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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 ? 


Yes because the end dependent variable is binary. 

Anonymous posted on Sunday, June 20, 2004  1:44 pm



Thank you Linda Muthén for your response. 

Anonymous posted on Tuesday, October 05, 2004  10:00 am



Hi Dr. Linda, When we present results of StdYX we must know S.E.or pvalue of StdYX. I'm not sure whether we can use Est./S.E. offered in the default display? If not how can I know the significance level of StdYX? Thanks 


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 pvalue of StdYX results? Thanks 


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



Thanks 

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. 


I have a couple of questions. First, the output for 'model indirect' in Mplus lists the estimates, standard errors, and twotailed pvalues for each direct and indirect effect. My question is: What are the listed pvalues testing? Are these pvalues 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>Selfefficacy>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? thanks so much in advance. 


The test is whether the indirect effect is different from zero. The pvalue is the value for the ztest 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 ztest. 

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 biascorrected SEs? 


I would use biascorrected confidence intervals. 

Jo Brown posted on Friday, July 06, 2012  2:55 am



Hi Linda, thanks for your reply. Would you this using the bootstrap option or is there an alternative command. Thanks 


See the BCBOOTSTRAP setting of the CINTERVAL option. 

Jo Brown posted on Monday, July 09, 2012  3:55 am



Thanks Linda, I now have one more question re. CIs for mediation analyses as I now need to repeat my analyses on a number of imputed datasets; however, when I specified output: CINTERVAL(bcbootstrap) I receive the following message: CINTERVAL option is not available with multiple imputation. Request for CINTERVAL is ignored. Is there a way around this problem that would allow me to obtain CI for imputed datasets? Could I simply calculate the CIs by using: estimate +or (1.96*SE) in this case? Many thanks, Jo 

Jo Brown posted on Monday, July 09, 2012  9:00 am



one more thing is: are the confidence intervals calculated using the CINTERVAL option based on a normality assumption? 


You can use plus/minus 1.96 times the standard error. The is not BCBOOTSTRAP. See the description of the settings of the CINTERVAL option in the user's guide. 

Jo Brown posted on Monday, July 09, 2012  12:10 pm



thanks Linda. If I use the formula above, should I use bootstrap to obtain bootstrapped SEs or is this not necessary? Are the CIs so calculated not accounting for potential bias? Many thanks again 


That would need to be your decision. The confidence intervals are symmetric. See the user's guide. 

Jo Brown posted on Tuesday, July 10, 2012  12:00 pm



thank you 


Hi Linda, I am using method WLSMV, and I have several binary mediators and binary covariates. I specified STDY in the OUTPUT, and no standardized estimates were produced. When I specified STANDARDIZED, the output only showed two columns w/ STDYX and STD (which are identical to the unstandardized estimates). Do we have to calculate the oneway standardization (STDY) by hand? Or is there a way to get it in the MPlus output? Thanks for considering this question, Selahadin 


You need to convert STDYX to STDY yourself. 


Thanks Linda. 

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 noncompliance, 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 i1i9 ; 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. Thank you! 


Please send the full output and your license number to support@statmodel.com. 


Dear Linda Muthen, 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? Thanks in advance, Evelien 


You need to read the paper on our website: Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling. 


Thank you, that is a very helpful paper indeed! 


Dear Bengt Muthén, 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*bym011)*mum1*mum1/(2*sig)); eym00=exp((bym00*bym001)*mum0*mum0/(2*sig)); pie=ey0*eym01ey0*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? Evelien 


And as a second question: my model is actually multilevel. I can apply the proposed approach (Muthen, 2011; Muthen & Asparouhov, 2014) at the betweenlevel, but I don’t think I can apply it at the withinlevel, since I cannot specify a mean for Y at the withinlevel. What would be a smart way to calculate the indirect effect at the withinlevel? 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, Evelien 


Mplus Version 7.2 does the counterfactuallydefined (causal) indirect and direct effects automatically  see the Version 7.2 Mplus Language Addendum. This includes the case of a count outcome. Multilevel counterfactual effects are more complex  see references at the end of the 2011 paper. Perhaps you should instead use Type=Complex to take care of it. 


