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Advanced Research Methods and StatisticsHC1 Multiple Linear Regression
Multiple linear regression
Adding variables to your model
Simple linear regression involves 1 outcome Y and 1 predictor X
o Outcome = DV = dependent variable
o Predictor = IV = independent variable
Multiple linear regression involves 1 outcome and multiple predictors
o Meerdere onafhankelijke variabelen
MLR examines a model where multiple predictors are included to check their unique linear effect on Y
Things that are important in a regression model to check if it is a good model
The amount of variance explained (R^2) i.e. the sizes of the residuals
o Smaller R^2 more residuals
o Larger R^2 higher proportion of variance that is explained by the model
The slope of the regression line (B1)
Things you need to
know about MLR
The model
Types of variables Nominal + ordinal = categorical or qualitative
Interval + ratio = continiou or quantitave or numeric
MLR requires continuous outcome and continuous predictors
Categorical predictors can be included as dummy variables
o Dummy variables has only values 0 en 1
o B1 notes the difference between 2 groups
Categorical predictors with more than 2 levels
o 3 colours 2 dummy variables
o Yellow = reference group
o
MLR and hierarchical Question 1: can life satisfaction (y) be predicted from age (x1) and years of education (x2)?
MRL hypotheses,
output, model fit: R^2,
adjusted R^2, and Question 2: are child support (x3) and spouse support (x4) improving the predicton of life satisfaction?
R^2 change,
regression
coefficients: B and
Beta (standardized B) Hypotheses
For each model
For question 2
For each predictor x within each model
R = multiple correlation coefficient (correlation between Y observed and Y predicted)
R² = proportion of variance explained: based on the sample you did the research on not a good predictor of the
variance in the population, it is always a bit too high; bias
Adjusted R² = based on estimated population value (inferential statistics) it adjust the value of R² on the basis of the
sample size (n) and the number of predictors in the model (k); lower than the proportion of explained variance in the
sample
R²-change = fit compared tot he previous model and i fit is significant does it improve the model significantly?
B (unstandardized coefficients) = what the slope is within the model it tells you what the one predictor gives of an
unique effect given the other variables are controlled for/fixed factor
Beta (standardized coefficients) = this is where you have to look to see which predictor has more effect on the outcome,
because the results are standardised
Model assumptions Independent observations
important to MLR Dependent variable should be continuous
Grasple Independent variable should be continuous or dichotomous
Linear relationship between predictors and dependent variable
Absence of outliers
Absence of multicollinearity
, Homoscedasticity
Normally distributed residuals
Artikel Kanazawa
Construct validity = the extent to which a conceptual variable is accurately measured or manipulated
The intelligence test and the methodological things +
Internal validity = the extent to which the research method can eliminate alternative explanations for an effect/relationship
No environmental explanations, the data is correlational -
Longitudinal study +
External validity = the extent to which the research results can be generalized to other populations, settings and times
Attrition, more people are excluded in the later models, babies were born on a exact data, old data -
Large sample, natural setting +
Statistical validity = the extent to which the results of a statistical analysis are accurate and reasonable
Tranparent, lot of information, tables +
A few assumptions are checked -
Assumption Multiple Linear Regression Explanation
Independent observations Observations (data of different participants) should be independent, basically meaning that the behavior of one
person does not influence the behavior of another.
Dependent variable should be continuous. The dependent variable should be a continuous measure (interval or ratio). If a dependent variable is nominal or
ordinal, it is not possible to use linear regression.
Independent variable should be continuous or The independent variable(s) should be continuous or dichotomous. A categorical predictor can be changed into
dichotomous. several dichotomous variables (dummy’s).
Linear relationship between predictors and The relationship between an independent and dependent variable should be described using a straight line.
dependent variable.
Absence of outliers (in X, Y and XY-space) Outliers should be absent from the data. Outliers are observations very different from others.
Absence of multicollinearity Independent variables should not be strongly correlated.
Homoscedasticity The residuals at each level of the independent variable(s) have similar variances.
Normality distributed residuals Residuals are the differences between the values predicted by the model and the values observed in the data
om which the model is based. These differences should be normally distributed.
HC2 Advanced Multiple Regression: Moderation & Mediaton
Moderation = the effect of predictor X1 on outcome Y is different for different levels of a second predictor X2, e.g. when X2 is gender
The effect of X1 on Y is different for males and females
Interaction effect
Path models
o Gender has an effect on the relation between X1 and Y gender = moderator
- Gender = 0 for males and 1 for females
-
- B3 shows the difference between females and males
- 2 outcomes and 5 avoidance
- 10 different analysis hoe meer analyses hoe groter de Type 1 error
o Gender and X1 together have an additional effect not captured in the two main effect
-
Further investigation of interaction is needed and called simple slope analysis
o Are the slopes of the relation of one predictor with the outcome different for different
levels of the other predictor
o GTMQ = misinterpretation
o Avoidance = independent variable
o Depression = problems = outcome
SPSS
Analyze – regression – linear: add 3 predictors
X1, X2 and X1*X2 (compute new variable)
Important: center the predictors before computing the product; this avoids multicollinearity
gemiddelde van de X1 en X2 afhalen en dan keer elkaar
Mediation = the effect of the independent variable on a dependent variabele is explained by a third
intermediate variable
Complete mediation = negative life event withdrawal behavior depression
Partial mediation = negative live event withdrawal behavior depression AND
negative live event depression
, Baron and Kenny A four step method involving 3 regression models
1. Is there a significant effect of X on Y?
2. Is there a significant effect of X on M?
3. Is there a significant effect of M on Y, controlled for X?
4. Is the effect of X on Y smaller when controlling for M?
o Criticism on 4-step method
- Step 1 = a significant effect of X on Y, that is, a significant
total effect c is not a requirement for mediation totale
effect is niet belangrijk verder voor mediatie
- The mediated effect is represented by the path a*b, that is,
the size of the indirect effect, but this method does not test
the significance of this path ze kijken niet naar de
significantie van het indirecte pad x-m-y
- Instead they use eyeballing to decide if c has become smaller, i.e., if the direct effect c’ is smaller than
the total effect c c’ vergelijken met c is geen goede manier
Sobel’s solution
o Sobel defined a test fort he indirect effect a*b
o Criticism on Sobel test
- It is based on the assumption that a*b is normally distributed but this is not correct
Bootstrapping
o Same idea as Sobel: test the significance of the indirect effect a*b
o But do not make normality assumptions
Total effect = significant
Direct effect = significant
Dus partial mediation
Bootstrap zit boven 0 dus effect is significant en de nulhypothese wordt
verworpen wel een mediator
Als er een 0 in het interval zit, dan is er geen effect en wordt de
nulhypothese aangenomen
Multiple mediator model
HC3 ANOVA & ANCOVA: comparing group means while controlling for a covariate
Analysis of variance ANOVA
Comparing groups on a continuous (interval-ratio) variable
Called analysis of variance because the analysis separates between group variation (variance explained by group) and within
group variation (unexplained/redisual variance)
ANCOVA = comparing groups means while controlling for a covariate. In an ANCOVA there is always a categorical predictor (factor) and
a covariate, which is a continuous variable.
The covariate in an ANCOVA is a variable of interval-ratio level, and can be thought of as a predictor of the DV, as in simple
regression analysis
But in an ANCOVA we also have multiple groups = hence we will havea regression line per group
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