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28 votes

How to implement a mixed model using betareg function in R?

The package glmmTMB may be helpful for anyone with a similar question. For example, if you wanted to include pond from the above question as a random effect, the following code would do the trick: <...
Kori K's user avatar
  • 406
25 votes
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Why Beta/Dirichlet Regression are not considered Generalized Linear Models?

Check the original reference: Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799-815. as the authors note, ...
Tim's user avatar
  • 140k
21 votes
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Why exactly can't beta regression deal with 0s and 1s in the response variable?

Because the loglikelihood contains both $\log(x)$ and $\log(1-x)$, which are unbounded when $x=0$ or $x=1$. See equation (4) of Smithson & Verkuilen, "A Better Lemon Squeezer? Maximum-Likelihood ...
Kevin Wright's user avatar
16 votes
Accepted

How to implement a mixed model using betareg function in R?

The current capabilities of betareg do not include random/mixed effects. In betareg() you can only include fixed effect, e.g., ...
Achim Zeileis's user avatar
16 votes
Accepted

Why use the logit link in beta regression?

Justification of the link function: A link function $g(\mu): (0,1) \rightarrow \mathbb{R}$ assures that all fitted values $\hat \mu = g^{-1}(x^\top \hat \beta)$ are always in $(0, 1)$. This may not ...
Achim Zeileis's user avatar
14 votes
Accepted

interpretation of betareg coef

Yes, the logit link can be interpreted like that. It's just not a change in "odds" (= ratio of probabilities) but a change in a ratio of proportions. More formally, the model equation for the ...
Achim Zeileis's user avatar
12 votes
Accepted

Regression Bounded Between -1 and 1

You can always use beta regression (Ferrari and Cribari-Neto, 2004). It's a model for response variable bounded in $(0, 1)$, but you can easily transform your variable by taking $\frac{Y+1}{2}$ (I ...
Tim's user avatar
  • 140k
12 votes

Why use the logit link in beta regression?

It is incorrect that the logistic regression can only be used to model binary outcome data. The logistic regression model is appropriate for any data where 1) the expected value of outcome follows a ...
AdamO's user avatar
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12 votes
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Proportion data with number of trials known (and separation?): GLM or beta regression?

The data you have are really a classic binomial setting and you can use binomial GLMs to model the data, either using the standard maximum likelihood (ML) estimator or using a bias-reduced (BR) ...
Achim Zeileis's user avatar
11 votes
Accepted

What is the difference between beta regression and quasi glm with variance = $\mu(1-\mu)$?

You're correct that the mean and variance functions are of the same form. This suggests that in very large samples, as long as you don't have observations really close to 1 or 0 they should tend to ...
Glen_b's user avatar
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11 votes
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variance vs. standard deviation in beta regression

I think there are two potential sources of confusion here: (1) What the variance pertains to. (2) What kind of intervals are computed. The variance is the predicted variance of the response and not ...
Achim Zeileis's user avatar
11 votes
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Zero inflated beta regression using gamlss for vegetation cover data

I have added preliminary support for gamlss to the emmeans package... ...
Russ Lenth's user avatar
  • 20.7k
11 votes
Accepted

Why is betareg() giving "invalid dependent variable" error?

The error message posted by R tells you what the problem is: invalid dependent variable, all observations must be in (0,1) In other words, your dependent variable should take values that are strictly ...
Isabella Ghement's user avatar
11 votes
Accepted

Beta regression shows a weird plot

Your regression has two inputs crop coverage ~ soil_moisture + weed_coverage but you've only plotted crop_coverage against ...
jcken's user avatar
  • 2,917
10 votes
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Logit transformation or beta regression for proportion data

They mean that once you transformed your dependent variable (e.g., from $y$ to ${\rm logit}(y)$), the parameters of the regression model tell you how independent variables affect ${\rm logit}(y)$, ...
Łukasz Deryło's user avatar
9 votes
Accepted

How do you report results from a Beta Regression (R output)?

