Introduction

Here you can find comparisons of results obtained in jamovi jAMM, jamovi (jmv), pure R, and SPSS. When not explicitly discussed, the code of different software is written with the aim of obtaining equivalent results across programs.

Simple mediation

Here we analyze the data discussed in the jAMM: simple mediation. Data can be downloaded from University of Virginia Research Data Service. Here we renamed the variables:

grades = X
selfesteem = M
happiness = Y

The mediation model is:

jAMM

As discussed in jAMM: simple mediation, jAMM estimation and standard statistical tests are:

The bootstrap confidence intervals (bias-corrected and accelerated) and z-tests are:

R lm()

Estimation of the regression coefficients can be obtained in vanilla R with two linear regressions:

data<-read.csv('../data/virginia_simple_mediation.csv')

mod1<-lm(selfesteem~grades,data=data)
summary(mod1)

## 
## Call:
## lm(formula = selfesteem ~ grades, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.3046 -0.8656  0.1344  1.1344  4.6954 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.49952    0.58920   2.545   0.0125 *  
## grades       0.56102    0.09448   5.938 4.39e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.639 on 98 degrees of freedom
## Multiple R-squared:  0.2646, Adjusted R-squared:  0.2571 
## F-statistic: 35.26 on 1 and 98 DF,  p-value: 4.391e-08

mod2<-lm(hapiness~selfesteem+grades,data=data)
summary(mod2)

## 
## Call:
## lm(formula = hapiness ~ selfesteem + grades, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.7631 -1.2393  0.0308  1.0832  4.0055 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.9043     0.6055   3.145   0.0022 ** 
## selfesteem    0.6355     0.1005   6.321 7.92e-09 ***
## grades        0.0396     0.1096   0.361   0.7187    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.631 on 97 degrees of freedom
## Multiple R-squared:  0.373,  Adjusted R-squared:  0.3601 
## F-statistic: 28.85 on 2 and 97 DF,  p-value: 1.471e-10

by multiplying 0.561 and 0.6355, one obtains the mediated effect 0.3565, as in jAMM. We can notice that the t-tests in R are slightly different from the z-tests in jAMM. This is simply due to the computation of the standard errors. jAMM is based on R lavaan package, that uses the expected information matrix obtain the standard errors.

C.I. with Rmediation package

In R, simple mediation models confidence intervals can be computed with the Rmediation package, which provides several methods of computation.

library(RMediation,quietly = T)
sumr1<-summary(mod1)
sumr2<-summary(mod2)
a<-sumr1$coefficients[2,1]
se.a<-sumr1$coefficients[2,2]
b<-sumr2$coefficients[2,1]
se.b<-sumr2$coefficients[2,2]

#### delta method #####
medci(a, b, se.a, se.b,type = "asymp")[1]

## $`97.5% CI`
## [1] 0.1939949 0.5190495

#### Monte Carlo method ####
medci(a, b, se.a, se.b,type = "MC")[1]

## $`97.5% CI`
##      2.5%     97.5% 
## 0.2090885 0.5326324

In R, simple bootstrap confidence intervals can be computed with the mediation package

Here are the results, again in line with the jAMM results.

library(mediation,quietly = T)

med<-mediate(mod1, mod2, treat='grades', mediator='selfesteem', sims=1000, boot = T, boot.ci.type = "bca")
summary(med)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the BCa Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME             0.3565       0.2181         0.53  <2e-16 ***
## ADE              0.0396      -0.2089         0.27    0.74    
## Total Effect     0.3961       0.1647         0.64  <2e-16 ***
## Prop. Mediated   0.9000       0.5791         3.64  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 100 
## 
## 
## Simulations: 1000

SPSS Process

In spss, one can estimate simple mediation and get confidence intervals for mediated effect using PROCESS macro. The results coincide with the jAMM results.

Recall that PROCESS uses the “percentile” method for bootstrap confidence intervals, thus, to get an even closer match between PROCESS and jAMM, one can ask jAMM to use this method as well. Here are the results, which align to PROCESS results to the second significant digit.

Notice that the “Completely standardized indirect effect” in PROCESS corresponds to jAMM \(beta\) effect, which is, as the name signals, the mediated effect obtained after standardizing all variables.

Rosetta’s files

Comments?

Got comments, issues or spotted a bug? Please open an issue on GAMLj at github“ or send me an email

Rosetta store: simple mediation