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
Hi I have read up on the counterfactual direct and indirect effects in the article you just mentioned above. I am still confused. Is there a syntax that I can follow in order to take into account these effects? How would I convert my probit coefficients into probabilities given these type of effects (causal/counterfactual)? I am having a hard time understanding the formulas in the paper.
If I have 3 Xs, 2 covariates, 1 mediator (which I also want to test the interaction between this variable and the Xs) and 3 outcome (binary) variables, can I isolate the probabilities?
what I mean: Is there a way I can make a statement such as: "Childhood aggression has a direct effect on violence charges such that for every standard deviation increase in aggression the probability of being charged with a violent crime increases by... Aggression also has a significant indirect effect on violence charges such that education partially mediated the effect between childhood aggression and violence charges, such that with a 1 standard deviation increase in aggression resulted in the probability of ...resulting in a X% decrease in probability..."
(I have sent my input, output and diagram to the support email)
I am now trying to run with MOD but I am getting a warning and an error
*** WARNING in DEFINE command The CENTER transformation is done after all other DEFINE transformations have been completed. *** ERROR in MODEL INDIRECT command Statements in MODEL INDIRECT must include the keyword IND or VIA. No valid keyword specified.
.. here is part of the input..
DEFINE: CENTER MELSEDUC(GRANDMEAN); AGGXED = MELSEDUC*PAGG1;
Analysis: Estimator = WLSMV; parameterization = theta; BOOTSTRAP IS 500; MODEL: MELSEDUC ON pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C; ASSCHZ5C ON pagg1 pwith1 plike1; RVIOLCH ON MELSEDUC pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C AGGXED; RPROPCH ON MELSEDUC pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C; RDRUGCH ON MELSEDUC pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C; pagg1 WITH ASVOIS76; pwith1 WITH ASVOIS76; plike1 WITH ASVOIS76; pwith1 WITH pagg1; plike1 WITH pwith1; plike1 WITH pagg1; MODEL INDIRECT: RVIOLCH MOD MELSEDUC AGGXED pagg1(-1,1);
Thank you very much for the answer through email. However I am still getting fatal errors, so perhaps I am not understanding the response that Linda graciously provided me with. Note my mediator and moderator are the same variable. from Linda: "The interaction term aggxed does not appear in the regression for either the outcome or the mediator. See the current user’s guide on the website to see the specifications of MOD." I removed the interaction term from the ON statements, but I am not sure I understand what Linda said.
USEVARIABLES ARE MELSEDUC PAGG1 PWITH1 PLIKE1 ASVOIS76 RVIOLCH ASSCHZ5C AGGxED;
CATEGORICAL ARE RVIOLCH; DEFINE: CENTER MELSEDUC (GRANDMEAN); AGGxED = MELSEDUC*PAGG1; Analysis: Estimator = WLSMV; parameterization = theta; BOOTSTRAP IS 500; MODEL: RVIOLCH ON MELSEDUC pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C; MELSEDUC ON pagg1 pwith1 plike1 ASVOIS76 ASSCHZ5C; ASSCHZ5C ON pagg1 pwith1 plike1; pagg1 WITH ASVOIS76; pwith1 WITH ASVOIS76; plike1 WITH ASVOIS76; pwith1 WITH pagg1; plike1 WITH pwith1; plike1 WITH pagg1; MODEL INDIRECT: RVIOLCH MOD MELSEDUC AGGxED pagg1 (1,-1);
In the MOD option, the variable before MOD is the outcome. The first variable after MOD is the mediator. The second is the interaction, and the third is the exposure variable. You should have the following regressions in the MODEL command. I do not find the second one.
rviolch ON medseduc; medseduc ON aggxed; rviolch ON pagg1;
Thank you. In an effort to isolate the problem I have taken out all other variables. It states that the input reading terminated normally and then at the bottom says a fatal error again, so I sent my output and input to the support email. thank you!!
Jiseun Lim posted on Sunday, February 26, 2017 - 8:31 pm
My path model has a binary dependent variable (D) and dummy independent variables (I1, I2, I3). How can I specify independent variables in Model INDIRECT ?
The following command seems to refer to I1 as a mediating variable.
Model INDIRECT: D IND I1 I2 I3
Jon Heron posted on Monday, February 27, 2017 - 3:02 am
If we include I1, I2, and I3 as indepedent variables of linear or logistic regression model, we interpret the coefficient for I1 as the effect of service compared to office job.
Q1: If we analyze direct effects using "MODEL: D ON I1 I2 I3;", what is the correct interpretation of coefficient of I1 between the effect of a service (reference = office job) and the effect of a servie (reference = office job, manual work, or unemployed)?
