# Risk Difference with: Normal likelihood + identity link + robust variance estimator?

**URL:** <https://discourse.datamethods.org/t/risk-difference-with-normal-likelihood-identity-link-robust-variance-estimator/5839>\
**Category:** data analysis\
**Tags:** logistic-regression, interpretation\
**Created:** [July 25, 2022, 8:53pm UTC](https://discourse.datamethods.org/t/risk-difference-with-normal-likelihood-identity-link-robust-variance-estimator/5839 "2022-07-25T20:53:18Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![R\_cubed](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/r_cubed/32/1518_2.png) [@R\_cubed](https://discourse.datamethods.org/u/R_cubed)\
**Post date:** [July 25, 2022, 10:57pm UTC](https://discourse.datamethods.org/t/risk-difference-with-normal-likelihood-identity-link-robust-variance-estimator/5839/2 "2022-07-25T22:57:39Z")

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Perhaps I’m misunderstanding the authors, but despite referencing @Sander in their paper, they recommend OLS on the risk difference, a variable which must be constrained to a finite range, since it is the difference between 2 probabilities. In this post, he agreed with Frank that the logistic is useful in a wide number of scenarios.

> Blockquote  
> The fitted logistic probabilities can be easily used to compute estimated risks, risk ratios, risk differences, attributable fractions etc. - whatever is called for by the study context. This is not a statistical choice, but one of topic relevance, e.g., if costs are proportional to risks then risks and their differences are more relevant than odds and their ratios.

> [@Why not use the inverse logit transformation to get fitted risks (probabilities) in epi?](https://discourse.datamethods.org/t/why-not-use-the-inverse-logit-transformation-to-get-fitted-risks-probabilities-in-epi/3930/8):
>
> This topic of model-based risk and rate estimation was being covered by authors like Cornfield, Bishop and Fienberg as far back as the 1960s and some say traces back to Deming in the 1940s. By the 1990s there was a sizeable literature on it. A few points I advise taking from that literature: I am with Frank in that if you have a binomial (or Bernoulli) outcome then the statistically sensible approach is to fit a logistic model (possibly hierarchical, as with a prior or random effects) and the…

In the OR vs RR mega-thread, he had this comment:

> Blockquote  
> You know Frank I agree completely with your response and have said the same thing to colleagues who have misguidedly promoted use of log-linear risk or (worse) linear risk models. In fact I’ve been advocating our shared view on that since the 1970s (although, as I cited earlier, I have encountered exceptions in pair-matched cohorts in which log-linear risk models outperformed logistic models for a common outcome).

> [@Should one derive risk difference from the odds ratio?](https://discourse.datamethods.org/t/should-one-derive-risk-difference-from-the-odds-ratio/4403/42):
>
> You know Frank I agree completely with your response and have said the same thing to colleagues who have misguidedly promoted use of log-linear risk or (worse) linear risk models. In fact I’ve been advocating our shared view on that since the 1970s (although, as I cited earlier, I have encountered exceptions in pair-matched cohorts in which log-linear risk models outperformed logistic models for a common outcome). So perhaps you can imagine why after over 40 years I get exasperated when someon…

Some further criticism of linear models on probabilities:

> **[Another Gripe About the Linear Probability Model](https://davegiles.blogspot.com/2012/06/another-gripe-about-linear-probability.html?m=1)**
>
> Econometrics blog with EViews applications Econometrics is fun!

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