In R, after running a logistic model
𝑚
𝑦
log
𝑖
𝑡
, what does
exp
(
𝑐
𝑜
𝑒
𝑓
(
𝑚
𝑦
log
𝑖
𝑡
)
)
provide?

Question

In R, after running a logistic model 
𝑚
𝑦
log
𝑖
𝑡
, what does 
exp
(
𝑐
𝑜
𝑒
𝑓
(
𝑚
𝑦
log
𝑖
𝑡
)
)
 provide?

BlackTom AI · Accepted Answer

Logistic regression coefficients represent log-odds, so exponentiating them converts those log-odds into multiplicative effects on the odds (odds ratios).

1) Relevant knowledge points and concepts
- A binary logistic model uses the logit link: logit(p) = log(p/(1−p)) = β0 + β1x1 + ... + βkxk.
- The fitted coefficients βj are log-odds changes: a one-unit increase in xj changes the log-odds by βj.
- Exponentiating a coefficient gives exp(βj), which is the odds ratio associated with a one-unit increase in xj (i.e., the factor by which the odds are multiplied).

2) Step-by-step reasoning
- Start from the model: log(p/(1−p)) = β0 + β1x1 + ...
- If xj increases by 1, the linear predictor increases by βj, so the new odds = exp(β0 + ... + βj*(xj+1) + ...) = exp(βj) * exp(original linear predictor).
- Therefore exp(βj) is the ratio: (new odds) / (original odds) = odds after 1-unit increase divided by odds before.

3) Example calculation (intermediate steps shown)
- Suppose β1 = 0.5. Then exp(β1) = exp(0.5) ≈ 1.6487.
- Interpretation: a one-unit increase in x1 multiplies the odds by ≈1.65 (a 65% increase in the odds).
- If β2 = −0.7 then exp(β2) = exp(−0.7) ≈ 0.4966, meaning the odds are multiplied by ≈0.50 (a 50% decrease).

4) Why the correct answer is correct
- exp(coef(model)) applies exp to each βj, converting log-odds to odds ratios. This is the standard interpretation of logistic regression coefficients and is exactly what that R expression returns.

5) Why the other options are incorrect
- The log-likelihood is a scalar given by logLik(model), not exp(coef()). 
- Predicted probabilities are obtained via plogis(predict(model)) or predict(..., type="response"), not by exponentiating coefficients.
- The odds of an event for a specific observation are exp(linear predictor) = exp(β0 + Σβj xj); exp(coef()) gives ratios (effects) not the actual odds for an observation.

6) Conclusion
Exp(coef(m_ylogit)) yields the Odds Ratios. This matches the provided correct answer: The Odds Ratios.

In R, after running a logistic model 𝑚 𝑦 log 𝑖 𝑡 , what does exp ( 𝑐 𝑜 𝑒 𝑓 ( 𝑚 𝑦 log 𝑖 𝑡 ) ) provide?Single choice

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