Advanced research methods - Lecture 3

Lecture 3 + notes

What can we say about the outcome of a logistic regression?

Outcome is always dichotomous / dummy (0/1 - yes/no).

How do RQ start?

How likely is it that …

What happens if you fit an OLS on this?

You get a weird, untrue line between outcomes.

Model suggests that the outcome can be *between* yes and no for X between -1 and +1

What if X < -1 or X>1 in logistic regression?

The curve approaches -1 and 1, but it takes much more time.

What is the difference in equation between OLS and logistic regression?

OLS: Y = β0 + β1 \* X1 + …

* Left side: X1 is linearly associated with the outcome
* Outcome = continous

Logistic = Ln(p/(1-p)) = β0 + β1 \* X1 + …

* Left side: X1 is linearly associated with the log of the odds of the outcome


* odds = (p/(1-p))
* Outcome = dichotomous

What can you use a OLS and logistic regression for?

OLS: Predict an outcome

* His predicted (*average*) weight is 80 kg (OLS)

Logistic: Predict the probability of an outcome

* There is a 15% chance that he weighs more than 70 kg (Logistic)

What is the difference in interpretation between OLS and logistic regression?

OLS

* presented in terms of B
* For each x increase, y incerases on an average …

→ **Direction and size of effect**

Logistic regression

* presented in terms of B or OR
* Positive or negative B indicates that the probability of being > 70 kg increases with height

**→ Direction of effect**
* OR >1 (or <1) indicates that the probability of being >70 kg is larger (or smaller) for people with more height

**→ Direction of effect**

How do you interpretate B coefficient for OLS?

For each unit increase in X, the outcome (Y) increases/decreases on average with … (coeffecient) (linear shape graph)

How do you interpretate B coefficient for logistic regression?

For each unit increase in X, the probability of the outcome (Y) increases / decreases. (S-shape graph)

OLS: How do you interpreate measures of association for weight?

Average weight men = 85, women = 72

* Absolute difference in means = 85-72= 13 kg
* Relative difference (ratio) = 85/72=1,18
* On average, men are 1.18 times as heavy as women
* On average, men are 18% more heavy than women

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Logistic regression: How do you interpretate measures of association for weight?

Proportion (/probability) men: 48%, women 40%

* Risk difference (absolute) = 48%-40%=**8% points**
* Risk difference (relative risk) = 48%/40% = 1.2
* Men are 1.2 times as likely to be overweight as woman.
* Men are 20% more likely to be overweight than women are.

Berekening kan ook andersom, wel resultaten anders interpreteren.

How do you interpretate the B coefficient and the OR odds ratio for logistic regression?

β = 0: no difference in probability (no effect) between groups

β > 0: higher X means *higher* probability of Y between groups

β < 0: higher X means *lower* probability of Y between groups

\
OR is the ratio between the odds of being overweight for men compared to the odds of being overweight for women

* OR = 1: no difference in odds (no effect)
* OR > 1: higher odds of Y
* OR < 1: lower odds of Y

What is the marginal effect?

Comparison between ‘everyone gets treated’ and ‘no one gets treated’ (i.e., we will simulate counterfactual outcomes)

What is table 2 fallacy?

Fallcy is t o interpret all coefficients in the same way.

* That it is wrong to assume that all coefficients from one regression model can be interpreted in the same way
* Some coefficients represent full effects, some partial effects
* Some coefficients are unbiased, some are biased

What about coefficients for confounders?

They may always be biased (there will likely always be some U for which you cannot adjust).

Confounders are not randomized.

Uncontrolled unknown confounding is possible in RCT. Careful with interpretating → table 2 fallacy.