Message/Author 

Emil Coman posted on Tuesday, January 13, 2015  1:50 pm



I am running the new 'causal mediation' command, using something like DV MOD M TxbyM Tx; However I would like to generate a new parameter besides the four listed in the output (PNDE, TNIE, TNDE, PNIE), based on VanderWeele's paper http://journals.lww.com/epidem/pages/articleviewer.aspx?year=2014&issue=09000&article=00019&type=abstract I would want specifically to estimate TNDEPNDE=IntRef as a new parameter. How could I do this, what labels does Mplus use by default for PNDE, TNIE, TNDE & PNIE behind our backs (if so), that I could use to generate IntRef? I would not want of course to calculate & labeled by hand TNDE and PNDE themselves as new parameters only to have them labeled... Thanks! 


Sorry, the PNDE etc quantities are not accessible but all have to be expressed as in my 2011 paper. 

Emil Coman posted on Wednesday, January 14, 2015  8:34 am



Thanks, Bengt; 1 more quick one: can you see a way to run causal mediation like a LDV MOD LM TxbyLM Tx; where however LM is now a latent, but a latent change/difference score, not a multiitem scale, so it is defined like: LM by wave2M@1; wave2M on wave1M@1; wave2M@0; [wave2M@0]; wave2M on LM@1; LM on wave1M *; !a good way to define LCS scores My problem of course is I cannot include a TxbyLM in the DEFINE section, as the LM latent is defined below that... The only (bad!) workaround I see is to compute mere difference score in DEFINE as DifM=(wave2M wave1M) and then compute a TxbyM =DifM*Tx. Any suggestion/comment? Thanks! 


You can define that interaction in the model statement using TxbyLM  Tx XWITH LM; and add type=random in the analysis command. 

Emil Coman posted on Wednesday, January 14, 2015  1:12 pm



Thanks, Tihomir, I found this option mentioned here in the listserv, and tried it... it gets to: "*** ERROR MODEL INDIRECT is not available for TYPE=RANDOM." 


You have to use the 2011 paper and model constraints to get the effects you need. 

John C. posted on Monday, February 15, 2016  12:09 pm



I would like to implement a model with a nominal mediator, based on the discussion in section 8 of your paper, “Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.” However, my model differs from in that the x variables are not necessarily binary. The framework presented in Muthen (2011) is for a binary x which acts as treatment, but I’m assuming the approach is fully extendable to models where x may be continuous or, in my case, a factor? For example, the formulation of a direct effect give in the paper is “ the conditional expectation, given the covariate, of the difference between the outcome in the treatment and control group when the mediator is held constant at the values it would obtain for the control group.” In the case where x is continuous, what would be the analogous formulation? 


Yes, you can have a continuous exposure variable. The effects are then evaluated by comparing two exposure values, for example, the mean and one SD above the mean. I will present a paper on nominal mediation at the M3 meeting at UCONN in May. 

John C. posted on Wednesday, February 17, 2016  8:23 am



Hello, I have a follow up on this as it means the Mplus code examples (Tables 50 and 51) would have to be modified appropriately. For example, as formulated: p10 is probability of mediator category 1 when x is zero p11 is probability of mediator category 1 when x is one so the formulas for these would have to be modified to take account of the two exposure values. Must the exposure values be hardcoded (in the Model Constraint section)? Second, the x in my case is actually a factor with categorical indicators. Does this then mean that I would have to perform the analysis in two stages, i.e., first derive the factor scores, then insert the appropriate hardcoded exposure values? 


The effects in those tables is for a change from x=0 to x=1. The formulas in Table 51 are making use of these simplifications for x. If you have a continuous x you need to consider say the mean of x and 1SD above the mean of x instead of 0 and 1. That changes the formulas because those x values enter into both the gamma and the beta terms of Model Constraint in line with equations (94) and (95). So it takes a little doing to modify the Table 51 input. 

John C. posted on Friday, February 19, 2016  3:16 pm



Just as a followup, in my case the x is a factor with ordinal indicators with values 1,2 or 3. However the continuous factor scores range from around 2.5 to +0.2. For the mediation equations above, should the mean and 1SD above the mean be in terms of the scale of the underlying factor scores? 


Yes. 

John C. posted on Wednesday, February 24, 2016  9:25 am



I have a follow up question on this which may be obvious but would like to check for sure. To proceed here I need to first generate the factor scores before I execute the fully specified model with the Model Constraint command. I can generate the factor scores either by running the measurement model alone, or by running the fully specified model (with the measurement model as part of it). I presume the latter is the best option to guarantee the factor scores I specify in the Model Constraint section are correct? In that case, there should be no reason to substitute the factor scores as predictors in place of the measurement model. Is that correct? 


You don't need to estimate factor scores. You just use the modelestimated factor variance (mean is zero I assume) to give the range. 

