitting multilevel models (with random slopes) in tech. appendices. Are there any papers you can suggest for me so to learn more about the FIML implemented in Mplus?

Thanks a lot for your great help!!
 Linda K. Muthen posted on Sunday, December 03, 2006 - 10:04 am
The paper describing this has not yet been written. A related paper is:

Muthén, B. & Asparouhov, T. (2006). Growth mixture analysis: Models with non-Gaussian random effects. Forthcoming in Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Advances in Longitudinal Data Analysis. Chapman & Hall/CRC Press.

You can download it from the website.
 yang posted on Friday, February 29, 2008 - 1:07 pm
Drs. Muthen,

I am running CFA/MIMIC on a multiple dimensional structure (with a mixture of categorical and continuous indicators and covariates). Some (about 15%) of the observations have missing values on the indicators, and I am using the WLSMV estimator (the default of Mplus for this situation). Since the percentage (15%) of observations with missing values is pretty high, I also run the analysis on the complete cases (by adding LISTWISE = ON in the DATA section), and did the sensitivity analysis.

My question is, what is the relation between the WLSMV and the FIML? I checked the outputs, and found that without LISTWISE = ON, WLSMV used all of the observations.

Thank you very much.

Yang
 Linda K. Muthen posted on Friday, February 29, 2008 - 3:08 pm
I think you are asking about missing data estimation with weighted least squares estimation versus maximum likelihood estimation. For censored and categorical outcomes using weighted least squares estimation, missingness is allowed to be a function of the observed covariates but not the observed outcomes. When there are no covariates in the model, this is analogous to pairwise present analysis.
 Utkun Ozdil posted on Tuesday, May 17, 2011 - 3:54 am
Hi,,

In a two-level model with unbalanced data, I preferred to use MUML. However, when I typed in the ANALYSIS command ESTIMATOR IS MUML the output warned me that MUML is not used with the two-level analysis. As far as I know MUML equals to ML with balanced data.

Does ML estimator handle the unbalanced case? (I have a large sample with sufficient number of groups (n=130)and continuous latent variables being under investigation)Which estimator is better for such an unbalanced case with continuous latents via Mplus 6.1?
Thanks...

Utkun
 Linda K. Muthen posted on Tuesday, May 17, 2011 - 6:57 am
MUML is allowed with TWOLEVEL and continuous outcomes. I would need to see your output to understand why you get this message.

Yes, ML can handle the unbalanced case. I would recommend using ML or one of the other maximum likelihood estimators. The default is MLR.
 Utkun Ozdil posted on Tuesday, May 17, 2011 - 10:55 am
Linda,, of interest I wanted to run a multilevel model by using total scores. And that, I got this message when I create a latent variable with the total scores on that variable.

I mean for instance,

f BY x1 x2 x3 (x1-x3 are 0/1 coded categorical variables)
g BY x4 x5 x6 (x4-x6 are 0/1 coded categorical variables)

I formed latent variables f' and g', such that by adding x1+x2+x3, as total score. Then I z-standardized the f' and g'. I wanted to model:

f' ON g'; with MUML estimator because my data are unbalanced. However I got the error message. And when I used ML to investigate this "total score" issue the data fit the model.

May be that z-standardization caused the problem? Because when I ran the multilevel model below with categorical indicators using a WLSM estimator I obtained a good fit...

f BY x1 x2 x3;
g BY x4 x5 x6;

f ON g;

Thanks...

Utkun
 Utkun Ozdil posted on Tuesday, May 17, 2011 - 11:10 am
Sorry Linda a follow-up question: if I am to go on the analysis with latents obtained by total scores,, may be I should have conducted covariance structure analysis following Bengt's 1994 article. Might the problem be that I did not use the covariance matrices?

Thanks again...

Utkun
 Linda K. Muthen posted on Tuesday, May 17, 2011 - 2:16 pm
MUML is allowed only with continuous factor indicators. See the ESTIMATOR option in the user's guide. There is a table that shows which estimators are allowed in different situations.
 Ananthi Al Ramiah posted on Thursday, June 23, 2011 - 7:56 am
Hello
I have run a 2 level regression model with a random slope. I find that when I run the model without a random slope, it converges and I get very reasonable estimates. However when I add the random slope (and I use algorithm=integration; integration=montecarlo), I get the following message:
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-POSITIVE DEFINITE FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES.
THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH. THE CONDITION NUMBER IS -0.116D-01.THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE
MCONVERGENCE OR LOGCRITERION OPTIONS.
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED.... PROBLEM INVOLVING PARAMETER 69.

I the provided the random slope model with start values from the model without the random slopes but get the following error.

THE ESTIMATED WITHIN COVARIANCE MATRIX COULD NOT BE INVERTED.COMPUTATION COULD NOT BE COMPLETED IN ITERATION 1. CHANGE YOUR MODEL AND/OR STARTING VALUES.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.

What do you think I could do to move forward? Thank you for your time.
 Linda K. Muthen posted on Thursday, June 23, 2011 - 8:51 am
If you look at the variance of the random slope on the between level, you will likely see that it is zero suggesting you fix it at zero or run the model as a fixed slope model.
 Ananthi Al Ramiah posted on Thursday, June 23, 2011 - 9:22 am
Hi Linda

Thanks very much for this suggestion. The model at the between level has:

s on efmsoa;

s has a residual variance of 1
efmsoa has a variance of .03

the residual variance of s being so large has to do I think with the fact that it didn't even start converging (s on efmsoa yields a beta of 0). However the fact that efmsoa (which is a between level variable) has such little variance across clusters suggests perhaps that the slope would not then vary according to this variable, and so it needs to be a fixed slope model. Is this right?

Thank you, Ananthi
 Linda K. Muthen posted on Thursday, June 23, 2011 - 11:34 am
Please send the output and your license number to support@statmodel.com.
 Dorien Van Looy posted on Wednesday, January 25, 2012 - 6:48 am
Hi,

I have to choose between MLM and MLMV, what are the supporting and non-supporting arguments of using each of the estimators?
Does anyone knows a useful reference?

Thanks a lot!
 Linda K. Muthen posted on Wednesday, January 25, 2012 - 11:32 am
Our informal simulation studies suggest MLM performs better.
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