I am doing two mediations, both controlling for covariates and using weighted data (and thus WLSMV):
walk --> PA --> health [BMI]
PA is binary, health is ordinal, and BMI is continuous.
ANALYSIS: bootstrap = 1000; MODEL: pa on walk [covariates] ; bmi [health] on pa walk [covariates]; MODEL INDIRECT: bmi via pa walk; OUTPUT: cinterval(bcbootstrap);
Questions: 1. Is there a reference for what exactly is happening with the bootstrap? I saw a reference mentioned of MacKinnon and Lockwood (2001) with the distribution of product method, but I cannot find it. This method is appropriate for binary mediators and ordinal outcomes, right?
2. Probit regression is being performed for health and pa since WLSMV is used, right? And its linear regression for BMI?
3. The indirect effect for BMI as the outcome is -0.361. How can I use this number in a sentence?
4. The indirect effect for health as the outcome is -0.068. How can I use this number in a sentence?
Note that "weight" in weighted data does not mean the same as "weight" in weighted least squares. By the former I assume you mean sampling weights. You can use ML as well with sampling weights.
With a binary mediator you should use the approach in the article on our web site:
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
1. The product method is not the same as the bootstrap. See for instance the book by Hayes (2013) for a gentle introduction to the bootstrap.
2. Yes (but see the article).
3-4 For down-to-earth interpretation of indirect effects I recommend Hayes (2013). The ordinal outcome of health calls for approaches in the article.
Thank you so much for your quick response! Yes, I did mean sampling weights. I forgot that it was the MODEL INDIRECT and not the weighted nature of the data that made WLSMV (and probit regression) be necessary as opposed to MLR (and logistic regression).
I looked at the article and book that you mentioned. From the article, I understood that categorical variables can be modeled as their underlying continuous latent response variables and are modeled using linear regression, and thus the indirect effect can be calculated normally but has a different interpretation. From this and the Hayes book, I understand that an indirect effect of .5 using this approach would mean that a one unit increase in X corresponds to a .5 unit increase in the outcome variable (or its underlying latent variable if ordinal/binary) through the latent mediator. Is this correct?
The approach I used above I found on Hayes's website: http://www.afhayes.com/macrofaq.html. It seems similar to the code in the article, just without starting values or moderation, and with a continuous or ordinal Y instead of binary. Is it my code or just my interpretation that needs to change? If it is just the interpretation, is it in terms of linear or probit/logistic regression?
This is correct if you consider PA* to be the mediator, not PA, where PA* is the continuous latent response variable underlying the binary observed PA variable. My article shows the new counterfactual - "causal" - effect approach which you can also get from Mplus 7.31 using IND or MOD in Model Indirect.
Answer to your last paragraph:
This code and interpretation represents "the old" (outdated?) way of getting indirect effects before the "causal" approach of Robins, Greenland, Pearl, VanderWeele, Vansteelandt, Imai, and others appeared on the scene several years ago. Unfortunately, the SEM world has been slow to adopt this approach.
Thank you again for the response! If I changed the VIA to IND and reported that pvalue, would that be reasonable for both my continuous and ordinal outcomes? I think that and the method of examining models with and without the mediator (which is more common in my field it seems) would be a decent combination to show absence or precense of mediation and would make sense to both my audience and me.
Look for the output heading that includes the word counterfactual for the best effect estimates. That is available for binary M and continuous Y, but I don't think version 7.31 has it for binary M and ordinal Y.
Analysis with and without the mediator isn't necessarily a good approach with a binary mediator.
Is there a good example of how those should be interpreted? I understand the basic interpretation of indirect effects now, but I am unclear of the coefficient type. Does it depend on the outcome? A continuous outcome has indirect effects interpreted as linear regression effects, while a dichotomous would have ones that should be exponentiated for odds ratios (assuming MLR and logit link)?
I know double-posting is frowned upon, but I wanted to save you the trouble of directing me to your article again. Binary outcomes have indirect effects in terms of probability metric for either probit or logit, and for continuous outcome it is in terms of linear regression betas. Continuous xs need to be written as xvar(2 5) in the model indirect code. Right? I feel like I am finally getting this, thank you so much!
Sorry again for the double post - didn't want to waste your time.
I imagined that you were thinking of the c - c' method to see the effect of mediation. That is not correct with a binary M or a binary Y. It is only correct with continuous M and Y, where it is the same as a*b.
I was actually thinking of just looking at Y <- X and Y <- M + X and seeing if the size of the effect or the significance of X changed. But I have gotten the counterfactual method to work, so I think I am fine.
However, I am a little confused with the "Odds ratios for binary X" in the output. I have a total natural IE of -.002, which is not significant, but the corresponding odds ratio is .988, which is significant. Having an odds ratio that close to one with a corresponding very small indirect effect makes sense, but I don't understand why the OR would be significant. Does this reflect a problem?
The standard output gives Est/SE which is the same as testing against zero: (Est-0)/SE. Here you are instead interested in (Est-1)/SE. But instead of this test I would recommend using/reporting the confidence interval.
Hello! I was wondering if it were possible to examine multiple mediators using survey data with sample weights in Mplus. The DV and mediators are continuous, and the IV is dichotomous. I know that Hayes has macros for multiple mediation in different softwares, but they cannot be used with sample weights. If this can be done in Mplus, what would that syntax look like? Many thanks!