Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [beta-regression]

Beta regression is useful when the dependent variable is bounded, or when it has a ceiling or floor effect. It can also be used for modeling both the mean and the variance.

A useful summary is Smithson and Verkullen.

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Regression for an outcome (ratio or fraction) between 0 and 1

I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a > 0$ and $b > 0$. So, the ratio would be between $0$ and $1$. I could use linear regression, although it doesn't naturally limit to 0..1. I have no reason to believe…
dfrankow
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Why Beta/Dirichlet Regression are not considered Generalized Linear Models?

The premise is this quote from vignette of R package betareg1. Further-more, the model shares some properties (such as linear predictor, link function, dispersion parameter) with generalized linear models (GLMs; McCullagh and Nelder 1989), but…
Firebug
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Beta regression of proportion data including 1 and 0

I am trying to produce a model for which I have a response variable which is a proportion between 0 and 1, this includes quite a few 0s and 1s but also many values in between. I am thinking about attempting a beta regression. The package I have…
Jonathan Bone
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Dealing with 0,1 values in a beta regression

I have some data in [0,1] which I would like to analyze with a beta regression. Of course something needs to be done to accommodate the 0,1 values. I dislike modifying data to fit a model. also I don't believe that zero and 1 inflation is a good…
dave fournier
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Why exactly can't beta regression deal with 0s and 1s in the response variable?

Beta regression (i.e. GLM with beta distribution and usually the logit link function) is often recommended to deal with response aka dependent variable taking values between 0 and 1, such as fractions, ratios, or probabilities: Regression for an…
amoeba
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Why use the logit link in beta regression?

Recently, I have been interested in implementing a beta regression model, for an outcome that is a proportion. Note that this outcome would not fit into a binomial context, because there is no meaningful concept of a discrete "success" in this…
Ryan Simmons
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How to implement a mixed model using betareg function in R?

I have a dataset comprised of proportions that measure "activity level" of individual tadpoles, therefore making the values bound between 0 and 1. This data was collected by counting the number of times the individual moved within a certain time…
Kat Y
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Variance-covariance matrix of the errors in linear regression

How is the var/cov error matrix calculated by statistical analysis packages in practice? This idea is clear to me in theory. But not in practice. I mean, if I have a vector of random variables $\textbf{X}=(X_{1}, X_{2}, \ldots, X_{n})^\top$, I…
Riccardo
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How can I model a proportion with BUGS/JAGS/STAN?

I am trying to build a model where the response is a proportion (it is actually the share of votes a party gets in constituencies). Its distribution is not normal, so I decided to model it with a beta distribution. I also have several predictors.…
Joël
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Dealing with regression of unusually bounded response variable

I am attempting to model a response variable that is theoretically bounded between -225 and +225. The variable is the total score that subjects got when playing a game. Although theoretically it is possible for subjects to score +225. Despite this…
Jonathan Bone
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interpretation of betareg coef

I have a data that where the outcome is the proportion of a species observed in an area by a machine on 2 separate days. Since the outcome is a proportion and does not include 0 or 1 I used a beta regression to fit the model. Temperature is used as …
user3022875
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What's a time series model for forecasting a percentage bound by (0,1)?

This must come up---the forecasting of things that are stuck between 0 and 1. In my series, I suspect an auto-regression component, and also a mean-reverting component, so I want something that I can interpret like an ARIMA---but I don't want it to…
Mittenchops
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How do you report results from a Beta Regression (R output)?

I am looking for advice/input on how to report results from a beta regression output. My data is bound between 0 and 1, as ratios, and I am looking at a simple relationship between the response variable (D_Ratio), and predictor (body length, or BL)…
Kat Y
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Negative deviance explained by GAM with betareg in R

I am fitting the following model in "mgcv" package in R using option family=betar to predict a percentage cover response variable (cyano %): g6 = gam(cyano/100 ~ s(SEGLOWFLOW) + s(SEGJANAIRT) + s(LOCHAB) + s(LOCSED) +…
jatalah
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What is the difference between beta regression and quasi glm with variance = $\mu(1-\mu)$?

First let me give some background; I will summarize my questions at the end. The Beta distribution, parameterized by its mean $\mu$ and $\phi$, has $\operatorname{Var}(Y) = \operatorname{V}(\mu)/(\phi+1)$, where $\operatorname{V}(\mu) = \mu(1-\mu)$…
Andrew Milne
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