Q2: How about the coefficient of I1 when analyzing indirect effect using " D IND I1;"?
I have a model with a binary outcome and several predictors both binary and continuous latent variables. I am using MLR estimation because I am interested in having odds ratios for the effect of predictors on the outcome. However, I also want to estimate some indirect effects.
Would you advise running the model with MLR estimation to get parameter estimates for all direct effects and then repeating the run with bootstrapping and ML estimation to get the indirect effects?
I understand that bootstrapping is preferable to delta method for looking at indirect effects, but that MLR is otherwise better for looking at the rest of the model? Many thanks
Hello, I am testing a WLSMV mediation model with a binary outcome, three continuous mediators (two latent, one manifest), and one binary x. I have done quite a bit of reading in the user guide, the discussion board, as well as the Muthén, B. & Asparouhov, T.(2015) article on causal mediation effects. I am testing the following indirect effects:
MODEL INDIRECT: PH IND hcreceip cond; MH IND hcreceip cond; employ IND PH hcreceip cond; employ IND MH hcreceip cond; employ IND PH cond; employ IND MH cond; employ IND PH hcreceip; employ IND MH hcreceip;
My questions: 1)The UG states that the counterfactually-defined indirect effects are only computed when there is one mediator. Is this correct? Does that mean that only the indirect effects I wrote in syntax above with ONE mediator are provided using the counterfactually-defined indirect effects? If so, how do I interpret the estimates in the output when there are two mediators?
2)From a post above it seems the estimates provided in the indirect effect output for the counterfactually-defined indirect effects are probabilities, not probit coefficients. So, for example, the estimate for the indirect effect “employ IND PH cond” is reported in the output as -.277. Does that mean that the indirect effect of cond=1, through PH, decreases the probability of employ by 27.7%?
1) For counterfactual effects with a binary Y and several mediators, you need to take the approach of
Nguyen, T.Q., Webb-Vargas, Y., Koning, I.K. & Stuart, E.A. (2016). Causal mediation analysis with a binary outcome and multiple continuous or ordinal mediators: Simulations and application to an alcohol intervention. Structural Equation Modeling: A Multidisciplinary Journal, 23:3, 368-383 DOI: 10.1080/10705511.2015.1062730
This paper uses Mplus, but writing out the effects in Model Constraint. Note that path-specific effects are not obtained but the indirect effect is for the total set of mediators.
2) An effect of -.277 means that the treatment reduces the probability by .277.
See also our book Regression and Mediation Analysis using Mplus which discusses both issues 1) and 2) in chapter 8.
Thank you Bengt. I will admit that I am limited in my understanding of many of the equations used in papers, but after many hours of studying I figured out the ones described in the UG and Muthén, B. & Asparouhov, T.(2015). The paper that you provided me with (thank you!) seems to refer to computing the total indirect effect for a set of mediators, when there are several indirect effects that include a single m between x and y. In my situation where I also have some indirect relationships (not "total") that pass through two mediators, (e.g., condition->healthcare->physical health->employment), does this change anything? Or is the author's method still applicable and I just need to spend time figuring out how? Thank you in advance for any help you can provide me.
You may want to email the author but I think special and much more complex considerations are needed to compute effects in the sequential mediation case. I give 2 references on page 209 of our book, referring to work by Daniel et al 2015 and DeStavola et al 2015, the first in Biometrics and the second in American Journal of Epidemiology.
An approximate approach is to use WLSMV or Bayes and consider effects on the continuous latent response variable - these effects are obtained using Model Indirect as usual.
Beth O'Neill posted on Saturday, February 24, 2018 - 7:51 pm
Hi Dr. Muthen, I have had more time to think through interpretation of my model results, and I am now questioning my initial thoughts about the results. I previously interpreted the information in the UG and message board as suggesting that my serial mediation model (Y IND M1 M2 X, with specific indirect effects specified as well) was providing me probit estimates for the latent response outcome variable for the specific indirect effects using both mediators (serial) with Sobel testing, and counterfactually-defined indirect effects for the specific indirect effects where there was only one mediator. However, now I think I have misinterpreted this, given that a "total indirect effects" is provided that is a sum of the estimates. I want to make sure that I am interpreting my mediation results correctly, thus I would greatly appreciate clarification regarding the estimates that would be provided from the model indirect statements that I posted above.
If I am using WLSMV, and I specify indirect effects that includes the possibility of both serial (two mediators) and simple mediation (just one mediator), are the estimates provided probit estimates for the continuous latent response variable for ALL specific indirect effects, or or those specific indirect effects that only include one mediator counterfactually-defined causal effects? Thank you!