I am modeling the reciprocal relationship between self-esteem (an observed continuous outcome) and English language use (a dichotomous outcome) using structural equations (and appropriate instrumental variables). Given that the categorical English language use outcome is conceptualized as a latent DV in the M-Plus framework, what is the interpretation of the endogenous variable's effect on self-esteem in the other equation? Do I still interpret its effect in the standard dummy-variable way (i.e. English language use increases self-esteem by an expected 'b' units)? Thanks -- Jason Schnittker
Just to reiterate what I think you have said. In the regression of SE ON EL when EL is endogenous, the regression coefficient is interpreted as the change in SE for a one unit change in the latent variable underlying EL.
I'm just not sure how to interpret the effect of EL: In the regression of SE on EL, how do I interpret the effect of EL given that EL is a dichotomous outcome in another equation? Is the interpretation still that for those who speak English (relative to the referent category) self-esteem is expected to change by 'b' units? Or, instead of a straight dummy-variable interpretation, is the interpretation with reference to some other unit-change in the underlying likelihood of EL (relative to the referent category)? Thanks again -- Jason Schnittker
Because EL is both a dependent variable in one equation and an independent variable is another equation, when it is the independent variable, it is a latent variable and thus is interpreted as a regular regression coefficient related to the latent variable not a probit regression coefficient. So there is no referent category.
Here's how you interpret it, for a .5 regression coefficient. For a one unit change in the latent variable underlying EL, y changes .5.
I thought that must be it. You can't identify both the y ON f1 slope and the covariance between the residuals of y and f1.
roger good posted on Wednesday, June 13, 2001 - 8:34 pm
I read somewhere that the exogenous variables are freely correlated. I have a recursive model and do not want my error terms to be correlated. Does Mplus correlate error terms by default? Thanks - roger good
Yes, exogenous variables are freely correlated. As far as residual covariances, it depends on the model. See page 159 of the Mplus User's Guide for the defaults for residual covariances. Residual covariances are not freed by default for models where they are not identifeid. In all cases, the residual covariances can be set to zero if this is not the default.
Anonymous posted on Tuesday, November 18, 2003 - 5:27 pm
I am doing a SEM with 3 latent variables (X, Y, and Z). I would like to know the directionality of the relationships. what does it mean when you get exactly the same fit statistics for all three directions / models given below: 1) X-->Y-->Z 2) Z-->Y-->X 3) XYZ How do we determine if a path is causal or correlational? Thanks in advance for your help
Statistics cannot differentiate between the models. You would need to have a substantive reason to choose one model over the other. They all fit the same. You may have a stronger argument for a causal order among the variables if they are observed at different time points, for example, if z was observed before y and y was observed before x, number 2 might be more reasonable.
I and a couple of my colleagues have been discussing the following simple SEMs for four variables, but have some problems interpreting both the models and the results:
model 1) A on D; B on C; A with B; model 2) A on B D; B on A C; model 3) A on D; B on A C;
In my mind, model 1 and model 2 are conceptualy the same model, while model 1 and model 3 are the same because we can always write P(A,B|C,D) = P(B|A,C,D)P(A|C,D).
The analyses shows that they actually are three different models, even though the fitted covariances are similar.
The chi squared tests for the three models are:
Model 1: Chisqr = 14.05 df = 2 p = 0.0009 Model 2: Chisqr = 8.669 df = 1 p = 0.0032 Model 3: Chisqr = 8.720 df = 2 p = 0.0125
We are also a little bit confused by the degrees of freedom. Model 3 is a simpler model than Model 2, where there is no effect of B on A. Despite this and despite the fact that the chisqr statistic is larger for Model 3 than for Model 2 (as expected) Model 3 appears to give a better fit to the data than Model 2 because the degrees of fredom for Model 2 is smaller than for Model 3.
It would be very much appreciated if you could give us a quick explanation of the differences between models and the fit of the simple but misfit of the more complex model (or if you could give us a reference to a paper where these things have been discussed).
I am running a latent class SEM in which i have the following:
SAT on D S DD SS DS; LP on SAT D S DD SS DS;
SAT on D S DD SS DS; LP on SAT D S DD SS DS;
It is a recursive model with one of the endo variables affecting the other.
I would also like to correlate the residual variances and free them across classes. However, after reading messages on this board, i gathered that "when there is y on x; then y with x is unidentified."
Am i correct?
Is there soem way i can estimate the model with both "y on x" and "y with x".
Your model refers to variances/residual variances of categorical variables which are only supported by THETA parameterization. To use THETA parameterization, add the following statement to the ANALYSIS command:
PARAMETERIZATION = THETA;
Anonymous posted on Thursday, March 31, 2005 - 5:47 pm
May I increase the number of iterations? Or that is not the solution. Where should I look and what should I change?
You can try increasing the number of iterations. Also verify that the variables are all on the same scale; check that there is no variances/residual variances that are much bigger than the others. If you have further problems, send your input, output and data to firstname.lastname@example.org.
Anonymous posted on Friday, April 08, 2005 - 10:46 am
Hi, I am running a SEM with censored regressors using WLSMV. From what I understood, for categorical data,the diagonal elements for the covariance matrix is set to unity for identification purpose in the first step of the regression because of their lack of metric properties. I would like to know how are these diagonal elements computed for censored variables?
Yes, they are the variances of the censored variables which are estimated by maximum likelhood assuming a censored normal distribution. See, for example, the Maddala reference on our website.
QianLi Xue posted on Friday, May 26, 2006 - 9:43 am
Hi, I'm trying to fit a Autoregressive and Cross-Lagged Model for Two Repeated Measures. Here is the code for the Model statement:
model: r3weak on r1weak (1) r1slow (2); r3slow on r1slow (5) r1weak (6); r5weak on r3weak (1) r3slow (2); r5slow on r3slow (5) r3weak (6); r7weak on r5weak (1) r5slow (2); r7slow on r5slow (5) r5weak (6); r1weak with r1slow; r3weak r5weak r7weak (3); r3slow r5slow r7slow (4); output: sampstat;
I have two questions: (1) In the output, the Results contain the estimate for "r7slow WITH r7weak", which I did not request. Why so? (2) How can I specify correlated errors between repeated measurements over time for each outcome?
1. This must be the default. It you don't want this paramter in your model, add r7slow WITH r7weak@0; to the MODEL command.
2. Use the WITH option.
Arpana posted on Tuesday, December 11, 2007 - 6:51 am
Dear Dr. Muthen,
I wish to examine the evidence for reciprocal causation (A <-> B) while controlling for correlated fixed effects. I have data on twins (A1, A2, B1, B2). I want to allow for correlated error covariance as well. I tried the following model, but I'm not sure this does the trick:
The model will not be identified unless you have covariates. I am not sure why you define factors but if you fix the factor variance to 1 you should free the first loading which is fixed as the default.
Kofan Lee posted on Thursday, December 09, 2010 - 11:47 am
I have a measurement model right now, the latent variable is measured by 9 indicators. On the other hand, 3 indcators are benefits of this latent variable, and thus those benefits reinforce the latent variable. I try to build a non-recursive model here, but I wonder how to write the code, like: latent by indicators latent on indicators