Overview

• Quick Mediation Recap

  • Total effects, indirect effects, & direct effects

• 1-Mediator Model

  • Defining our model
  • Fitting our model
  • Summarising our model
  • Interpreting our model
  • Building our model

• 2-Mediator Model

  • Defining our model
  • Fitting our model
  • Summarising our model
  • Interpreting our model
  • Building our model

Mediation Recap

• Mediation occurs when the relationship between a predictor and an outcome, can be explained by their relationship to a third variable: the mediator

• We're looking at how variables are related, we're attempting to further our understanding by explaining the relationship between the predictor and the outcome

• With mediation, we're interested in pathways between variables:

Mediation Recap

• We start with the Total Effect, which is the simple relationship between predictor and outcome, where we're not adjusting for any other variables:

Mediation Recap

• We then partition this Total Effect into:

  • An Indirect Effect which is the effect of the predictor on the outcome, through the mediator

  • & a Direct Effect which is the effect of the predictor on the outcome, adjusting for the mediator

Mediation Recap

• The Total Effect is comprised of the Indirect Effect AND the Direct Effect

• Even though we call it the Total Effect, it's still just the simple relationship between predictor and outcome - we haven't accounted for any other variables

• By adding in a mediator, we can see how much of this Total Effect is a Direct Effect of our predictor, and how much can be explained by our mediator (i.e., the Indirect Effect)

Mediation in R

• Relatively straightforward to do in R with a 3-step process:

  • Define model

  • Fit model

  • Summarise model

• We can then interpret our results and build our model!

Step 1: Define Model

• We define our model by writing out the paths as a string of text

• We then save it into an object ('my_mod') that we can call on when we fit our model in step 2...

  • The code looks scarier than it really is, we're just labelling and defining each pathway:

my_mod <- 'outcome ~ c*predictor + b*mediator
           mediator ~ a*predictor
           indirect_effect := a*b
           total_effect := c + (a*b)
          'Copy Code

Step 1: Define Model

• So, we can use this syntax, replacing the 'outcome', 'predictor' and 'mediator' with the names of the variables in our data:

my_mod <- 'maths_att ~ c*ses + b*parent_inv
           parent_inv ~ a*ses
           indirect_effect := a*b
           total_effect := c + (a*b)
          'Copy Code

Step 2: Fit Model

• To fit our mediation model we use the sem() function from the lavaan package

• Here we specify the name of the model we just defined in step 1, the name of our data, how we want to handle missing data, and the estimation method we want to use...

my_fit <- lavaan::sem(my_mod, data = my_data, 
                    missing = "something", estimator = "something")Copy Code

A Missing Data Detour...

• By default, the sem() function will use listwise deletion to deal with any missing data

• Listwise deletion this is where an entire participant is excluded from analysis if any single variable is missing

• A better method to use that's available in the sem() function is full information maximum likelihood estimation (aka FIML - no, not FML...)

• FIML produces unbiased parameter estimates and standard errors where there are missing data 🥳

  • We would use missing = "FIML" in the previous code to change this option!

A Missing Data Detour...

• We can only use FIML when we use maximum likelihood estimators

• Maximum likelihood estimators work by choosing the parameters that make the data most likely to have happened

• We would use estimator = "ML" in the previous code to change this option!

• We can also use estimator = "MLR" instead to get robust standard errors (always a good idea!)

• So our code becomes:

my_fit <- lavaan::sem(my_mod, data = my_data, 
                            missing = "FIML", estimator = "MLR")Copy Code

Step 3: Summarise Model

• Once we've fit our model using appropriate methods for handling missing data, we can summarise it with a few different functions():

• broom::glance() allows us to look at how good our model is - the model fit statistics:

                   broom::glance(my_fit)Copy Code

• broom::tidy() allows us to look at our actual effects - the model parameters:

              broom::tidy(my_fit, conf.int = TRUE)Copy Code

Step 4: Interpret Model

• The output of broom::tidy() is the part we're most interested in!

Step 4: Interpret Model

• The key parts are in bold:

Step 5: Build Model

• We can use semPlot::semPaths() to build a diagram of our model, but making it look pretty is quite tricky

• Instead we can use any other software to create it (Word, PowerPoint etc.)

• We can take each of the estimates from our broom::tidy(my_fit, conf.int = TRUE) summary, putting them into the correct paths:

2-Mediator Model

• We can extend our mediation model to include an additional mediator:

2-Mediator Model in R

• To give this a go in R, let's have a look at the following model:

• Here our predictor is maths anxiety, our outcome is maths attainment, our first mediator is general anxiety, and our second mediator is test anxiety

• With this model, we're saying that the relationship between maths anxiety and maths attainment can be explained by general and test anxiety

2-Mediator Model in R

• With 2 mediators, our model is largely the same - we just have to add in another a pathway, another indirect pathway, & model the relationship between our two mediators

my_mod_2 <- "outcome ~ c*predictor + b1*med_1 + b2*med_2
                  med_1 ~ a1*predictor
                  med_2 ~ a2*predictor
                  indirect_med_1 := a1*b1
                  indirect_med_2 := a2*b2
                  total_effect := c + (a1*b1) + (a2*b2)
                  med_1 ~~ med_2
                  "Copy Code

• We just need to change the labels to match the variables in our dataset like we did before!

2-Mediator Model Interpretation

• The interpretation of our mediation is the same as before:

  • We can look at the parameter estimates, confidence intervals, and p-values to see if we have a mediation effect

*all results are fictional 😉

That's all - foreveR! 😱💔