34
votes
Accepted
Why use odds and not probability in logistic regression?
The advantage is that the odds defined on $(0,\infty)$ map to log-odds on $(-\infty, \infty)$, while this is not the case of probabilities. As a result, you can use regression equations like
$$\log \...
- 32.2k
23
votes
Why use odds and not probability in logistic regression?
The odds is the expected number of "successes" per "failure", so it can take values less than one, one or more than one, but negative values won't make sense; you can have 3 successes per failure, but ...
- 21k
18
votes
Accepted
Interpretation of coin toss: odds of getting a tail in two coin flips
These are answers to different questions.
$75\%$ or $0.75$ is the answer to the question "What is the probability of at least one Tail when tossing a fair coin twice". You might calculate ...
- 39.6k
13
votes
Flipping Coins : Probability of Sequences vs Probability of Individuals
By default, str_count does not count overlapping occurrances of the specified pattern. The substring 1111 can overlap with ...
- 125k
11
votes
Accepted
Why is E(θ / (1 - θ)) different than E(θ) / (1 - E(θ))?
Taking an expectation does not commute with all arithmetic operations. While $E(X+Y)=EX+EY$, such a "distributivity" does not hold for other operations. For instance, the expectation of a ...
- 124k
9
votes
Accepted
A statistical interaction is significant, but the author denies it. Why?
I don't have the required reputation to vote, so I'll add it as an answer instead.
I fully agree with what @whuber said. The typical approach in this kind of study is to a priori declare a level of ...
- 449
8
votes
Why is relative risk not valid in case control studies?
I'll try to explain this more intuitively and with an illustration.
The risk ratio and the odds ratio can be interpreted and calculated as probabilities. These probabilities depend on the study ...
- 233
8
votes
Accepted
Probability of Dice and Coin flips
You have 19 sequential and independent trials, and need to be successful in all of them.
The first trial is a die roll, with a success probability of $\frac{1}{6}$.
The second trial is a coin toss, ...
- 124k
7
votes
Accepted
Why odds ratio in logistic regression
You are right. If the book said that, it is wrong. I do wonder if it is a typo or a poorly phrased passage that lends itself to misunderstanding, though. As you show, $\exp(\beta_0 + \beta_1X)$ is ...
7
votes
How should I interpret categorical with continuous variables in a logistic regression output?
Your first bullet is right for a person with a BMI of 0. Of course, no one has such a BMI. (That's assuming BMI wasn't centered or scaled).
In your second and third bullets, you left out "by a ...
- 120k
7
votes
How should I interpret categorical with continuous variables in a logistic regression output?
Programming suggestions:
Remove the asterisks from the output as this represents bad statistical practice
Don’t use long-winded function calls in formulas as this messes up all the later model output
...
- 92.1k
6
votes
Interpretation of coefficients in logistic regression output
Summary
The question misinterprets the coefficients.
The software output shows that the log odds of the response don't depend appreciably on $X$, because its coefficient is small and not ...
- 323k
6
votes
Accepted
How to get log odds from these results of logistic regression
The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the ...
- 60.8k
6
votes
Interpretation of coin toss: odds of getting a tail in two coin flips
Let $T_1$ and $T_2$ denote the respective events that each of the tosses come up tails. The second statement is effectively asserting that:
$$\mathbb{P}(T_1 \cup T_2) = \mathbb{P}(T_1) + \mathbb{P}(...
- 125k
6
votes
Interpretation of coin toss: odds of getting a tail in two coin flips
The term "expectation" in statistics means the probability-weighted average over the whole possibility space. It does not mean "the result that will happen with 100% probability". ...
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5
votes
Why use odds and not probability in logistic regression?
McCullagh and Nelder (1989 Generalized Linear Models) list 2 reasons.
First, analytic results with odds are more easily interpreted: the effect of a unit change in explanatory variable x2 is to ...
5
votes
Why is relative risk not valid in case control studies?
To obtain the relative risk you have to know the risk for each level of the exposure. If you sample people with each level of the exposure then you can estimate their risk of disease. You can then ...
- 17.8k
5
votes
Accepted
SPSS - Binary logistic regression: classification cutoff
It's easy to get confused between the two different types of probabilities that you face in this type of study. One is the probability, before you've run any tests, that someone with such a tumor has ...
- 92.4k
5
votes
Accepted
Beta regression: slope of scaled predictor
What you seem to want is an (average) marginal effect. I am not an R person, so I cannot tell you what to type, but I would be very surprised (dare I say dissapointed) if there wasn't a package to do ...
- 21k
4
votes
Accepted
Odds ratio and hazard ratio - why does this paper use both?
The assessment of severe postoperative complications was done at a fixed time (30 days) after surgery. This is a standard time point at which to evaluate short-term complications of surgical ...
- 92.4k
4
votes
Interpreting odds ratio of multiple comparisons from a logistic regression model (using R)
Here is a reproducible example:
...
- 5,353
4
votes
Accepted
Crude odds ratio
The former definition is correct. Logistic regression gives us a notion of odds ratios for continuous regressors. In the past, we preferred binary regressors because the models could be calculated ...
- 62.7k
4
votes
Accepted
3 D6 pick 2 vs 2 D6 with 1 reroll
If the goal is to obtain 7+ eyes and there is no preference about the total score otherwise - then there is no difference between rolling 3 vs rolling 2 and re-rolling the lower one when their sum is ...
- 5,051
4
votes
Difference in logits to difference in probabilities
Here are two pairs of probabilities with $\operatorname{logit} p_1 - \operatorname{logit} p_2$ equal but $p_1 - p_2$ not equal:
$p_1 = \tfrac{3}{4}$, $p_2 = \tfrac{1}{2}$
$p_1 - p_2 = \tfrac{1}{4}$
$...
- 20.1k
4
votes
Computation and Interpretation of Odds Ratio with continuous variables with interaction, in a binary logistic regression model
If your predictors A and B are both continuous and they interact in their effect, then your binary logistic regression model is:
$$
\text{log(p/(1-p))} = \beta_0 + \beta_1 A + \beta_2 B + \beta_3 A \...
- 20.3k
4
votes
Computation and Interpretation of Odds Ratio with continuous variables with interaction, in a binary logistic regression model
As others have noted, it is probably easier to interpret this graphically. I will make certain assumptions to demonstrate the thought process for interpreting interactions like this:
$A$ is my ...
- 5,197
4
votes
Accepted
What probability or weight should I assign to X so that it has a Y% chance of being one of the 6 items selected out of a population of 12?
At first, I thought a solution might require summing over all possible sequences of draws, with a resulting combinatorial explosion. But, thinking about the problem from a slightly different angle, ...
- 32.5k
4
votes
Probability of Dice and Coin flips
Instead of flipping a coin in between, you can roll a die with twelve sides. (for instance: construct the die so that there are light and dark sides numbered 1..6)
The coinflip is not needed after the ...
- 2,211
4
votes
Flipping Coins : Probability of Sequences vs Probability of Individuals
EDIT
The reason you are getting a different percentage for HHHH and HHHT is that you are calculating the instances of 1111 and 1110 in a very long string. you are not breaking these into blocks of 4. ...
- 299
4
votes
Interpretation of continuous variable in an odds ratio for logistic regression
Let's say your model, expressed in terms of odds,
$$ \dfrac{p}{1-p} = \exp(\beta_0 + \beta_1x) = B\exp(\beta_1x) $$
Here $B = \exp(\beta_0)$, and $\exp(\beta_1)=1.02$ as per your question. A ten year ...
- 36.5k
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