Slides presented at the Greater Cleveland R User Meetup group on the statistical concept of mediation using the lavaan package for structural equation modeling.

1. Path Analysis and Mediation in lavaan
George Mount - george@georgejmount.com - @gjmount

2. LAtent VAriable ANalysis
lavaan is available as a beta package for structural equation modeling.
In this example we will examine the mediating effects of self-esteem on the relationship
between grades and happiness.
#call lavaan
library(lavaan)
## This is lavaan 0.5-23.1097
## lavaan is BETA software! Please report any bugs.
#read file, name columns
myData <- read.csv('http://static.lib.virginia.edu/statlab/materials/data/mediat
colnames(myData) <- c("grades","selfesteem","happiness")

3. In classical statistics, a mediation model is one in which the dependent variable is
influenced by the mediator variable (B), which is influenced by the independent variable
(A). Thus the direct effect from the independent to dependent variable is insignificant
(C).

4. First we must specify the model. In lavaan the model is put in quotation marks. The
usual ~ mark is used for a regression and parameters are labeled for model specification.
set.seed(1234)
med.model <- '#direct effect
happiness ~ c * grades
#mediators
happiness ~ b * selfesteem
selfesteem ~ a * grades
#indirect effects
indirect := a*b
#direct effects
direct := c
#total effects
total := c + (a*b)'

5. To run the model, we use the sem function.
fit <- sem(med.model, data = myData)
Then we look at the results. We will choose to look at the standardized results and
model fit statistics.

6. summary(fit, standardized=T, fit.measures = TRUE, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 14 iterations
##
## Number of observations 100
##
## Estimator ML
## Minimum Function Test Statistic 0.000
## Degrees of freedom 0
## Minimum Function Value 0.0000000000000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 77.413
## Degrees of freedom 3
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -576.601
## Loglikelihood unrestricted model (H1) -576.601
##
## Number of free parameters 5
## Akaike (AIC) 1163.203
## Bayesian (BIC) 1176.229
## Sample-size adjusted Bayesian (BIC) 1160.438

7. ##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## happiness ~
## grades (c) 0.040 0.108 0.367 0.714 0.040 0.034
## selfesteem (b) 0.635 0.099 6.418 0.000 0.635 0.593
## selfesteem ~
## grades (a) 0.561 0.094 5.998 0.000 0.561 0.514
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .happiness 2.581 0.365 7.071 0.000 2.581 0.627
## .selfesteem 2.633 0.372 7.071 0.000 2.633 0.735
##
## R-Square:

8. ## Estimate
## happiness 0.373
## selfesteem 0.265
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## indirect 0.357 0.081 4.382 0.000 0.357 0.305
## direct 0.040 0.108 0.367 0.714 0.040 0.034
## total 0.396 0.110 3.600 0.000 0.396 0.339

9. Compare this to the results of regression happiness on grades.
set.seed(1234)
med.model.b <- '#direct effect
happiness ~ c * grades
#direct effects
direct := c'
fit.b <- sem(med.model.b, data = myData)

10. set.seed(1234)
med.model.b <- '#direct effect
happiness ~ c * grades
#direct effects
direct := c'
fit.b <- sem(med.model.b, data = myData)
summary(fit.b, standardized=T, fit.measures = TRUE, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 11 iterations
##
## Number of observations 100
##
## Estimator ML
## Minimum Function Test Statistic 0.000
## Degrees of freedom 0
## Minimum Function Value 0.0000000000000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 12.185
## Degrees of freedom 1
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000

11. ## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -403.548
## Loglikelihood unrestricted model (H1) -403.548
##
## Number of free parameters 2
## Akaike (AIC) 811.096
## Bayesian (BIC) 816.307
## Sample-size adjusted Bayesian (BIC) 809.990
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## happiness ~

12. ## grades (c) 0.396 0.110 3.600 0.000 0.396 0.339
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .happiness 3.645 0.515 7.071 0.000 3.645 0.885
##
## R-Square:
## Estimate
## happiness 0.115
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## direct 0.396 0.110 3.600 0.000 0.396 0.339

13. Last but not least, let’s plot our mediated model.
library(semPlot)
semPaths(fit, "model", "est", layout = 'spring',
edge.label.cex=1.25, fade=FALSE)
0.04 0.64
0.56
2.58
2.633.01
hpp
slfgrd

14. THANK YOU
Contact me:
george@georgejmount.com
@gjmount