Research Methods - Mediation and Moderation

What does the presence of this error tend to produce? (Baron & Kenny, 1986)

- Presence of this error tends to produce underestimated effect of med and overestimated effect of IV on DV when all coefficients are positive

What are 3 different categories of tests of mediation (according to MacKinnon et al., 2002)?

-Causal-steps test -Difference-in-coefficients test -Product-of-coefficients test

Why is mediation often challenging with cross-sectional data?

-Does not take into account necessary time for antecedent to affect mediator -Or mediator to outcome -May also make interpretation of ES diff. because there is no indication of time interval to which effect applies -Thus, this violates temporal precedence and greatly decreases the validity of causal inference

What are some issues with using multiple regression for moderation?

-If the distribution is not normally distributed, then bootstrapping with replacement -This term's slope represents the change in the relationship between the IV and DV given a one-unit increase in Z, however it's important to note that is does not change the causal relationship between the IV and DV as in a mediation model.

What assumptions must be met to correctly estimate mediated effect? (Fritz & MacKinnon in Laursen, Little, & Card, 2012):

-Relations between variables are correctly specified -There be no omitted variables that cause the observed effects or influence these effects, such as a moderator -Requires that X, M, and Y are valid and reliable measures of the constructs of interest -And that residuals are uncorrelated with predictors, homoscedastic, and independent of other residuals

What are the problems with using an ANOVA for moderation?

-Requires normal distribution -Assumes homodecasitity

Briefly, what are several problems with Baron & Kenny's method

-assumes IV/DV relationship has to be significant. -Assumes normal distribution -Multiple comparisons -Lack of power

Although the Baron and Kenny (1986) method is still used, it has been found to be flawed in 3 ways: (Preacher & Hayes, 2004; Hayes, 2009)

-lower powered: based on simulation studies and the multiple tests that need to be run to conduct the analysis -logically flawed: it does not explicitly test the indirect effect of the mediator, but rather infers mediation through the reduction of the effect between X and Y -too conservative: requires the experimenter to stop analysis if all steps aren't met although there may be suppression effects (Preacher & Hayes, 2004; Hayes, 2009)

What are 3 major statistical methods that can be used to analyze mediation?

1) the causal steps approach (Baron & Kenny method) , 2) the Sobel test, and 3) bootstrapping

Explain moderation in the context of an experiment

A moderator is a variable that influences effects of treatment (Shadish, Cook, & Campbell, 2002)

Explain the product-of-coefficients test

Assesses mediation by testing the product of the a and b paths for significance by dividing the product by the SE of the product and comparing the resulting quantity with a normal distribution for significance (Fritz & MacKinnon in Laursen, Little, & Card, 2012)

What are 3 positive things about bootstrapping?

Bootstrapping can be done with small samples, directly tests the indirect effect without the need to multiple tests (e.g., Baron and Kenny, 1986) and does not assume normality

Explain bootstrapping (Preacher and Hayes, 2004; Hayes, 2009).

Bootstrapping generates a sampling distribution (with replacement) of the indirect effect, and then provides a 95% confidence interval.

One common statistical method for moderation is ____________ _______________

Factorial ANOVAs

How do you determine whether or not there is a significant mediation using bootstrapping?

If 0 is within the range of the confidence interval, the mediation effect (e.g., indirect effect) is not significant. However, if 0 is not within the range of the confidence interval, there is a significant mediation

What is another major issue with the Baron & Kenny method of mediation? (Sobel, 2008)

Makes implicit assumption that the mediator itself does not suffer from unobserved confounding (Sobel, 2008)

What is a second method for statistically address moderation

Multiple Regression

What is a modern approach to addressing mediaton?

PROCESS (Hayes, 2009)

An alternative to the causal steps approach is the __________ test

Sobel

The ________ test (1982) is a very conservative test that evaluates the significance of the mediating pathway (c') by evaluating the ratio between the product of both pathways compared to the pooled variance.

Sobel

What are two issues with the Sobel test?

Sobel (1982) -Assumes normality (which typically doesn't occur) -Over corrects for multiple comparison

The causal steps approach, also known as the Baron and Kenny (1986) method follows a series of steps to determine mediation. What is the first step?

Step 1: the independent variable (X) must significantly predict the dependent variable (Y). If X does not significantly predict Y, mediation analysis stops (i.e., don't continue to next steps).

The causal steps approach, also known as the Baron and Kenny (1986) method follows a series of steps to determine mediation. What is the second step?

Step 2: X must significantly predict the mediator. Again if this requirement is not met, mediation analysis stops.

The causal steps approach, also known as the Baron and Kenny (1986) method follows a series of steps to determine mediation. What is the third step?

Step 3: the mediator must significantly predict Y, while controlling for X. Again if this requirement is not met, mediation analysis stops.

The causal steps approach, also known as the Baron and Kenny (1986) method follows a series of steps to determine mediation. What is the fourth step?

Step 4: when predicting Y from X, while controlling for the mediator, the effect between X and Y should be 0 (full mediation) or reduced from when X predicted Y without controlling for the mediator (partial mediation).

How did Baron & Kenny (1986) suggest we test mediations?

Suggested using a series of regressions

____________ ____________ is needed so that the effect one variable has on another variable requires some amount of time to occur (Fritz & MacKinnon in Laursen, Little, & Card, 2012). With what kind of data is this an issue?

