Anonymous posted on Sunday, June 20, 2004 - 11:08 am
I have a model with two continuous latent variables F1 and F2, and one categorical variable X (a binary 0/1 variable). I am interested by the standardized indirect effect from F1 to X. The statements of model are: F2 ON F1; X ON F2; X VIA F2 F1; Is it correct to consider the STDYX coefficient of the indirect effect as standardized probit regression coefficient ?
The standard errors given in the output are for the raw coefficients. They are not the standard errors for the standardized coefficients. You would need to compute these standard errors using the Delta method.
Anonymous posted on Tuesday, October 05, 2004 - 12:02 pm
Do you mean in Analysis command using Parameterization=delta; ?
This is the default paramerization of Mplus. The results are the same with or without using Parameterization=delta. if Type=general.
I do not know anything else about Delta method. Could you tell me the syntax needed for calculating S.E. or p-value of StdYX results?
No, it is not PARAMETERIZATION = DELTA. You will need to read about the Delta method for computing standard errors in a book like Bollen's SEM book.
Anonymous posted on Tuesday, October 05, 2004 - 12:34 pm
Daniel posted on Wednesday, March 30, 2005 - 10:34 am
I used bootstrap standard errors to assess the significance of an indirect effect on an ordered categorical dependent variable. The indirecte effect was signficant. Is it possible to compute an odds ratio (exponentiating the log odds Beta) and confidence interval using the indirect effect, or does that not make sense?
BMuthen posted on Saturday, April 02, 2005 - 8:27 pm
I think that makes sense if you are using maximum likelihood estimation which uses the logit model. The indirect effect still refers to a slope.
First, the output for 'model indirect' in Mplus lists the estimates, standard errors, and two-tailed p-values for each direct and indirect effect. My question is: What are the listed p-values testing? Are these p-values an indication of whether the indirect effects are significant?
Second, my model includes multiple mediators regressed upon each other. For example, one of the indirect paths is SES-->Social support-->Negative affect-->Self-efficacy-->Smoking relapse (categorical/binary). Is there a test to determine if this complex mediational/indirect path is significant? Is that what is already reported in the indirect output?
The test is whether the indirect effect is different from zero. The p-value is the value for the z-test given in column three, the ratio of the indirect effect to its standard error.
If you define the indirect effect as described above, it will be tested against zero. This is what is reported in the output.
Michael B posted on Tuesday, July 28, 2009 - 6:20 am
A reviewer requested that I describe how the indirect effects were tested. Can you refer me to a paper that describes what Mplus does to test this type of complex indirect effect? Is there a name for this type of test?
The standard errors for the indirect effects are estimated using the Delta method. The ratio of the parameter estimate to its standard error is a z-test.
Jo Brown posted on Wednesday, July 04, 2012 - 8:30 am
In the post above you mention that the SEs of the indirect effects are estimated using the Delta method. Is this robust to potential bias or should I still use bootstrapping to estimate bias-corrected SEs?
Elina Dale posted on Wednesday, September 18, 2013 - 9:37 am
Dear Dr. Muthen, I have 2 groups randomized into trx & contr. As there was a high % of non-compliance, I used CACE to estimate the effect of trx on M, which was my outcome here (Ex 7.23 & 7.24 in MPlus 7 Guide). It worked fine. M is a latent variable measured through 3 f's.
Now I need to specify a mediation model (trx-->M-->y). I modified input commands from paper 1 (I still need to use CACE b/c of high % NC w/ trx)[see below]. But I got error message [below]. I don't know what to change. Please, advise! CATEGORICAL = u i1-i9 ; CLASSES = c(2) CLUSTER = clus; Analysis: TYPE = COMPLEX MIXTURE ; Model: %OVERALL% f1 BY i1 i2 i3 ; f2 BY i4 i5 i6 ; f3 BY i7 i8 i9 ; f1 ON trx ; f2 ON trx ; f3 ON trx ; c ON z1 z2 z3 ; y ON f1 ; y ON f2 ; y ON f3 ;
%c#1% [u$1@-15] ; f1 ON trx ; f2 ON trx ; f3 ON trx ;
%c#2% [u$1@15] ; f1 ON trx @0; f2 ON trx @0; f3 ON trx @0; f4 ON trx @0;
*** ERROR The following MODEL statements are ignored: * Statements in the OVERALL class: Y ON F1 Y ON F2 Y ON F3
Elina Dale posted on Wednesday, September 18, 2013 - 9:40 am
Sorry, it's me again! I am lost because I am not sure how to specify a model when I have to use CACE and I have a mediating latent variable. I couldn't find any such examples in MPlus Guide or the Shrout and other papers.
