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ARMS - Advanced Research Methods and Statistics UU
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Hoorcollege aantekeningen ARMSWoensdag 5 februari 15:15
Introductie ARMS & multiple linear regression
Tentamens general part: 60% van het cijfer. Theorie is 45% en SPSS skills is 15% (open
boek). Grootste deel is MC.
Alles is in Engels, dus ook vragen op het discussiebord en tentamen.
Birth order effect is an example of questionable correlational research. Watch out for 3rd
variables and don’t think correlation means causation.
Simple linear regression involves 1 outcome (Y) and 1 predictor (X)
- Outcome = dependent variable
- Predictor = independent variable
- Yi = B0 + B1Xi + ei
- Equations are in the book as well so you don’t need to study those! If necessary they
will be in the Field book as well. These ones they don’t consider being equations so
you do have to study those.
Multiple linear regression involves 1 outcome (Y) and multiple predictors.
- Yi = B0 + B1X1i + B2X2i + B3X3i + ei
Relevance of a predictor:
- R2 = amount of explained variance by the model. Larger = less residuals and so the
dots are closer to the line of Yi.
- B1 = slope of the regression line. Steep = high B value = more relevant.
- How well does it explain the data and how important is the effect?
Look at slide to see what exactly you need to know for the test.
The model: Yi = B0 + B1X1i + B2X2i + B3X3i + ei
- B0 = intercept
- B1/2/3 etc. = slope
- E = residual
ŷ = prediction of y = multiple linear regression and the statistical part = additive linear model.
Yi = observed score = ŷi + ei.
4 levels of measurement:
- Nominal
- Ordinal
- Interval
- Ratio
,Most important distinghuishments: nominal vs ordinal (qualitative, categorical) or interval vs
ratio (quantitative, continuous).
MLR requires continuous outcome and continuous predictors. But categorical predictors can
be included as dummy variables.
- Dummy variables = categories made numerical with labels. Always values 0 and 1.
- ŷi = B0 + B1 x D1,i
- So ŷ1 = B0 + B1 and ŷ0 = B0, and so the value of B1 here is the difference between
groups.
- More than 2 levels: D is replaced with variables for every category. So B1bluei +
B2redi + B3yellowi for example. Its red or not, so red = 1, blue, green and yellow = 0.
Always one dummy variable less than the amount of categories!
- Intercept here is the average of y for the reference group.
Hypothesis:
- 2 factor model:
o H 0 = R2 = 0
o Ha = R2 > 0.
- 4 factor model as replacement:
o H0 = R2 – change = 0
o Ha = R2 – change > 0
o Additional predictors do (not) improve the model.
- For each predictor x within each model:
o H 0 = B1 = 0
o H a = B1 ≠ 0
o No unique effect of x within this model.
Adjusted R2 in output = estimated population value instead of sample value.
R2 change in output = model 2 instead of model 1.
Significance in table of R2 change? There is a significant improvement of adding extra
predictors to the model. Significance in the ANOVA table is about whether the model 2 itself
is significant.
R2 = multiple correlation coefficient = Y - ŷ.
Inferential statistics = generalising outcomes to the population, estimating the population
values.
More predictors = more optimistic, so a lot of predictors = big chance of a bias. Adjusted R2 is
adjusted for this bias, needed when you want to say something about the population.
R2 change for the first model is the same as the normal R2 for the model, only when you look
at model 2 you see the difference in R2 between the two models. The R2 change is based on
the normal R2 and not the adjusted version, because calculations are based on the sample.
, B1 values can change between models 1 and 2 because there are different predictors. So all of
the values can change when switching models, even the already present ones!
B2 value is the difference between people when controlled for the other variables. So
everything is fixed except for the B value you are looking at. What does this variable do when
all others are encountered for, the unique variable effects.
Bivariate correlation versus unique contribution within a model??
Beta can be negative and positive, the minus isn’t important, you only look at the numbers!
(skipped slide 24 and 25 or 26 and 27)
Woensdag 12 februari
Moderation and mediation
Linear additive model: more effects, they add up to each other. All linear relationships.
Moderation
Moderation: the effect of predictor X1 on outcome Y is different for different levels of a
second predictor X2. ‘The effect of X1 on Y is different for different groups/people’. =
interaction effect.
Two ways to graph: first one more theoretical, second
one more statistical (via MLR).
Statistical model moderation and interaction is the
same, the difference is in theory. In the statistical
model you don’t see which variable is the moderator,
in the theoretical model you see what the moderator
is. So statistically the same, but from the research
question it will be clear which one you are testing.
ŷ = b0 + b1X1i + b2Genderi + b3X1iGenderi
- Moderator = gender, both variables have their
own intercept and slope, combined in this equation.
- Men = 0, female = 1.
- So equation for men only contains the first two bits. The slope is B1.
- Females score 1 on both gender variables. The slope is B1+B3. Intercept is B0 + B2,
because they don’t contain an X.
o B0 + B2 + B1X1i + B3X1i = (B0 + B2) + (B1 + B3)X1i
o B3 tells us what the difference in slopes is between males and females.
o Statistical tests will tell if this difference in slopes is significant.
You can see a moderator as a form of therapy, you cannot change that things happen, but you
can help people cope with them and reduce their problems.
Hierarchical regression: does adding the extra predictor improve the model? Last week.
Mostly looking at values of R2 change.
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