Temporal precedence -Issue for cross-sectional data

Under Baron & Kenny's method, the ______________ test is not a requirement for mediation in this process (Preacher & Hayes, 2004)

The indirect test (Preacher & Hayes, 2004)

Define mediator (Shadish et al., 2002)

Third variable that comes between a cause and effect and that transmits causal influence from cause to effect (Shadish, Cook, & Campbell, 2002) Causal chain that describes how the first link in the chain, the IV, affects the last link, the DV, through all intermediary links (Fritz & MacKinnon in Laursen, Little, & Card, 2012)

Moderation: Factorial ANOVAs are the simplest design (2x2 design). Explain this method

This design has two main variables each with two levels investigating an outcome. For example two categories might be Light and Temperature with light having two levels 300lux intensity (low) and 1600lux intensity (high) and temperature having two levels 96 F (low) and 101 F (high).

Why is the Baron & Kenny method susceptible to type 2 errors?

This method suffers from low statistical power

How does Mediation improve the description and explenation of developmental processes, according to Baron & Kenny (1986)

This research is oriented in mechanism rather than exogenous variable itself (Baron & Kenny, 1986) -Speaks to why effects occur

What is assumed in the Sobel test?

This test assumes both pathways are normally distributed. Significant values suggest mediating pathways are different from zero.

Hayes' (2009) PROCESS T or F: This method doesn't assume a direct association between the IV and DV and doesn't calculate the standard error.

True

T or F: Moderation: an interaction (XZ) signifies that regression of Y on X depends on specific value of Z at which the slop of Y on X is measured (Aiken & West, 1991)

True

T or F: A mediator in one context may not mediate in another (Shadish, Campbell, & Cook, 2002)

True

Define moderation

a variable that changes the relationship between and IV and a DV. A moderator partitions the effect between the IV and DV into subgroups, rather than causally interfering with the relationship as in mediation (Baron & Kenny, 1986).

______________________ _____________ use all of the available data and allow a researcher to investigate the stability, stationarity, and equilibrium of the variables (Fritz & MacKinnon in Laursen, Little, & Card, 2012)

autoregressive models

A more recent method to test mediation is ____________ (Preacher and Hayes, 2004; Hayes, 2009).

bootstrapping (Preacher and Hayes, 2004; Hayes, 2009).

What are three flaws of the Sobel test?

can be too conservative, requires large samples, and assumes normality

Interaction exists between the IV and the third variable; such that the effect of the IV on the DV is _____________ on values of the moderator (Laursen, et al., 2012)

conditional

Moderation: With _____________ ___________, must choose several values of Z to generate series of simple regression equations

continuous variables

Explain using multiple regression for moderations

creates an interaction term and interprets the interaction term as the focal variable (IV) differs depending on the level of the moderator (Z).

How did MacKinnon (2008) describe the first-order SE test that was derived by Sobel (1982)

described that this test has higher statistical power in most situations and can test specific mediated effects for significance, as well as the overall mediated effect

Mediators are often measured with ________ (Baron & Kenny, 1986)

error

The Sobel test tests the significance of the _________ effect

indirect (i.e., the product of a and b paths, ab).

When only mediator is measured with error, the coefficient representing direct effect of D-->F is ___________ (Cole & Preacher, 2004)

inflated

Moderation: The intervening third variable in a moderation (Z) is typically investigated using an _____________ ___________

interaction term.

How does the sobel test compare to the Baron & Kenny (1986) method?

it is a more direct test of mediation than the Baron and Kenny (1986) method.

The product-of-coefficients test generalizes best to _________ data (Fritz & MacKinnon in Laursen, Little, & Card, 2012)

longitudinal

A ______________ is a variable that is intermediate in the causal pathway between the independent variable (IV) and the dependent variable (DV). The intermediate variable (M) is affected by the IV which then in turn affects the DV. (Baron & Kenny, 1986)

mediator

For both quantitative and qualitative, the ____________ is a variable that affects direction and/or strength of relation between IV and DV (________ & _____________, 1986)

moderator Baron & Kenny, 1986

What is a complete mediation?

occurs when entire effect of IV on DV passes through mediator

What is a partial mediation?

occurs when only part of overall effect of IV on DV is mediated

The Baron & Kenny method has several shortcomings. What is a potential issue that may arise (a type 1 error)?

one can see change of sig. X on Y to non-sig X on Y with addition of med with small change in absolute size of coefficient, which may lead one to conclude that a mediation effect is present when it isn't (Preacher & Hayes, 2004)

The Baron & Kenny method has several shortcomings. What is a potential issue that may arise (a type 2 error), and in what type of sample is it likely to occur?

possible to observe large change in X to Y path with addition of med without a big drop in statistical sig. (Preacher & Hayes, 2004) -This is especially true for large samples

For a moderation, one needs to probe the interaction and test ___________ ____________

simple slopes

Explain simple slopes

slope of the regression of Y on X at (conditional on) a single value of Z (b1 + b3Z) o Combines regression coefficient of Y on X (b1) with interaction coefficient (b3)

Hayes' (2009) PROCESS is a modified ____________ test focusing on effect size and confidence intervals.

sobel

PROCESS (Hayes, 2009) is now the preferred method for testing simple mediation models. More complex models should use _____________ _____________ ____________

structural equation models.

A moderator implies that....

the causal relation between two variables changes as a function of the moderator variable -Speaks to when certain effects will hold

For moderations, a hierarchical multiple regression can be conducted, where an interaction term tells you....

the change in the X to Y slope for a 1-unit Δ in Z

What is the most commonly used estimate of SE of the product ?

the first-order SE derived by Sobel (1982)

Define interaction term

the product of the independent variable and the moderating variable

What is the indirect effect (mediation)

· effect of IV on DV transmitted by mediator (Laursen, Little, & Card, 2012)