Reciprocal Causation Interpretation PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Jason Schnittker posted on Thursday, April 26, 2001 - 8:46 pm
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
 Linda K. Muthen posted on Friday, April 27, 2001 - 7:13 am
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.
 Jason Schnittker posted on Sunday, April 29, 2001 - 1:40 pm
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
 Linda K. Muthen posted on Monday, April 30, 2001 - 7:08 am
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.
 Jason Schnittker posted on Monday, April 30, 2001 - 12:44 pm
Given that interpretation, is there any good way to assess the magnitude of the effect? I am comparing the structual equation results with results from an OLS equation. Thanks -- Jason
 Linda K. Muthen posted on Tuesday, May 01, 2001 - 7:32 am
That comparison is difficult because OLS works with a dichotomous EL treated as continuous. Sign and significance are probably the only things you can compare.
 Anonymous posted on Friday, May 25, 2001 - 9:26 am
Is it possible to specify that the error term for an x variable is correlated with the error of an outcome variable in Mplus ?
 bmuthen posted on Friday, May 25, 2001 - 5:51 pm
Yes it is.
 Anonymous posted on Thursday, May 31, 2001 - 9:38 am
Is this done using WITH or PWITH ?

I.e., if the outcome is y and x variables are x1, x2, x3... the specification in the MODEL statement would be:

y WITH x1;


y PWITH x1 x2 x3; ?
 Linda K. Muthen posted on Thursday, May 31, 2001 - 11:45 am
To use PWITH you must have the same number of variables before and after PWITH. These variables are paired. For example,

x1 x2 PWITH X3 x4;

results in

x1 WITH x3 and
x2 WITH x4;

If you want y with x1 and y with x2 and y with x3, you would say:

y WITH x1 x2 x3;

which is equivalent to:

y WITH x1;
y WITH x2;
y WITH x3;
 Anonymous posted on Friday, June 01, 2001 - 11:10 am
I am trying to correlate the error terms of a latent (causal) variable with a categorical outcome variable, y.

My latent causal variable is f1. Other causal variables in the model are x1, x2, x3. Indicators for the latent factor f1 are i1, i2, i3, etc.

y and i1...i5 are based on the same scale and thus y and f1 would seem to be prone to the same types of errors.

When I use the following statements in my command file, Mplus returns an error msg:

i1 i2 i3 i4 i5 y;

f1 by i1 i2 i3 i4 i5;

f1 on x1 x2 x3;

y on f1 x1 x2 x3;

y with f1;

Have I not specified the relationships properly ?
 Linda K. Muthen posted on Friday, June 01, 2001 - 2:56 pm
What is the error message?
 Anonymous posted on Friday, June 01, 2001 - 3:10 pm
"Model not identified".


y with f1@0;

is identified however, and converges normally. WLS df is same as when statement is rem'd out as when is included.

I get the same result for a number of different categorical y outcomes.
 Linda K. Muthen posted on Friday, June 01, 2001 - 4:18 pm
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
 Linda K. Muthen posted on Thursday, June 14, 2001 - 3:05 pm
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
 Linda K. Muthen posted on Tuesday, November 18, 2003 - 6:51 pm
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.
 Svend Kreiner posted on Thursday, October 07, 2004 - 7:14 am
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).

Thanks Svend
 Linda K. Muthen posted on Tuesday, October 12, 2004 - 4:58 pm
We would need to see the three outputs and the data to answer this question. The information you provide may not give a full picture. You can send them to
 Girish Mallapragada posted on Thursday, March 17, 2005 - 7:02 am
Hello Dr. Muthen,

I am running a latent class SEM in which i have the following:





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".

 Linda K. Muthen posted on Thursday, March 17, 2005 - 8:56 am
You can correlate the residual variances of SAT and LP. Those are the only residual variances in your model.
 Anonymous posted on Thursday, March 31, 2005 - 5:08 pm
I get the following error message when I run Mplus. What does it mean?

" The model is not supported by DELTA parameterization. Use THETA parameterization."

Thank you!
 Thuy Nguyen posted on Thursday, March 31, 2005 - 5:19 pm
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:

 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?:(

 Thuy Nguyen posted on Friday, April 01, 2005 - 9:45 am
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
 Anonymous posted on Friday, April 08, 2005 - 10:46 am
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?

Thanks much
 Linda K. Muthen posted on Saturday, April 09, 2005 - 3:46 am
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:

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);

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?

Thanks for your help!
 Linda K. Muthen posted on Friday, May 26, 2006 - 9:59 am
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:

A by A1@1 A2@1;
B by B1@1 B2@1;
A1 ON B1 (1);
A2 ON B2 (1);

I'm using the theta parametrization. Thanks!
 Bengt O. Muthen posted on Tuesday, December 11, 2007 - 11:22 am
I think of reciprocal influence as

a1 on b1;
b1 on a1;

and same for twin 2. This model is identified only with covariates where one covariate is specific to each of the 2 dependent variables in the reciprocity.