I would greatly appreciate it if you could help me & modify my commands from the previous posting.
I used the MODEL CONSTRAINT command to calculate indirect effects, and I understand that the standard errors of these indirect effects are computed in Mplus using the multivariate delta method. According to Bollen (1987), this method assumes a normal distribution of the direct paths. However, in my model, the indirect effects are calculated for a combination of linear and loglinear direct paths. In what way would this affect the interpretation of the standard errors of the indirect effects?
I tried to ‘translate’ the inputfile in Table 54 from Muthen (2011) to my own model (count Y, continuous X and M, no XM interaction term, only estimating PIE) and I believe I need the following command: MODEL: [DQ1](beta0); DQ1 on rpeer Gend ethn parm SC age(beta1); DQ1 on US Gend ethn parm SC age(beta2); [rpeer](gamma0); rpeer on US (gamma1); rpeer(sig); MODEL CONSTRAINT: new(ey0 mum1 mum0 ay0 bym01 bym00 eym01 eym00 pie); ey0=exp(beta0); mum1=gamma0+gamma1; mum0=gamma0; ay0=2*sig*beta1; bym01=(ay0/mum1+2)/2; bym00=(ay0/mum0+2)/2; eym01=exp((bym01*bym01-1)*mum1*mum1/(2*sig)); eym00=exp((bym00*bym00-1)*mum0*mum0/(2*sig)); pie=ey0*eym01-ey0*eym00;
Is this correct? The estimates for the direct paths to Y have strange values and the estimated indirect effect is unlikely large. Is this because I don’t use Monte Carlo simulations?
And as a second question: my model is actually multilevel. I can apply the proposed approach (Muthen, 2011; Muthen & Asparouhov, 2014) at the between-level, but I don’t think I can apply it at the within-level, since I cannot specify a mean for Y at the within-level. What would be a smart way to calculate the indirect effect at the within-level? Could I just use beta1*sig+beta1*gamma1 (given the parameters as specified above)?
Thanks in advance! The 2011 and 2014- papers are a great help by the way,
1. Yes. 2. Yes, it is the change in the latent response variable. 3. Yes. 4. Only to other probits. 5. Using WLSMV, all dependent variables are continuous so this is not a problem. See the following paper on the website for further information:
Muthén, B. & Asparouhov, T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.
Shiny posted on Friday, September 05, 2014 - 10:36 am
I am also testing a mediaton model with categorical data. I used Model constraint as WLSMV produces latent Response variables. Is the indirect effect coefficient under the new Parameter unstandardized? Can I get standardized indirect effect coefficient?
I am estimating a mediation model with binary outcome (Y) using WLSMV estimation. I am using bootstrap=1000 under the analysis command and cinterval (bcbootstrap), to get 95% bias-corrected confidence intervals for the indirect effect.
By comparing the output from the non-bootstrapped analysis and the bootstrapped analysis, I noticed the following:
1. The bootstrapped analysis has smaller standard errors for the indirect effect. Hence indirect effects become significant.
2. But the bootstrapped analysis has larger standard errors for direct effects of binary variables (Xs) in the mediation model. Hence these direct effect become insignificant.
Is this typical of bootstrapping? I do not understand why this has happened, and I am not sure if bootstrapping is appropriate for my model.
Bootstrap SEs and confidence intervals are usually quite reliable. But in some applications one of the limits of the confidence interval may be very close to zero so different approaches may give different conclusions. For instance, Cinterval(bootstrap) may give a different answer than Cinterval(bcbootstrap). Bayes is useful as a third option that also takes into account non-normality of the effects.
Note also that if you have a binary outcome, you should read up on the counterfactual effects discussed in the paper on our website:
Muthén, B. & Asparouhov, T. (2015). Causal effects in mediation modeling: An introduction with applications to latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 12-23. DOI:10.1080/10705511.2014.935843