John C. posted on Friday, February 26, 2016  10:47 am



I asked above if one has to specify the mean and 1 SD above the mean for the mediation equations (Tables 50 and 51) in terms of the scale of the underlying factor scores to which you indicated "Yes." Now you're saying I don't need to estimate the factor scores. Perhaps it would be easier if you could provide the Mplus syntax for: p10 is probability of mediator category 1 when f is at the mean p11 is probability of mediator category 1 when f is 1 SD above the mean. 


When you said scale of the underlying factor scores I thought you meant the scale of factor variable in the model  people often refer to it that way. I couldn't imagine that you thought you needed estimated factor scores. You should just treat the factor as an observed variable in the formulas  if it has mean zero and estimated standard deviation SD, then the 2 values are 0 and SD. You can make it easy by setting the metric of the factor as variance fixed at 1. See also Section 13.4 in the 2011 paper. 

John C. posted on Wednesday, March 02, 2016  5:55 am



Thanks, here is what prompted my original concern. If I look at the factor scores, the mean is .09, and the range goes from 2.5 to .245, so highly skewed. If I add the SD (around 0.5) to the mean, I'm way out of range of any of the factor scores. Is this a little strange, or is it still ok to just use, f*0 for the mean and f*0.5 for 1 SD above the mean (in the model constraint command). Apologies for dragging this out. 


Yes, I would go by the metric of the factor in the model which is assume normal and gets an estimated factor SD. The model distribution is like the prior and the estimated factor scores like the posterior so they can be different. 

John C. posted on Wednesday, March 09, 2016  1:40 pm



Hello, Thanks, if I could shift to a different topic related to this model. With my factor as a predictor in this mixture model I specify ALGORITHM=INTEGRATION, as indicated as required in the Mplus output This works but then I run into a problem when modeling error correlations across the indicators. The first error is that "For covariances between categorical variables, specify PARAMETERIZATION=RESCOV in the ANALYSIS command." However, when I add this specification, I get the following error: "Categorical variables are not allowed as factor indicators for PARAMETERIZATION=RESCOV." In short, can these mixture models work with covariances across categorical indicators? 


You will have to put a factor behind the pair of indicators to let their residual correlate. 


Dear Drs. Muthen, Quick question: the user guide provides the following code for the MOD option with 4 arguments, when there’s a separate moderator that interacts with the mediator: MODEL INDIRECT: y MOD m z (1 1 0.1) mz x; where y is the outcome, m is the mediator, z is the moderator, mz is the interaction between m and z, and x is a binary exposure variable Do the total natural indirect effects (TNIE) then incorporate xtoy paths through: 1. m and mz, OR: 2. m, z and mz? I.e., is the moderator z also treated as a mediator, such that the path through it is incorporated into the TNIE? Many thanks, Bobby Das 


The answer is: 1. See our book at http://www.statmodel.com/Mplus_Book.shtml 

Lynne W posted on Wednesday, January 10, 2018  1:41 pm



Dear Drs. Muthen, I want to estimate a twolevel mediation model with a binary mediating variable using the Bayes estimator. I would also like to get counterfactual causal effects using the INDIRECT command, but I run into the following error: MODEL INDIRECT is not available for TYPE=TWOLEVEL with ESTIMATOR=BAYES. I tried other estimators but they also fail. Is there a way to estimate such models or to calculate the counterfactual effects in another way? Many thanks, Lynne 


Yes, you can always express the effects in terms of model parameters using the Model Constraint command. I don't know if your exposure variable is a withinlevel or a betweenlevel variable and which level the binary mediator is on. 

Lynne W posted on Wednesday, January 10, 2018  3:09 pm



My exposure variable (kkz_dens) is on the between level and the binary mediator (LPART) is on the within level. It looks like this VARIABLES: CATEGORICAL = LPART; ANALYSIS: TYPE = TWOLEVEL; ESTIMATOR=BAYES; MODEL: %WITHIN% L_DIFF ON LPART(W); %BETWEEN% L_DIFF ON kkz_dens; LPART ON kkz_dens(B); I assume I can calculate the conventional indirect effects using the MODEL CONSTRAINT command and the product method: MODEL CONSTRAINTS: NEW(CON_LANG); CON_LANG = A * B; but how would I calculate the counterfactual effects? 


a*b is indeed the indirect effect. But you have to fix a couple of things in your input:  put kkz_dens on the Between list  add on Between: Lpart on kkz_dens (a); L_diff on Lpart (b); The withinlevel L_diff on Lpart slope does not play into the indirect effect. See e.g. Preacher's Appendix E for "211 (MSEM)". 

Lynne W posted on Thursday, January 11, 2018  12:17 am



Thank you for very much for the corrections and clarifications. 

