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Summary topic 1 & topic 2 AMDA SPRING
- Instelling
- Universiteit Leiden (UL)
Summary of all topics in AMDA. Each topic is described in detail, including explanations, additional clarifications, and relevant exam questions
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AMDA SPRING SUMMARY 2024Topic 1: Moderation Analysis
Two roles for the 3rd variable: Moderation & mediation
Moderators: Moderation refers to the influence of a third variable (Z) on the
relationship between two other variables (X and Y). In other words, Z moderates
or modifies the effect of X on Y.
Moderation
Characterized by an interaction effect: Relation X-Y depends on the level
or presence of Z.
The impact of X on y is not constant but changes across levels of Z.
The arrow from Z to Y is necessary.
Not too explicit about the causal process that leads to XZ interaction
Statistical analysis: ANOVA tests moderation by including the interaction term in the model. If the
interaction term is significant, it indicates that the effect of X on Y varies across levels of Z.
Nothing in the correlational structure is associated with the degree of moderation/mediation.
Mediator: Mediation refers to the process by which the effect of an independent
variable (X) on a dependent variable (Y) is transmitted through a third variable (Z),
known as the mediator.
Mediation
Indirect effect: The effect of X on Y is explained by (partly) Z. The pathway
from X to Y through Z is called the indirect effect.
Helps understand the mechanism or process through which X affects Y.
Statistical analysis: Examine the direct and indirect effects
Four cases based on measurement levels:
1. X & Z interval: Regression
2. X nominal, Z interval: ANCOVA
3. X interval, Z nominal: ANCOVA
4. X and Z nominal: ANOVA
To be sure:
Nominal = categorical variables. Without specific unity or order. Like gender.
Interval: Variables where the distance between time points is equal. The zero/starting points
are not necessary. Like temperature and IQ.
1. Regression:
Standard regression: Main effect only. With identical regression weights (parallel lines
Interaction added: Product term. y=b 0+b 1 X +b 2 Z + B 3 XZ
o Different regression weights > nonparallel regression lines interaction
o Choose values that suit the research purpose best
,Linear-by-linear interaction: The interaction term ‘ XZ’ describes a linear relationship between Z and
the regression weight for the X-Y relation.
Testing the interaction effect: To see if there is a significant interaction between X and Z.
We examine the coefficient b3 H0: b3 =0, Ha: b3≠0.
Graphing the interaction: Plot regression lines for different values of Z.
Choose values of Z such as Mz – SDz and Mz + SDz
Regression lines within the observed range of Z
The XZ product is not the interaction on its own. It becomes the interaction when the
lower-order effects X and Z are also in the regression equation. So when computing
interactions, always include all relevant lower-order effects, also for AN[C]OVA.
Centring X and Z = Transforming them into deviations from their mean. This is preferable:
To prevent multicollinearity: The interaction is usually highly correlated with X and Z.
Centring lowers the correlations of XZ with X and Z.
To interpret the main effects: After centering, b1 gives the effect of X on Y at the mean of Z,
providing an average effect.
o Without centering, the regression weight b1 refers to the specific effect of X on Y
when Z=0, which may be unnatural or out-of-range. How: Descriptive the variables
used in the regression analysis.
Compute the variables:
Centred Variable = [variable] – [mean variable]
Centered interaction term = centered variable a * centered variable b
When you compare the centered and uncentered analyses with each other:
When the interaction term is not included in the regression model, the regression weights
(coefficients) for the predictors X and Z will be the same whether the predictors are centered
or uncentered. The only difference will be in the constant (intercept) term.
o Uncentered predictors: The intercept represents the expected value of Y when X and
Z are both zero.
o Centered predictors: The intercept represents the expected value of Y when X and Z
are at their respective means.
Results with the interaction term: The main effect regression weights differ between centered
and uncentered predictors
o Centered predictors make the interpretation clear, as zero corresponds to the mean
o Uncentered predictors use raw values, making zero a numerical placeholder without
a clear interpretation
Testing the interaction using Hierarchical regression:
Model 1 includes X and Z:
Y= b0 + b1X + b2Z
Model 2 includes X, Z, and interaction XZ:
Y=b0+b1X+b2Z+b3XZ
The interaction effect is significant if the interaction term b3 is significant in model 2. If not, we prefer
the simpler model 1 without.
, Interpretation:
Use unstandardized weights (b’s) for interpretation
Negative interaction regression weight means that the positive stress-depression relationship
becomes weaker with higher levels of social support. agrees with buffering hypothesis
Compute regression lines for three levels of support They will have different slopes
In SPSS example:
1. Compute the means and SD descriptives
2. Compute the centered variables and interaction term:
o Centered: Subtract the mean from each value.
o Interaction: Multiply the centered variables
3. Hierarchical regression analysis:
o Block 1: 2 predictors
o Block 2: add the interaction term
4. Interpretation: Look at the coefficients and significance of both models 1 and 2.
Does adding the interaction term change the main effects?
Unstandardized weights: Use these for interpretation
5. Computing regression lines for different levels of Z (average, one SD below and above)
Interaction in ANCOVA (nominal & interval predictor):
Case 2: Nominal X, interval Z.
Differences between groups (x) on Y vary with different levels of Z
Case 3: X interval, nominal Z.
Regression slopes of Y on X differ across groups defined by Z.
Regardless of which variable is the predictor/moderator, The interaction is the same, swapping the
direction of which one is the moderator.
Violation of parallel assumption: Standard ANCOVA assumes that the relationship between the
covariate (interval predictor) and the dependent variable (Y) is the same across all groups defined by
the nominal preditor. Interaction violates this assumption: The slopes are not parallel.
Step 1: Standard ANCOVA with only main effects of factor and covariate. Test the main effects.
Step 2: Add covariate x factor interaction (model window SPSS)
Ignore all main effects. This is highly misleading since they assume that the other predictor is
zero, which is not meaningful.
Step 3: Decide. If the interaction is significant: Compute/draw separate regression lines for the
different groups. If the interaction is significant, this indicates that the effect of one predictor on the
dependent variable depends on the level of the other predictor.
Compute simple regression lines of Y on the covariate after a ‘’split file…’’ by the groups of the
factor
Draw regression lines via a scatterplot of Y with the covariate with markers set by the factor.
Double-click the graph in your output. Ask for separate lines for each group (fit liens at
subgroups in the elements menu).
Interaction in ANOVA (nominal predictor & nominal moderator):
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