The beta regression model can have two submodels: (1) a regression model for the mean - similar to a linear regression model or a binary regression model; (2) a regression model for the precision ...
Achim Zeileis's user avatar
9 votes

Dealing with 0,1 values in a beta regression

I think the actual "correct" answer to this question is zero-one inflated beta regression. This is designed to handle data that vary continuously on the interval [0,1], and allows many real 0's and 1'...
colin's user avatar
  • 1,242
9 votes

Why Beta/Dirichlet Regression are not considered Generalized Linear Models?

The answer by @probabilityislogic is on the right track. The beta distribution is in the two parameter exponential family. The simple GLM models described by Nelder and Wedderburn (1972) do not ...
Sextus Empiricus's user avatar
8 votes
Accepted

Why are my beta regression results biased?

The parameterization you use is not the same as in betareg hence you cannot recover your original parameters. The rbeta() ...
Achim Zeileis's user avatar
8 votes

Proportion data with number of trials known (and separation?): GLM or beta regression?

It isn't that beta regression on its own solved the problem. It's that you adjusted the data with a line of code: ...
EdM's user avatar
  • 95.5k
8 votes
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Modeling a 0-1 Bounded Dependent Variable That is Not a Proportion/Probability

Beta regression still makes perfect sense. It is in no way limited to, or even mainly motivated by, data that are probabilities or proportions. (If your data are "far" away from the ...
Stephan Kolassa's user avatar
7 votes

Beta regression: how to interpret the p-value of the phi coefficient

In beta regression you assume that the dependent variable is beta-distributed with expectation $\mu$ and variance $\mu \cdot (1 - \mu)/ (1 + \phi)$. Thus, $\phi$ is a precision parameter: the higher $\...
Achim Zeileis's user avatar
7 votes

Why does my beta regression look linear when plotted?

The first thing I notice is that the relationship between the input and output is approximately linear, so from an empirical point of view I'd expect the fitted model to replicate this relationship. ...
jcken's user avatar
  • 2,917
7 votes

Can the Beta-regression be written in the GLM form?

GLMs assume that the response distribution is an Exponential Dispersion Model (EDM): $$y_i \sim \mbox{ED}(\mu_i,\phi/w_i)$$ where $\phi$ is the dispersion parameter and $w_i$ is a known weight. EDMs ...
Gordon Smyth's user avatar
  • 13.2k
6 votes

Variance-covariance matrix of the errors in linear regression

OLS estimation of the error variance, $\sigma^2$: $$s^2=\frac{\hat \varepsilon^\top\hat \varepsilon}{n-p}$$ This is included in Practical Regression and Anova using R by Julian J. Faraway, page ...
Antoni Parellada's user avatar
6 votes
Accepted

Regression when both the predictor and outcome variables are proportions

A glm with a binomial distribution and a logit link should work fine. If there are no probabilities of $0$ or $1$, beta regression is another possibility. In this case, they yield almost ...
COOLSerdash's user avatar
6 votes
Accepted

Interpretation of the beta regression coefficients with logit link used to analyse percentage 0-100%

I assume that you have scaled your percentages to values in [0,1] (or in the open interval (0,1) after you've added/subtracted 0.001; you might want to consider adjusting by smaller values, as values ...
Ben Bolker's user avatar
  • 44.5k
6 votes
Accepted

Which link function could be used for a glm where the response is per cent (0 - 100%)?

Nice question! You can start your modelling efforts by converting your cover variable so that it is expressed as a proportion rather than a percentage (i.e., simply divide the values of your original ...
Isabella Ghement's user avatar
6 votes

Why does my beta regression look linear when plotted?

When the outcomes are very close to 0.5, the model on the response scale is nearly linear. The plot below demonstrates this. In black, I have plotted the inverse of the logit function (which is what ...
Demetri Pananos's user avatar
6 votes
Accepted

Modeling the precision and location parameters in beta regression

I wouldn't be aware of any such reason. I think it's a reasonable default to assume that all predictor variables that affect the mean $\mu$ of the response variable actually affect its entire ...
Achim Zeileis's user avatar

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