# Simple mediation and mediation with covariates

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### andrew....@gmail.com

Aug 18, 2018, 12:41:38 PM8/18/18
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Dear all,

I am relatively new to the Lavaan package and I was wondering how I could carry out a simple mediation analysis with and without covariates.

The first scenario (simple mediation without covariates. This is similar to the example given on the Lavaan website; http://lavaan.ugent.be/tutorial/mediation.html)

My outcome (Y) is binary
My mediator (M) is binary
My predictor (X) is continuous

From what I understand from the lavaan website I can use binary exogenous categorical variables as 0/1 coding. This coding should be done for both M and Y (treat them as numeric variables).
However my M, depending on the path (see below), is both exogenous (Y ~ b*M) and endogenous (M ~ a*X). Should I declare my M as ordered??

``````model <- ' # direct effect
Y ~ c*X
# mediator
M ~ a*X
Y ~ b*M
# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)
'
fit <- sem(model, data = Data)
summary(model, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)``````

In my first attempt I decided to leave the M as numeric (not ordered). Is my above reasoning sound for carrying out a simple mediation with a binary outcome and binary mediator?

In my second scenario I would like to extend the model by adding covariates (Sex and SES). I would like to control for Sex and Age in the entire analysis.

``````model_2 <- ' # direct effect
Y ~ c*X + Sex + SES
# mediator
M ~ a*X + Sex + SES
Y ~ b*M
# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)
'
fit <- sem(model_2, data = Data)
summary(model_2, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)``````

Am I correct to specify the model as above? Thank you in advance.

Andy

### Terrence Jorgensen

Aug 18, 2018, 3:30:04 PM8/18/18
to lavaan
Am I correct to specify the model as above?

Yes.  Make sure M and Y are recognized as binary/ordered, if they are not stored that way in Data.

`sem(..., ordered = c("M","Y"), ...)`

Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

### Mo Abd

Sep 25, 2018, 6:36:37 AM9/25/18
to lavaan
Dear Terrence,

Do you know if the decomposition into direct and indirect would be accurate given that either the mediator and or the outcome is binary?

Kind regards,

Mo

Op zaterdag 18 augustus 2018 21:30:04 UTC+2 schreef Terrence Jorgensen:

### Terrence Jorgensen

Sep 25, 2018, 7:10:01 AM9/25/18
to lavaan
Do you know if the decomposition into direct and indirect would be accurate given that either the mediator and or the outcome is binary?

Categorical outcomes are handled by assuming they have an underlying latent normally distributed response, which is how the effects are interpreted.  So the decomposition works the same way, but is interpreted relative to the latent responses, not observed discrete responses.  But this is an empirical question that you could answer yourself by fitting mediation models and direct-effect-only models to see if the numbers add up.

Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

### walkywalky

Sep 26, 2018, 4:54:22 AM9/26/18
to lavaan
Dear all,

I have a similar problem and I am not sure whether my code to run a multiple mediation analysis works.

I do not get any output when running it so apparently it does not work.

Here my code and variables:

