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Instructions – Part 3 Create a dataset based on the observed coefficient estimates from the results on page 13 for the Passion → Locomotion → Grit portion of the model. Set your number of observations equal to 204, which is the same as that reported in the paper, and use set.seed(080203) for your simulation.

Then conduct a sensitivity analysis using the mediation package using this data, determining the estimated value for rho where the indirect effect would be zero. Based on this analysis, what do you conclude about the threat of omitted variable bias in the paper?

         Mean   S.D.    1    2     3

1.Passion 32.12 10.77 1 .41 .26 2.Locomotion 5.01 .57 .41 1 .43 3.Grit 3.77 3.77 .26 .43 1

N = 204 Seed 080203

Creating the correlation matrix

cov.matrix <- matrix(c(1,.41,.26,.41,1,.43,.26,.43,1),
                     nrow = 3, ncol = 3,
                     dimnames = list(c("Passion","Locomotion","Grit")))
cov.matrix

           [,1] [,2] [,3]
Passion    1.00 0.41 0.26
Locomotion 0.41 1.00 0.43
Grit       0.26 0.43 1.00

The above is the covariance matrix intended

library(MASS)
set.seed(080203)
my.ds = mvrnorm(n=204,
                mu = c(32.12, 5.01,3.77),
                Sigma = cov.matrix,
                tol = .1,
                empirical = TRUE)
my.df <- as.data.frame(my.ds)
myCov.matrix <- cov(my.df, method = c("pearson"))
round(myCov.matrix,2)

           Passion Locomotion Grit
Passion       1.00       0.41 0.26
Locomotion    0.41       1.00 0.43
Grit          0.26       0.43 1.00

The intended dataset has been obtained.

Performing the mediation analysis:

library(lavaan)
mediation.model <- 'Locomotion ~ a*Passion
                    Grit ~ b*Locomotion
                    ab: = a*b'
mediation.model.fit<- sem(mediation.model, data= my.df)
parameterestimates(mediation.model.fit)

         lhs op        rhs label   est    se      z pvalue ci.lower ci.upper
1 Locomotion  ~    Passion     a 0.410 0.064  6.420      0    0.285    0.535
2       Grit  ~ Locomotion     b 0.430 0.063  6.803      0    0.306    0.554
3 Locomotion ~~ Locomotion       0.828 0.082 10.100      0    0.667    0.988
4       Grit ~~       Grit       0.811 0.080 10.100      0    0.654    0.969
5    Passion ~~    Passion       0.995 0.000     NA     NA    0.995    0.995
6         ab :=        a*b    ab 0.176 0.038  4.669      0    0.102    0.250

fitmeasures(mediation.model.fit, c("chisq", "df", "pvalue"))

 chisq     df pvalue 
 2.119  1.000  0.146 

The chisquare shows that the model estimated is not free from alternative explainations.

library(mediation)
# We first set up our two regression equations
mediator.model <- lm(Locomotion ~ Passion, data = my.df)
outcome.model <- lm(Grit ~ Passion + Locomotion, data = my.df)
# Now we specify the full model using the 'mediate' function
mediation.si.fit <- mediate(mediator.model, outcome.model, treat = "Passion", 
                            mediator = "Locomotion", robustSE = TRUE, sims = 1000)
summary(mediation.si.fit)

Causal Mediation Analysis 

Quasi-Bayesian Confidence Intervals

               Estimate 95% CI Lower 95% CI Upper p-value
ACME             0.1593       0.0969       0.2348    0.00
ADE              0.0969      -0.0396       0.2306    0.15
Total Effect     0.2561       0.1166       0.3877    0.00
Prop. Mediated   0.6250       0.3392       1.3087    0.00

Sample Size Used: 204 


Simulations: 1000 

Calculation of Rho:

sensitivity.fit <- medsens(mediation.si.fit, rho.by = 0.1, 
                           effect.type = "indirect", sims = 1000)
summary(sensitivity.fit)

Mediation Sensitivity Analysis for Average Causal Mediation Effect

Sensitivity Region

     Rho    ACME 95% CI Lower 95% CI Upper R^2_M*R^2_Y* R^2_M~R^2_Y~
[1,] 0.3  0.0324      -0.0165       0.0813         0.09       0.0604
[2,] 0.4 -0.0168      -0.0651       0.0315         0.16       0.1074

Rho at which ACME = 0: 0.4
R^2_M*R^2_Y* at which ACME = 0: 0.16
R^2_M~R^2_Y~ at which ACME = 0: 0.1074 

The above table shows the value of ρ at which the confidence invervals contains zero for the Average Causal Mediaiton Effect. In the above analysis, we find that the confidence intervals for the ACME contains zero when ρ is between 0.3 and 0.4.

plot(sensitivity.fit, sens.par = "rho", main = "Mediator")