ARMS Advanced Research Methods and Statistics (201900076)
Class notes
College notes ARMS Advanced Research Methods and Statistics ()
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Course
ARMS Advanced Research Methods and Statistics (201900076)
Institution
Universiteit Utrecht (UU)
This is a summary of lectures 1 to 5 + seminars 1 and 2 in the Advanced Research Methods and Statistics (ARMS: ) course, given at Utrecht University. With this summary, I ended this course with an 8.5.
- Y = observed outcome
- Ŷ = predicted outcome
- B0 = intercept
- B1 = slope of x1
- e = residual = error
Types of variables in MLR:
- All the variables should be Interval or ratio level (quantitative, continuous, numerical). Not
nominal or ordinal (categorical, qualitative)!
- Exception: categorical predictors can be included as dummy variables
Hierarchical MLR
- To test if the addition of a new variable is relevant. Is this model significantly and relevantly
better than the other model?
- Hypotheses:
, - Hypothese 1 → kijken naar ANOVA
Hypothese 2 → kijken naar de model summary: R2-change
- Output (voorbeeld):
- R = multiple correlation coefficient = correlation between Y and Ŷ
- R2 = proportion of the outcome explained by the model. What you compute for your sample.
- Adjusted R2 = proportion of the outcome explained by the model, corrected for the bias.
Computed for the population.
- R2-change = the difference between the first model and the additional model, with an
significance test added.
- B = unstandardized, what the relation (slope) is between the predictors in the model when the
other variable is controlled for (when age is the same, but years of education differs by one:
what is the effect on the model?). So other variables are included (unique contribution), there
is no bivariate correlation (where other variables are ignored).
- Beta = standardized B, on the same scale. Makes it possible to compare with the other
variables. Answers the question: which variable is the most important in the model?
Deciding if you have a good statistical model:
- R2 = the amount of variance explained → how well does the model fit the data?
- The slope of the regression line (B1) → the relevance of a predictor: how important is my
predictor for predicting the outcome?
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