When to use logistic regression and when to use beta regression in statistical modeling for given data? How do know the difference between them? And when can I fit just a linear regression and not worry about anything for data?
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For the question of
When to use logistic regression and when to use beta regression in statistical modeling for given data?
- A logistic regression is most commonly used when modelling a response variable $Y_i$ which can only take on two values $\{0, 1\}$ or $\{\text{false}, \text{true}\}$ (depending on your modelling scenario).
- A Beta regression can be used when your response variable can only take on values within open interval $Y_i \in (a, b)$ $a,b \in \mathbb{R}$. The most natural interval for the beta distribution being $[0,1]$ or $(0,1)$, however, and it can be generalised to apply to any open interval $(a,b)$ through the appropriate transformation.
How do know the difference between them?
- A Logistic regression typically models a binary response, whereas a beta regression models a continues a continuous response which must lie in the open interval $(0,1) \ \text{or} \ (a,b)$
And when can I fit just a linear regression and not worry about anything for data?
In all cases, when fitting a linear regression there are a set of assumptions that that must be verified this to be an appropriate model for the data at hand, and for any insights garnered from that model to be valid. These are assumptions for linear regression are listed here. This is also true for the assumptions behind Beta Regression (See "Variable dispersion beta regression" section) and those behind Logistic Regression.
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1$\begingroup$ Your first two bullets are fine, but your last bullet is misleading. Logistic regression does not assume normality of residuals (I think you probably know that, but the way you've written could lead to confusion). Probably better to list the assumptions of logistic and beta regression separate.y. $\endgroup$ Commented Jun 8 at 11:43
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$\begingroup$ @PeterFlom sorry for the confusion. The third bullet point was in answer to the third part of the question "And when can I fit just a linear regression and not worry about anything for data?". It has been edited now. $\endgroup$– den173Commented Jun 8 at 12:23
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$\begingroup$ Logistic regression doesn't have to model just a binary response. As far as I know, it can also fit models which contain count proportions which range between $0$ and $1$ using a quasibinomial fit. $\endgroup$ Commented Jun 8 at 12:29
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1$\begingroup$ Just use the standard proportional odds semiparametric ordinal logistic regression model, which unlike beta regression does not assume a specific distribution for Y and allows for arbitrary lumpiness in the distribution. Resources are here. $\endgroup$ Commented Jun 8 at 13:00