# I have 5 mediators (PE, EE, SI, HM and FC), 1 outcome variable (BI), three predictors (CarUse, PublicTransportUse, TechAcceptance)mod.PE <-' PE =~ V2_PE1 + V2_PE2 + V2_PE3 EE =~ V2_EE1 + V2_EE2 + V2_EE3 SI =~ V2_SI1 + V2_SI2 + V2_SI3 BI =~ V2_BI1 + V2_BI2 + V2_BI3 HM =~ V2_HM1 + V2_HM2 + V2_HM3 FC =~ V2_FC1 + V2_FC2 + V2_FC3BI ~ b1 * PE + b2 * EE + b3 * SI + b4 * FC + b5 * HM + c1 * CarUse + c2 * PublicTransportUse + c3 * TechAcceptance PE ~ a1 * CarUse + a1 * PublicTransportUse + a1 * TechAcceptance EE ~ a2 * CarUse + a2 * PublicTransportUse + a2 * TechAcceptance SI ~ a3 * CarUse + a3 * PublicTransportUse + a3 * TechAcceptance FC ~ a4 * CarUse + a4 * PublicTransportUse + a4 * TechAcceptance HM ~ a5 * CarUse + a5 * PublicTransportUse + a5 * TechAcceptance indirect1 := a1 * b1 indirect2 := a2 * b2 indirect3 := a3 * b3 indirect4 := a4 * b4 indirect5 := a5 * b5 total := CarUse + (a1 * b1) + (a2 * b2) + (a3 * b3) + (a4 * b4) + (a5 * b5) + PublicTransportUse + (a1 * b1) + (a2 * b2) + (a3 * b3) + (a4 * b4) + (a5 * b5) + TechAcceptance + (a1 * b1) + (a2 * b2) + (a3 * b3) + (a4 * b4) + (a5 * b5) PE ~~ EE PE ~~ SI PE ~~ FC PE ~~ HM EE ~~ SI EE ~~ FC EE ~~ HM SI ~~ FC SI ~~ HM FC ~~ HM’ fit.PE <- sem(model = mod.PE, data = Datensatz_neu.sav) summary(fit)Many thanks!!!!

### Terrence Jorgensen

Sep 28, 2018, 5:47:01 AM9/28/18
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I do not get any output when running it so apparently it does not work.

There do not appear to be line breaks between the regression models for different outcomes:

# BI ~ b1 * PE + b2 * EE + b3 * SI + b4 * FC + b5 * HM + c1 * CarUse + c2 * PublicTransportUse + c3 * TechAcceptance PE ~ a1 * CarUse + a1 * PublicTransportUse + a1 * TechAcceptance EE ~ a2 * CarUse + a2 * PublicTransportUse + a2 * TechAcceptance SI ~ a3 * CarUse + a3 * PublicTransportUse + a3 * TechAcceptance FC ~ a4 * CarUse + a4 * PublicTransportUse + a4 * TechAcceptance HM ~ a5 * CarUse + a5 * PublicTransportUse + a5 * TechAcceptance

### Mo Abd

Sep 28, 2018, 8:33:19 AM9/28/18
to lavaan
Dear Terrence,

Thank you for taking the time to answer my question. I don't completely follow your explanation; apologies I am new to structural equation modeling and mediation analysis. If I understand correctly, in a case where we have a continuous exposure, continuous mediator, and a binary outcome Lavaan treats all variables the same and therefore the coefficients are multiplied to derive the indirect effect?

I have been reading up on the topic and found a guide by Nathaniel Herr that deals with the exact problem (when the either the mediator or the outcome is binary): http://www.nrhpsych.com/mediation/logmed.html and is also described in the paper by Mackinnon & Dwyer, 1993 (http://journals.sagepub.com/doi/abs/10.1177/0193841X9301700202). It seems that standardizing of the coefficients is required to estimate the indirect effect. I have applied this method and found similar estimates compared to the ones that Lavaan was giving. I am guessing at this point that Lavaan "correctly" handles a situation when either the mediator or the outcome is binary?

Kind regards,

Mo

### Terrence Jorgensen

Oct 11, 2018, 5:25:41 AM10/11/18
to lavaan

Put your regression equations on separate lines in the syntax

BI ~ b1 * PE + b2 * EE + b3 * SI + b4 * FC + b5 * HM + c1 * CarUse + c2 * PublicTransportUse + c3 * TechAcceptance

PE ~ a1 * CarUse + a1 * PublicTransportUse + a1 * TechAcceptance

EE ~ a2 * CarUse + a2 * PublicTransportUse + a2 * TechAcceptance

SI ~ a3 * CarUse + a3 * PublicTransportUse + a3 * TechAcceptance

FC ~ a4 * CarUse + a4 * PublicTransportUse + a4 * TechAcceptance

HM ~ a5 * CarUse + a5 * PublicTransportUse + a5 * TechAcceptance