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Similar question here.

The question I highlighted above provides an overview of how generalized linear models work. However, I find people often want more and ask about how the coefficients were calculated, and how the coefficients are then turned into odds-ratios or predicted probabilities.

So if I were explaining logit models to someone with no experience with statistical modeling, how would you explain the process of going from data to coefficients, and then on to odds ratios and/or predicted probabilities with as limited math as possible?

  1. How does the model take data and produce specific coefficients?
  2. How do we get useful information from these coefficients? It's difficult to avoid math on this one, as it's important to point out how the probability curve or odds ratios are calculated.

My question deals more with 1. than 2.

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    $\begingroup$ If I had only a short period (say an hour) to discuss something like this w/ an audience that has no statistical background, I simply wouldn't try to explain these things. I would just say something like, 'we believe $X_1$ is related to whether or not we get a success, but that $X_2$ isn't'. Even 'simple' concepts like what odds & odds ratios are, are pretty foreign to most people & take a while to come to grips w/ (e.g., see my answer here: interpretation of simple predictions to odds ratios in logistic regression). $\endgroup$ – gung - Reinstate Monica May 23 '13 at 16:21
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Like @gung I would avoid part 1 altogether. But I think the odds and odds ratio can be explained fairly simply. People are familiar with odds (from betting) and a ratio is a fraction. I wrote logistic regression on my blog, it is written for neophytes.

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I've had some success at explaining logistic regression to educated non-statisticians by drawing the logistic curve, with the y-axis as probability from 0 to 1, and explaining how the coefficient indicates that marginal change in location along the S curve, which corresponds to a given probability. It helps people understand that the model assumes that the coefficients are only additive on the logit scale, which is quite nonlinear and uses a different interpretation than, say, a linear probability model. For example, a large coefficient (on a dummy variable for example) means less when the intercept is very large or small than it would if the intercept is near zero.

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