I don't see reciprocity in your setup. Perhaps I misunderstand what you want to do.
 Arpana posted on Tuesday, December 11, 2007 - 12:44 pm
Dear Dr. Muthen,

Thanks - I do have the model set up to go A1 On B1 (1);
B1 On A1 (2);

A2 On B2 (1);
B2 On A2 (2);

except, I need to constrain the variance of the latent factors (A and B) at 1:

A by A1 A2;
B by B1 B2;
A@1; B@1;

to model both paths - does this matter at all if my variables are dichotomous?

 Bengt O. Muthen posted on Wednesday, December 12, 2007 - 6:38 am
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
 Linda K. Muthen posted on Thursday, December 09, 2010 - 1:00 pm
I'm not sure I understand your question. See the Topic 1 course handout on the website under MIMIC model and formative indicators to see if either of these is what you want.
 lamjas posted on Wednesday, April 25, 2012 - 6:22 pm
Hi Dr. Muthen,

I submitted a manuscript which tests two models as follows:

Model A:

y5 y6 on y4 y3 y2 y1;
y4 y3 on y2 y1;

Model B:
y5 y6 on y4 y3 y2 y1;
y2 y1 on y4 y3;

Note: All variables are latent.

One reviewer asked me to combine two models and test the reciprocal effects of y1 y2 y3 y4. That is:

Model C:
y5 y6 on y4 y3 y2 y1;
y4 y3 on y2 y1;
y2 y1 on y4 y3;

However, I only use cross-sectional data. Is it a good idea to do so?

Actually, I ran the combined model, but the coefficents become difficult to interpret. Any advice is welcome.
 Linda K. Muthen posted on Thursday, April 26, 2012 - 1:41 pm
I don't believe MODEL C is identified.
 Jinyoung Park posted on Friday, December 20, 2013 - 10:37 am
Dear Dr. Muthen,

I am trying to analyze a path model, which includes a couple of reciprocal path (feedback loop).

That is, the model contains following statements.

A on B
B on A

The both coefficients of reciprocal path are significant at the 0.05 level, but the signs show opposite directions.

Is it possible? or the model lacks in stability?

If it is possible situation, how to interpret these conflicting and significant estimates?

Thanks a lot.

 Bengt O. Muthen posted on Friday, December 20, 2013 - 1:57 pm
This question is suitable for SEMNET.
 Jinyoung Park posted on Sunday, December 22, 2013 - 7:03 am
Thanks. I`ll search the SEMNET.
 David Merolla posted on Thursday, March 27, 2014 - 1:57 pm
I am trying to explore a simple non-recursive model:





- the program just runs and does not give output (waited about 30 minutes). If use control C to cancel and view the output file it says that the estimation terminated normally and I have results, but I am not sure I should trust them

Any advice?
 Linda K. Muthen posted on Thursday, March 27, 2014 - 2:05 pm
Either download the most recent version of the program or run without the Diagrammer. There was a problem with the Diagrammer and non-recursive models in Version 7.
 David Merolla posted on Thursday, March 27, 2014 - 3:16 pm
Thank you!
 David posted on Monday, August 03, 2015 - 11:48 pm
Dear Dr. Muthen,

Suppose that the true nature relationship between two varibles is reciprocal and there is a positive relation in both directions:

Y1 -> Y2 + X1
Y2 -> Y1

If instead a recursive system is specified, for example only the Y1->Y2 + X1 equation, would the direct effect from Y1 to Y2 absorb the mediated effect (Y2->Y1->Y2 and so on) and therefore be biased upwards?

I know that in a recursive system mediation effects are abosrved into the direct effects when the mediator variable is omitted but would like to know if this works the same way in a nonrecursive system.

 David posted on Tuesday, August 04, 2015 - 12:06 am
Sorry Dr. Muthen, I misspelled the arrows and did not make explicit the coefficients.

Y1 <- b12*Y2 + X1
Y2 <- b21*Y1

would be the true model.
Assume b12*b21 <1,>0, b21>0

Instead, suppose only Y1 <- b12*Y2 + X1 is estimated

Would the coefficient of Y2, b12, absorb mediation and therfore biased upwards?

Thanks again,
 Bengt O. Muthen posted on Tuesday, August 04, 2015 - 2:15 pm
You can check that out by using matrix algebra on the reciprocal model, thereby being able to express Y1 in terms of Y2 and see what the slope looks like. Or, ask on SEMNET and someone may do it.
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