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| Sanjoy posted on Tuesday, May 10, 2005 - 6:49 pm
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Dear Professor/s … from earlier MPlus discussions I realize that MLR in effect stands for ML(Full Information) with Huber-White covariance adjustment, which gives us robustness in presence of Non-normality and non-independence of observation … also on page 366 MPlus User’s Guide, u are suggesting MLR as an alternative for WLSMV … I have couple of quick questions in this regard
Q1. My dependent (indicator) variables are categorical, hence non-normal … but ARE THEY SAME in the sense non-normality is being handled in “Sandwich” estimator a.k.a. Huber-White
Q2. Can we use MLR in SEM where we have both measurement model (on multiple categorical indicator) and structural equation system inclusive of covariates (X’s).
Q3. If yes, then can u please suggest me some reference which is kind of counterpart of your (83,84,95,97) articles
Q4. Again (iff we have an yes to Q2.), …now FIML makes difference from Limited information ML (LIML) only when we are estimation some system of equations, I mean at least more than one-equation system (say e.g. ours is a three equation system with endogeneity) … so what numerical method is being used in MPlus when it runs FIML not LIML in order to solve high-order integral
Q5. Now if my understanding about your WLSMV is correct … then it starts with 2 stage least square approach (which is LIML) and later adjusts the covariance matrices using appropriate weight matrix (ur 97 paper which upgraded ur earlier WLS estimator to a more robust WLSMV) … and doing so, we simply circumvent the computational burden of FIML (which sometimes become infeasible) and yet at the same time get a mean –covariance adjusted roust coefficients … then what is the real need for MLR, are we still missing anything substantial in weighted approach
Below is my model
R by R1-R3;
B by B1-B3;
Y on R B X1;
R on B X2;
B on R X3;
R1-R3 and B1-B3 are 5-point categorical, Y is in 1/0 …X’s are the covariate and they do share some common elements
Thanks and regards |
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| bmuthen posted on Wednesday, May 11, 2005 - 8:23 am
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Q1. No, declaring your outcomes as categorical leads to non-linear models. The non-normality adjustments by Huber-White refers to treating the outcomes as continuous.
Q2. Yes.
Q3. See Hu & Bentler in a fairly recent Soc Meth article.
Q4. If the ML estimation requires numerical integration, Mplus offers 3 methods with variations such as adaptive quadrature or not, and Cholesky decomposition (see User's Guide).
Q5. WLSMV is not as efficient as ML, although the loss seems small. ML handles MAR whereas WLSMV cannot given its pairwise variable orientation. |
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| Sanjoy posted on Wednesday, May 11, 2005 - 2:33 pm
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Thank you Prof ...I couldn't find any "Hu & Bentler" article on SEM with Categorical (ordinal) indicator outcome variable ... as per your suggestion, I have looked for it, made a search through “Google”, except their 1999 article on Model Fit index (SEM: AMJ, Vol6 (1), 1-55), which I have already requested from Inter-Library loan, I couldn't find any
And in "Sociological methodology" I could not find any article written by them in particular, instead I found three articles by Prof. Bentler coauthored with some other folks
1.“Assessing the Effect of Model Misspecifications on Parameter Estimates in Structural Equation Models” Ke-Hai Yuan, Linda L. Marshall and Peter M. Bentler, Sociological Methodology, Volume 33, Issue 1, Page 241-265, January 2003
2. “Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data” Ke-Hai Yuan; Peter M. Bentler, Sociological Methodology, Vol. 30 (2000), pp. 165-200
3. “Structural Equation Modeling with Robust Covariances” Ke-Hai Yuan; Peter M. Bentler, Sociological Methodology , Vol. 28 (1998), pp. 363-396
and in “Sociological methods & research.” I couldn’t find any article even written by Dr. Bentler (assuming our Library online Journal search engine works ok)
Could you please mention the name of the article?
Using your WLSMV, I got the satisfactory result, however I want to use a ML(Full Information) if at all there is some established statistical theory (like the yours one for WLSMV) which can handle SEM with categorical(ordinal) indicator outcomes along with covariates and I hope, in that case MPlus is able to handle that theory … since all I have is MPlus and one month of time in my hand
Thanks and regards |
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| bmuthen posted on Wednesday, May 11, 2005 - 4:31 pm
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I should have said Yuan & Bentler (2000). Please also see references in Mplus Web Note #2. There is nothing written on ordinal outcomes, only non-normal continuous outcomes.
