# 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.

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### Accounting for uncertain information (few observations) in a prior (empirial Bayes)

I did not really know how to choose an adequate title for this question, so please feel free to change it. I have a weird case wherein frequentist and Bayesian philosophies come together. I am ...
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### Proportion as outcome in a regression (as a ratio of two continuous variables) - a problem with beta regression

Let's say we have two continuous variables, $a$ and $b$, both being positive with $a\leq b$ and the outcome in a regression is their ratio. The typical solution is beta regression (see for example ...
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### Similar to beta regression for Generalized Additive Models and Generalized Linear Models

My thesis is based on GAM and GLM. But my dependent variable is a proportion, meaning that $y \in (0,1)$ then I thought a better fit for this was the beta regression but this one is not considered in ...
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### fitting a betareg model with weights in R

I am using the betareg package in R to model a proportional response and would like to incorporate information about the level of confidence in each observation ...
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### Interpretation of proportion dependent variable with beta reg

I'm trying to interpret this, let's say my dependent variable $y$ is the proportion of drinking beer in the last month, and my independent variable is x.1 if you have sleep well during the last week (...
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### Can distributions that are in the exponential family, but not the natural exponential family, be formed as GLM?

The lognormal and beta distributions are in the exponential family but not the natural exponential family. Generalized Linear Models are often advertised as being models for response variables that ...
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### Multivariate zero_one_inflated_beta regression

I want to run a zero_one_inflated_beta regression with brms on the following multivariate formula: ...
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### Is beta regression appropriate for this question?

I have a data set with death rate per 1000 birth as the response variable. The range of values for the response variable is [0.03 - 0.89]. The question to find association between death rate and other ...
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### Interpretation of zero-one-inflated beta models in brms

I have 20 participants who have watched 18 clips. Every clip belongs to one category of pleasure (p_cat: negative, neutral, positive) and one category of intensity (i_cat: low, medium, high). I have 2 ...
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### Is it possible to fit a Dirichlet Regression to changing response variables?

A toy problem to illustrate my issue: We put a 100 people in a room with 10 candy bars. Each bar is different and has a different brand, flavor, size, color, etc. We ask each person in the group to ...
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### How could one estimate $Y = X\beta \times \epsilon$ with $\epsilon \sim \text{Beta}(a,b)$?

Suppose the data generating process is $$Y_i=f(X_i)M_i.$$ where $M_i$~$Beta(a,b)$ and $f$ linear, for example,$f(X_i)=\alpha_0+\alpha_1X_i$. This is equivalent to $$M_i=Y_i/f(X_i).$$ I'm trying to ...
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### Can I plot a beta distributed model with percentage rather than proportion? [closed]

I am analyzing a response variable (herbivory) which is a proportion, so I am using betareg function from the betareg package. The structure is similar to the GasolineYield dataset, so using it as ...
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### Beta regression betareg () output from independent ordinal and continuous variables

I am investigating the effects of leaf toughness, leaf's Nitrogen content and fire on the proportion of herbivory of plants. My fire treatment is ordinal (fire severity): I have 75 plants located in ...
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### Betareg error when running bootstrap-like simulations (Error in chol.default(K) : the leading minor of order 16 is not positive definite

A previous post discussed a similar case on non-positive definite covariance matrices resulting when producing half-normal residual plots using the package betareg. However, I would like additional ...
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### Betareg Half-Normal Plot “Error in chol.default(K)”

I am running into a very odd problem when calling plot.betareg (betareg package in R) to produce half normal plots: Sometimes I receive a plot, sometimes I get for the same model with the same data an ...
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### multiple linear regression for bounded variable

I am aware that there are special models that deal with bounded variables (binomial, logistic, beta regression) and all have different benefits and are used for different data types. However, I read ...
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### Literature on conceptual understanding of beta regression

I am researching beta regression models to decide if they are appropriate for my data. My very first search yielded this basic introduction, that also describes the zero-one inflated beta regression. ...
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### Evaluating model fit for glmmTMB with beta distribution

I am looking for a way to evaluate model fit (e.g. R2, %deviance explained) for the following model: m1<-glmmTMB(AUC_indep~woody+dispersal+log_densitys+log_seedwts+I(log_seedwts^2)+(1|modeltype), ...
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### Is fair to compare Dirichlet to a Multivariate Beta regression?

I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions. I am trying to investigate the effect of a categorical variable (cl) to ...
406 views

### Relationship between Beta regression of Y on X and linear regression of X on Y. (where Y is a proportion)

I am trying to model the relationship between school district funding and a district's poverty rate. If I treat funding as the independent variable then the dependent is a proportion on [0,1]. This ...
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### Modelling and interpreting brms output

I do apologize in advance for this might be very basic questions. I am not really familiar with Bayesian statistics and too, unfortunately, this is the very first time I am analysing data in general. ...
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### Beta Regression Model Selection with CV Lasso in R

Is there a package that will do a cross-validatation with regularization for beta regression in R? I'm looking for an equivalent of glmnet for the betareg package.
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### Fitting Beta Distribution Parameters to Y conditional on X

