ARMS College 1 – Multiple Linear Regression
- Birth order effects: scientific research has demonstrated that firstborns
have higher IQ than later born (Galton, 1874). --> You have to critically
review the way the studies were performed and critically consider
alternative explanations for the statistical association. (association is not
causation).
- Adding variables
o Simple linear regression: involves 1 outcome (y) and 1 predictor
(x). (dependent variables and independent variable).
o Multiple linear regression: involves 1 outcome and multiple
predictors.
To what extend does the model explain variation in the data –
the amount of variance (R²) i.e. the sizes of the residuals.
Large R²: dots/scores are close to the line.
Smaller R²: dots/score are not very close to the line.
The slope of the regression line (B1): The predicted outcome
increases with the slope of the line. If the slope is steep, the
B1 value is large. If it is horizontal, B1 is close to 0.
- Things you need to know about Multiple linear regression (MLR)
o The model
o Types of variables in MLR
o MLR and Hierarchical MLR
Hypothesis
Output
Model fit: R², adjusted R² and R²-change
Regression coefficients: B and Beta (=standardized B)
o Exploratory MLR (stepwise) versus confirmatory MLR (forced entry)
o Model assumptions important to MLR (grasple)
- The model
o
- Types of variables
o Nominal & Ordinal are categorical or qualitative.
o Interval & Ratio are continuous or quantitative or numerical.
o MLR requires continuous outcome and continuous
predictors.
o But categorical predictors can be included as dummy
variables.
Dummy coding: dummy has only values 0 and 1.
Categorical predictors with more than 2 levels, by example
colour: multiple dummy variables.
,
- MLR and hierarchical MLR
ARMS College 2 – Moderation and Mediation
- Linear additive model: two predictors, for each of them we assume a linear relation with the
outcome variable. These effects add up.
- This week: moderation and mediation.
- Moderation: the effect of predictor X1 on outcome Y is different for different levels of
second predictor X2. Gender affects the relationship between X1 and Y.
Gender affects the relationship between X1 and Y.
Gender and X1 together have an additional effect not
captured in the two main effects.
o
- How many regression models you will see: number of outcomes * number of measures.
- Inflated type 1 error: risk of making a mistake is usually at a=0.05. They inflate when there is
multiple testing.
- Testing for interactions:
- Mediation: the effect of the independent variable on a dependent variable is explained by a
third intermediate variable.
There can be complete or partial mediation.
Notation:
- Birth order effects: scientific research has demonstrated that firstborns
have higher IQ than later born (Galton, 1874). --> You have to critically
review the way the studies were performed and critically consider
alternative explanations for the statistical association. (association is not
causation).
- Adding variables
o Simple linear regression: involves 1 outcome (y) and 1 predictor
(x). (dependent variables and independent variable).
o Multiple linear regression: involves 1 outcome and multiple
predictors.
To what extend does the model explain variation in the data –
the amount of variance (R²) i.e. the sizes of the residuals.
Large R²: dots/scores are close to the line.
Smaller R²: dots/score are not very close to the line.
The slope of the regression line (B1): The predicted outcome
increases with the slope of the line. If the slope is steep, the
B1 value is large. If it is horizontal, B1 is close to 0.
- Things you need to know about Multiple linear regression (MLR)
o The model
o Types of variables in MLR
o MLR and Hierarchical MLR
Hypothesis
Output
Model fit: R², adjusted R² and R²-change
Regression coefficients: B and Beta (=standardized B)
o Exploratory MLR (stepwise) versus confirmatory MLR (forced entry)
o Model assumptions important to MLR (grasple)
- The model
o
- Types of variables
o Nominal & Ordinal are categorical or qualitative.
o Interval & Ratio are continuous or quantitative or numerical.
o MLR requires continuous outcome and continuous
predictors.
o But categorical predictors can be included as dummy
variables.
Dummy coding: dummy has only values 0 and 1.
Categorical predictors with more than 2 levels, by example
colour: multiple dummy variables.
,
- MLR and hierarchical MLR
ARMS College 2 – Moderation and Mediation
- Linear additive model: two predictors, for each of them we assume a linear relation with the
outcome variable. These effects add up.
- This week: moderation and mediation.
- Moderation: the effect of predictor X1 on outcome Y is different for different levels of
second predictor X2. Gender affects the relationship between X1 and Y.
Gender affects the relationship between X1 and Y.
Gender and X1 together have an additional effect not
captured in the two main effects.
o
- How many regression models you will see: number of outcomes * number of measures.
- Inflated type 1 error: risk of making a mistake is usually at a=0.05. They inflate when there is
multiple testing.
- Testing for interactions:
- Mediation: the effect of the independent variable on a dependent variable is explained by a
third intermediate variable.
There can be complete or partial mediation.
Notation:
