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I have a mediation model with two continuous mediators (m1; m2), a continuous input variable (x) and a dichotomous output variable (y).

The two mediators are different mechanisms of the input variable. I understand mediation should be useful to determine whether one, both or none of the mediators increases the chances of the outcome variable to be 1.

I have tried to calculate the model with two different methods: a) the lavaan package for R, and b) Baron and Kenny's steps.

One difference in the calculations is that the lavaan modeling approach calculates the input variable x based on regression coefficients of 4 predictors, whereas for the Baron and Kenny approach the variable x is just the mean of these 4 predictors (I just didn't know how to do it).

The outcomes of the two models differ quite a lot as can be seen in the attached figures. However the main problem I have at this moment of time, is the interpretation of the coefficients. In figure 3 and 4 the estimates as they are returned from R are on the respective arrows.

Lavaan model with estimates

Lavaan model with estimates

Baron and Kenny model with estimates

Baron and Kenny model with estimates

To make some sense out of these estimates, I tried to transform then into a percentage. A percentage increase of the odds ratio of the dependent variable in case of increasing the respective predictor by 1. These are in figures 5 and 6.

Lavaan model with standardized estimates

Lavaan model with standardized estimates

Baron and Kenny model with standardized estimates

Baron and Kenny model with standardized estimates

To do so I did the following for the regression coefficients with binary outcomes:

round((exp(COEFF)-1)*100,2)

Now if I look at the lavaan model, could I say:

(1) The total effect of x on y is high (11.52%), the direct effect of x on y is rather low (-4.78%).

(2) An increase of 1 in m1, increases the odds of Y to be 1 by 90%.

Generally, is it a bad idea to try some kind of transformation here? I can't really understand how to make sense out of the different coefficients in the indirect effects paths.

#### Minimum Working Example ####

library(QuantPsyc)
library(psych)
library(lavaan)

data <- read.csv("http://dl.dropboxusercontent.com/u/63191123/data.csv", header = TRUE, sep ="\t", stringsAsFactors=TRUE)
sapply(data, mode);sapply(data, class);attach(data);head(data);psych::describe(data)


model <- ' 
# measurement model
m1 =~ m11 + m12 + m13 + m14 + m15 + m16
m2 =~ m21 + m22 + m23 + m24 + m25
m24 ~~ m25
m13 ~~ m14
m16 ~~ m21
m25 ~~ m22
m23 ~~ m24
m13 ~~ m15
m12 ~~ m13
m24 ~~ m22
'

# fit model
fit <- cfa(model, mimic="Mplus", data=data)

m1 <- (parameterEstimates(fit)[1,4] * m11 + parameterEstimates(fit)[2,4] * m12 + parameterEstimates(fit)[3,4] * m13 + parameterEstimates(fit)[4,4] * m14 + parameterEstimates(fit)[5,4] * m15 + parameterEstimates(fit)[6,4] * m16)/6
m2 <- (parameterEstimates(fit)[7,4] * m21 + parameterEstimates(fit)[8,4] * m22 + parameterEstimates(fit)[9,4] * m23 + parameterEstimates(fit)[10,4] * m24 + parameterEstimates(fit)[11,4] * m25)/5


#### Baron and Kenny ####

#<<<<<< Baron and Kenny - Step 1 >>>>>>#
Baron_c.mod <- glm(Y ~ X, family = binomial(link = "logit"))

#<<<<<< Baron and Kenny - Step 2 >>>>>>#
Baron_a1.mod <- lm(m1 ~ X)
Baron_a2.mod <- lm(m2 ~ X)

#<<<<<< Baron and Kenny - Step 3 >>>>>>#
Baron_b.mod <- (glm(Y ~ X + m1 + m2, family = binomial(link = "logit")))

# Baron and Kenny Summary:
Path_a1 <- summary(Baron_a1.mod)$coefficients[2,] 
Path_a2 <- summary(Baron_a2.mod)$coefficients[2,]
Path_b1 <- summary(Baron_b.mod)$coefficients[3,]
Path_b2 <- summary(Baron_b.mod)$coefficients[4,]
Path_c <- summary(Baron_c.mod)$coefficients[2,]
Path_c_ <- summary(Baron_b.mod)$coefficients[2,]

Baron <- rbind(Path_a1, Path_a2, Path_b1, Path_b2, Path_c, Path_c_)
print(Baron, digits=3)

#Baron.std <- rbind(lm.beta(Baron_a1.mod), lm.beta(Baron_a2.mod), lm.beta(Baron_b.mod)[2], lm.beta(Baron_b.mod)[3], lm.beta(Baron_c.mod)[1], lm.beta(Baron_b.mod)[1])
#Baron.std <- Baron.std[,1]
#Baron <- data.frame(Baron, Baron.std)


################
#### Lavaan ####
################ 


data$m1 <- m1
data$m2 <- m2

mediation <- '
X =~ x1 + x2 + x3 + x4
Y ~ b1*m1 + b2*m2 + c*X
m1 ~ a1*X
m2 ~ a2*X
indirect_m1 := a1*b1
indirect_m2 := a2*b2
total := c + (a1*b1) + (a2*b2)
'

mediation.fit <- sem(mediation, std.lv=FALSE, ordered = "Y", data=data) # 
summary(mediation.fit)


###### Standardized coefficients for logit regressions:
# e.g. for the logistic regressions:
# Baron and Kenny Model
round((exp(summary(Baron_b.mod)$coefficients[3,1])-1)*100,2) # b1
round((exp(summary(Baron_b.mod)$coefficients[4,1])-1)*100,2) # b2
round((exp(summary(Baron_c.mod)$coefficients[2,1])-1)*100,2) # c
round((exp(summary(Baron_b.mod)$coefficients[2,1])-1)*100,2) # c'

# Lavaan Model
round((exp(parameterEstimates(mediation.fit)[5,5])-1)*100,2) #b1
round((exp(parameterEstimates(mediation.fit)[6,5])-1)*100,2) #b2
round((exp(parameterEstimates(mediation.fit)[28,5])-1)*100,2) #c
round((exp(parameterEstimates(mediation.fit)[7,5])-1)*100,2) #c'
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  • $\begingroup$ I'm confused by a couple of things - your estimates are 0.109 (from glm?) and 0.172 (from lavaan?). Why aren't these the same? Second, are the percentage of variance? I'm not sure this is appropriate with a dichotomous variable. $\endgroup$ – Jeremy Miles Oct 1 '13 at 18:34
  • $\begingroup$ Also, could you post some code with a toy example? $\endgroup$ – Jeremy Miles Oct 1 '13 at 19:35
  • $\begingroup$ Thanks for your comments Jeremy. I think the differences from lavaan to glm come from my different approach in how I calculated X. I am not sure about the percentages, or the estimates in general. I can't quite understand how to find whether there is mediation or not when my mediating paths (a1*b1 and a2*b2) consist of different types of estimates (log odds and betas from lm). $\endgroup$ – Roman Oct 2 '13 at 12:44
  • 1
    $\begingroup$ You can multiple the two values, and this gives you a log odds. $\endgroup$ – Jeremy Miles Oct 2 '13 at 13:39

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