Hi, I have the following path model with a binary dependent variable and several continuous independent variables. I am using WLSMV to estimate the model: Categorical are Rang_CDU; (all other variables are continuous / dummys). Analysis: Type = general; Model: Rang_CDU on RE_W3_Au W1_UmfrW W1_Dummy W1_Dumm0 alter CDU_Dumm I_Wiss; W1_UmfrW on W1_InBTW I_Strate I_Heuris RE_W3_Au I_Wiss; RE_W3_Au on W1_InBTW I_Wiss; Model indirect: Rang_CDU ind I_Wiss; Rang_CDU ind W1_InBTW; Output: sampstat standardized stdyx modindices; I have some very basic questions: 1. The StdYX path coefficients between the continious dependents and continious independents are standardized regression coefficients, right? 2. The StdYX path coefficients between the binary dependent and continious independents are standardized probit coefficients, right? How can they be interpreted? 3. And can they be compared to other standardized probit coefficients within the same model in terms of strenght? 4. Can they be compared to standardized regression coefficients within the same model in terms of strenght? 5. How can the indirect effects be interpreted including paths with standardized regression coefficients and standardized probit coefficients (e.g. Rang_CDU ind I_Wiss)? Thank you very much for your help! 


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? Thanks! 


Q1. Yes. Q2. Yes, as usual, just divide by the estimated SD(Y*) and multiply by the sample SD(X). 


Hello, 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% biascorrected confidence intervals for the indirect effect. By comparing the output from the nonbootstrapped 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. Any help appreciated. Thanks, Dharmi 


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 nonnormality 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), 1223. 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) Thank you very much!  Kathleen 


The syntax is given in the Appendix under Mplus Scripts but also more fully in the UG on our website (see UG index under Counterfactual). You have moderation so you use MOD. Note that you also have a continuous exposure variable. And yes, you will be able to make such statements. The printed counterfactuallydefined causal effects are given in a probability metric so no conversion is needed. Later on, you will have our book (Regression and Mediation Analysis using Mplus) to go by with worked examples of how to do this and give interpretations. 


Thank you! this helps so much!! 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 so much again! 


I just realized that it might be because I don't have the most recent version for Mac OS X. I would need version 7.4 to use MOD correct? Sorry about posting in two windows. If this is the case I will ask my university to get the most recent one! Thank you! 


Yes, you need Version 7.4. 


Hi again, 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



Hi. 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



I think you'll need to do them one at a time. Model INDIRECT: D IND I1; !D IND I2; !D IND I3; 


And when you have a binary DV you want to use the new counterfactuallydefined effects that you get when you specify Model Indirect: D IND M I1; where M is the mediator. This is described in our new book, Chapter 8. 

Jiseun Lim posted on Monday, February 27, 2017  5:26 pm



Thanks to Jon & Bengt. I would like to ask about confusing points compared to when dummy variables are used as independent variables for linear regression or logistic regression. My original independent variable is occupation, which has values of office job, service, manual work, and unemployed. The dummy variables were constructed as follows. if occupation=office job then I1=I2=I3=0 if occupation=service then I1=1, I2=I3=0 if occupation=manual work then I2=1, I1=I3=0 if occupation=unemployed then I3=1, I1=I2=0 Therefore, the values of I1 are as follows. I1=1 : service, I1=0 : office job, manual work, unemployed. 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;"? 


Q1, Q2: The interpretations are the same as in regular linear/logistic regression. 

Jiseun Lim posted on Wednesday, March 01, 2017  9:35 pm



Dear Bengt, Thank you very much! 


Hi 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 


The parameter estimates for ML and MLR are identical. Only the standard errors differ. 

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