ML can be quite time consuming if you need many dimensions of integration. |
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| Sanjoy posted on Wednesday, May 11, 2005 - 8:05 pm
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yes professor, I'm going through their 2000 article
... practically speaking apart from your and Prof. Arminger(JASA,92 and his chapter in 95 Handbook) I haven't seen any statistical articles comprehensively dealing with ordinal indicator variables in SEM framework, if I'm not wrong "GLLAMM" can't do that either, I mean not in scenario where latent factors being regressed on other latent factors along with covariates ...
following ur advice I started reading Little's book on missing data(2002 ed.), well if I got them correctly then their chapters on categorical data is primarily concerned about categorical (nominal) rather than categorical(ordinal)one ...I haven't finished their book yet, however this is my first impression
thanks and regards |
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| Bpnnie posted on Friday, December 16, 2005 - 12:57 pm
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Hi,
In my model, the mediator is categorical while the outcome is continuous. I learned that WLSMV estimator would use probit regression results and ML would report logistic regression results. Which one is better? The default one or logistic results? Would appreciate it !
-Bonnie |
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| Maximum likelihood is a more efficient estimator than weighted least squares. If you can use it to estimate your model, then I would. |
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Hello,
I have a cross-lagged panel design and I am using Mplus to test the following model:
VARIABLE:NAMES ARE clus g u2-u5 x1-x5;
CATEGORICAL IS u3-u5;
CLUSTER IS clus;
USEVARIABLES u2-u5 x2-x5;
ANALYSIS: TYPE = COMPLEX;
PARAMETERIZATION = THETA;
ITERATIONS = 2000;
MODEL: x5 ON x4 x3 x2 u5;
x4 ON x3 x2 u4;
x3 ON x2 u3;
x2 ON u2;
u5 ON u4 x4;
u4 ON u3 x3;
u3 ON u2 x2;
OUTPUT: modindices standardized;
SAVEDATA: DIFFTEST = deriv.dat;
Mplus automatically chooses the WLSMV estimator.
I recently received a comment of a Reviewer to support the use of this estimator. Can you direct me to a reference or an article where the appropiateness of the use of this estimator is explained (in my case/ in this model)? He/she refers to Firth (1992) and McCullagh (1992) who question the use of a sandwich estimator in adjusting covariance matrices.
The same reviewer also asks me to give a rationale for the reporting of the fit indices CFI, TLI and RMSEA. I know that these are (some of) the standard fit indices that Mplus produces but is there a rationale behind the choice of these fit indices above others and if so, can you direct me to a reference where this is explained?
Thank you very much! |
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The following paper which is available on Bengt Muthen's UCLA website studies the WLSMV estimator:
Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Accepted for publication in Psychometrika.
The sandwich estimator is a commonly accepted approach which is widely used.
See Hu & Bentler several years ago in Psycho Methods regarding a variety of fit statistics. See the Yu dissertation on this website for a study of fit statistic behavior for WLSMV. |
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| I have SEM output with ordinal indicators thus WLSMV estimates. I need to learn how to interpret and report the estimates and how missing data is handled. Will you please point me to appropriate references. Thank you. |
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With WLSMV, probit regressions are estimated. One good reference is one of the Agresti books on categorical data analysis.
With WLSMV and no covariates, pairwise present is used. This means that each correlation is estimated using all available data. The Little and Rubin book may cover this topic. |
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| Thank you, Linda. There are covariates in my model. What does this mean with regard to missing. |
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Dear professors,
In a paper we use the WLSMV estimator because we have a continuous mediator and categorical dependent. I have 2 questions concerning the estimator.
1. I have difficulty finding out whether WLSMV automatically executes the Huber-White correction or whether I should do this manually by providing a weight in the syntax. Could you help me on this?
2. One of the reviewers wants some more information on the estimator and I am looking for a good reference on this. I tried to find the reference mentioned above by Muthen et al. in Psychometrika, but I can't find in anywhere. Do you have (another) suggestion for a good reference describing the ins and outs of WLSMV?
Many thanks,
Serge Rijsdijk |
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You can also use maximum likelihood estimation in this case.
1. The standard errors are like Huber-White. MLR provides Huber-White standard errors. With WLSMV you do not need to provide a weight.
2. The Muthen et al paper is on the website under Papers. See also
Muthén, B. & Satorra, A. (1995). Technical aspects of Muthén's LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60, 489-503. |
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