Tor Neilands posted on Thursday, September 20, 2018  9:45 am



Dear Bengt, I'm helping a colleague to fit a ColeMaxwell type longitudinal mediation autoregressive SEM to data with 5 fixed time points. The exposure E is randomized assignment (0=control; 1=intervention), there are 3 observed mediators (1 continuous; 2 ordinal), and either a latent Y or observed Y (we haven't decided which, yet). The residuals of the mediators are pretty weakly correlated and we will use nested testing or BIC to see if we need to retain those correlations, but for now let's assume we'll retain them. There is some interest in estimating causal direct, total, and indirect effects of X on Y through the M variables. I assume those effects are not available through MODEL INDIRECT at this time? (I would be overjoyed to be wrong about that). If I am correct that those effects are not presently available through MODEL INDIRECT, could the MODEL CONSTRAINT examples of your 2011 paper be applied directly here? Or would more complex expressions be required due to the presence of the multiple mediators, correlated mediator residuals, and various autoregressive pathways? If not, I suppose we could use WLSMV or Bayes (I imagine Bayes would be better due to some data missing due to loss to followup) to estimate the traditional noncausal indirect effects of X on Y through M* as long as we can demonstrate no XM interactions on Y. Thanks as always, Tor Neilands 


Are E, M's, and Y repeated 5 times? Counterfactuallydefined effects would be needed only if it is important to treat the 2 ordinal mediators as ordinal (as opposed to continuous). My writing does not cover the case of multiple mediators where some are ordinal. 


Thanks, Bengt. E is not repeated. It is randomization assignment/study arm assignment (0 = control; 1 = intervention). I suppose I should've called it X for consistency with the way such variables are described in the Mplus documentation and related literature. M and Y are repeated 5 times. By the way, I really enjoyed your 13minute video on mediation linked from the Mplus home page this week. I found it very relevant to several applied data analyses I'm helping earlycareer scholars with presently. One comment you made in the video that I found especially interesting was your remark that there may be benefits to including XM interactions and using the causal effects framework even if the XM interaction is not statistically significant. Could you elaborate further on why that's the case? I found that statement to be very interesting and was hoping to learn more. Thanks! Tor 


The idea of including an XM interaction comes from the 2015 VanderWeele book, page 46. He points to the low power to detect the XM effect and suggests checking for the need to include it by seeing if the indirect and direct effect estimates change much. There has been several recent articles (MBR, Psych Meth?) on longitudinal mediation in addition to Maxwell's 2010, 2011 articles. See for instance Huang & Yuan (2016; online). Bayesian dynamic mediation analysis. Psychological Methods and also the work by Lijuan Wang, University of Notre Dame 

Adam Garber posted on Wednesday, March 13, 2019  9:20 pm



Hello, I would like to run a casual effects model including the MX interaction (i.e. case 3 from the Mplus mediation book) but with 3 continuous mediators. Therefore, the model would include the following variables: x (binary), m1, m2, m3, y, mx1, mx2, mx3, & c(continuous covariate) To my knowledge it is not possible to use the MODEL INDIRECT (y mod m mx x) command with multiple mediators. I am aware of the relevant input example from your Muthen(2011) paper but am unable to translate this input (table 25) from the simulation to the data context. Could you direct me to an example input to run a model which estimates the four causal effects (TNIE,PNIE,TNDE,PNDE) which could be extended to the case of multiple mediators? 


Let me think about that and try to answer you later. 

Adam Garber posted on Wednesday, March 27, 2019  1:36 pm



Hello Dr. Muthen, Would this work to specify a 3mediator model with the MX interaction term? Y (outcome) X (predictor) M1 (mediator 1) M2 (mediator 2) M3 (mediator 3) define: MX1 = M1*X; MX2 = M2*X; MX3 = M3*X; analysis: bootstrap = 10000; model: Y on M1 (b1) M2 (b2) M3 (b3) X (b4) MX1 (b5) MX2 (b6) MX3 (b7); M1 on X (g1); M2 on X (g2); M3 on X (g3); [Y] (g0); model constraint: !x1=1, x0=0 PNIE1=(b1+b5*0)*(g1); TNIE1=(b1+b5*1)*(g2); PNIE2=(b2+b6*0)*(g1); TNIE2=(b2+b6*1)*(g2); PNIE3=(b3+b7*0)*(g1); TNIE3=(b3+b7*1)*(g2); PNDE1=b4+b5*(g0+g1*0); TNDE1=b4+b5*(g0+g1*1); PNDE2=b4+b6*(g0+g2*0); TNDE2=b4+b6*(g0+g2*1); PNDE3=b4+b7*(g0+g3*0); TNDE3=b4+b7*(g0+g3*1);  Many thanks, Adam 


You may be right but I haven't derived that particular case. But you can derive it using the approach of Section 4.5.2 of our RMA book. 


Thank you Dr. Muthen for the reference, I believe I was able to correctly specify a multiple mediator model using the potential outcomes approach derived in section 4.5.2 *There is an error in the syntax above from my comment, the gamma coefficients for the indirect effects should look as follows: PNIE1=(b1+b5*0)*(g1); TNIE1=(b1+b5*1)*(g1); PNIE2=(b2+b6*0)*(g2); TNIE2=(b2+b6*1)*(g2); PNIE3=(b3+b7*0)*(g3); TNIE3=(b3+b7*1)*(g3); 

Back to top 