<p>Coefficients from logit have essentially no practical interpretation.</p>
<p><span class="math-container">$$Pr(y = 1 |X) = \frac{e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}{1+e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}$$</span></p>
<p>It's really not obvious how to interpret <span class="math-container">$\beta_j$</span> for any <span class="math-container">$j$</span>.</p>
<p>The marginal effect is: <span class="math-container">$$\frac{\partial Pr(y=1|X)}{\partial Xj}= \beta_j \frac{e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}{(1+e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}})^2} $$</span></p>
<p>The marginal effect is the derivative of <span class="math-container">$Y$</span> with respect to <span class="math-container">$X$</span>, this is easier to interpret. Marginal effects can be evaluated (1) for a specific individual, plugging that individual's X values, (2) for the mean individual, plugging in the average of X for all individuals, or (3) for all individuals, then averaged.</p>
<p>The third option is &quot;average marginal effects&quot;, and typically considered &quot;best&quot;.</p>
<p>My slides on this are <a href="https://drive.google.com/file/d/1U4cdqA-22O1k4CtrF9o7kt85681Cn6eI/view" rel="nofollow noreferrer">here</a>. Logit starts around slide 20 and I talk about marginal effects around slide 30.</p>
<p>I'm not sure if I answered your question, so feel free to follow up.</p>

CC BY-SA 4.0
2022-04-29T10:11:59.510Z
2022-05-02T08:52:58.043Z
2022-05-02T08:52:58.043Z
Michael Gmeiner
<p>I am asked to interpret the coefficients of the specification showed the marginal effects of <a href="https://quantifyinghealth.com/interpret-logistic-regression-coefficients/" rel="nofollow noreferrer">Logit regression</a>.</p>
<p>I am wondering if there is any reference for this work. I am finding <a href="https://quantifyinghealth.com/interpret-logistic-regression-coefficients/" rel="nofollow noreferrer">a link that is quite useful in interpreting the coefficients in the Logit model</a> but not sure if it is different from the &quot;marginal effects of Logit regression&quot;.</p>

<econometrics><reference-request>
How to explain the coefficients in the marginal effects of Logit regression?
Phil Nguyen
# How to explain the coefficients in the marginal effects of Logit regression?

(Asked by: username_0 on 2022-04-29)

I am asked to interpret the coefficients of the specification showed the marginal effects of [Logit regression](https://quantifyinghealth.com/interpret-logistic-regression-coefficients/).

I am wondering if there is any reference for this work. I am finding [a link that is quite useful in interpreting the coefficients in the Logit model](https://quantifyinghealth.com/interpret-logistic-regression-coefficients/) but not sure if it is different from the "marginal effects of Logit regression".

**Tags:** econometrics, reference-request

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## 1 answers

### Answer by username_1 on 2022-04-29. Score: 3

Coefficients from logit have essentially no practical interpretation.

$$Pr(y = 1 |X) = \frac{e^{\beta\_0 +\beta\_1 x\_{1i}+...+\beta\_k x\_{ki}}}{1+e^{\beta\_0 +\beta\_1 x\_{1i}+...+\beta\_k x\_{ki}}}$$

It's really not obvious how to interpret $\beta\_j$ for any $j$.

The marginal effect is: $$\frac{\partial Pr(y=1|X)}{\partial Xj}= \beta\_j \frac{e^{\beta\_0 +\beta\_1 x\_{1i}+...+\beta\_k x\_{ki}}}{(1+e^{\beta\_0 +\beta\_1 x\_{1i}+...+\beta\_k x\_{ki}})^2} $$

The marginal effect is the derivative of $Y$ with respect to $X$, this is easier to interpret. Marginal effects can be evaluated (1) for a specific individual, plugging that individual's X values, (2) for the mean individual, plugging in the average of X for all individuals, or (3) for all individuals, then averaged.

The third option is "average marginal effects", and typically considered "best".

My slides on this are [here](https://drive.google.com/file/d/1U4cdqA-22O1k4CtrF9o7kt85681Cn6eI/view). Logit starts around slide 20 and I talk about marginal effects around slide 30.

I'm not sure if I answered your question, so feel free to follow up.


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