I have a bi-variate data set where Y is in [0,1]. X is some measure of intensity and in this example is (0,~200) though there is no hard upper bound. X has a strong positive skew but I am not ...
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### Modelling a percentge as a dependent variable

I have a dataset containing 4 variables: Y - the dependent variable. This is a percentage of students in a school that choose to take an external exam. The values vary from 20% to 70%. X - the ...
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### Beta regression - interpret coefficients using loglog link

Although a number of similar questions (some of them duplicates) have been asked around the interpretation of the coefficients from a beta regression, these seem to be focused on models that have used ...
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### Beta regression - calculate predicted value from coefficients using loglog link

Firstly, I would like to say, I have read a great post but it doesn't quite answer my question. This post came very close, but I still couldn't solve my issue from it. I would like to be able to run ...
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### Negative lower confidence limit in beta regression?

I fitted a beta regression on some proportion data using the betareg() function from the betareg package. The proportion was ...
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### Regression when both the predictor and outcome variables are proportions

I am using $X$ The estimated pre-game win probability of a sporting team playing on its Home field (estimated according to a certain model) to predict $Y$ Actual proportion of points scored by ...
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### Beta regression estimates and confidence intervals on response scale

I'm using GLMMadmb for my beta regression. I'm having a bit of trouble. I understand beta regression uses the logit link function and I know how to get from logits to probability. Here's selected ...
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### Beta regression where fractional response adds up to 100%?

I have a data set of people switching brands. Say #people switching from Brand A to Brand B, C or D. My data looks like this ...
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### Weighted least squares estimator

I have this linear model: 𝑦𝑖 = 𝛽𝑥𝑖 + 𝜖𝑖, 𝑖 = 1, … , n with variance proportional to the covariate, like $𝐸(𝜖_𝑖) = 0$ and $𝑉𝑎𝑟(𝜖𝑖) = 𝜎^2_{𝑥𝑖}$. I need the weighted least squares ...
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### Reporting betareg outcome - how to compare non-nested models?

I am looking for advice how to gain and report results using beta regression for an ANCOVA-like model. My model is as follows: ...
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### Logit transformation or beta regression for proportion data

I'm interested in knowing about the difference in interpretation between (1) linear regression on a logit transformed variable with values between 0 and 1 and (2) beta regression where the values ...
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### Attempting to interpret both Beta Regression and transformed DV model results

After reading a good amount of the answered questions on interpreting Beta Regression results (Best explanation here) and reading through the Betareg vignette, I still feel a lack of confidence ...
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### Diagnostic residuals for Beta GLMM weighted by sample size (Meta-analysis) using glmmTMB

I am conducting a GLMM for a meta-analysis using the beta distribution with the package glmmTMB. My response variable is a vector of correlations (No exact 0 or 1), but Fisher’s transformation fails ...
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### betareg returns values outside of bounds [closed]

The betareg function returns estimates for mu and phi. I received the following output for ...
594 views

### Beta regression (betareg) with caret and train [closed]

I have a dataset with a dependent in range (0,1) and numerical/categorical predictors. Chiefly to streamline the code and easily accomplish cross validation (feature selection/model fitting), I would ...
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### Standardised coefficient interpretation (beta reg. with logit link)

If I standardize the coefficients (scale() command in R) of a beta regression with a logit link, how do I interpret them? I would say: Of how many standard ...
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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 ...
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### Homoscedasticity and normal distribution on proportion data - beta regression necessary?

I have a couple of datasets with proportion data. For some datasets the values are nicely normal-distributed and show homoscedasticity. Is it fine to run a two-way ANOVA or Scheirer-Ray-Hare test? Or ...
172 views

### How do I specify a random effect in Bayesian beta regression model?

My response data are proportions that I want to model with one continuous predictor and a random effect of group. Here's my winbugs code: ...
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### interpreting results of beta regression [duplicate]

Looking here at the beta reg packge: https://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf The code below is using a categorical batch variable and a continuous temp variable to ...
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### How do I interpret a betareg coefficient of 6.6970 for a categorical variable with only two categories, given that the response is a proportion?

I cannot seem to find an exact answer to my question online. I used the betareg package in R to run a glm with a response variable that is a proportion, so it is between 0 and 1. One of my predictor ...
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### How to conduct significance testing for percent outcome based on summary statistics only?

I have three groups A, B, and C, with corresponding sample size. I have gender variable as a binary variable, with M vs. F. For each group, it's summarized into "percentage woman". I only have the ...
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### Classification when each level has probability assigned to it

The response variable in my dataset is a factor with six levels. For each observation, each level has been assigned a probability to be interpreted as the probability that the given observation is ...
3k views

### Zero inflated beta regression using gamlss for vegetation cover data

My goal is to analyse vegetation cover data. The way the data collection works is that you throw a quadrat (0.5m x 0.5m) in a sample plot and estimate the percent cover of the target species. Here is ...
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### Regression model to predict an individual's race

I have a database of individuals containing data about age, gender, place of living (census tract level) and income but nothing about race. Beside this, I have aggregate race data at census tract ...