Beta Regression

Beta regression models an outcome that lies strictly between 0 and 1 by assuming a beta distribution, linking its mean to predictors through a logit and estimating a precision parameter.

베타회귀는 0과 1 사이의 비율 결과가 베타분포를 따른다고 보고 평균을 로짓 연결로 설명변수와 잇는 회귀모형입니다.

My outcome is a rate or proportion between 0 and 1 for each unit; which regression should I use instead of ordinary least squares?

결과가 0과 1 사이 비율(예: 점유율)인데, 일반 회귀 대신 어떤 모형을 써야 하나요?

Beta regression assumes the proportion follows a beta distribution whose mean depends on predictors through a logit link, so predictions stay inside 0 and 1 and the variance shrinks near the bounds. A precision parameter φ describes how tightly values cluster around the mean, and exact 0 or 1 values must be transformed or handled with an inflated model.

When to use Beta Regression

• The outcome is a continuous proportion or rate strictly between 0 and 1
• The spread of the outcome is smaller near 0 and 1 than in the middle
• You want a full likelihood model with AIC for model comparison

When to use something else

• The outcome contains many exact 0s or 1s; use fractional logit regression instead
• The outcome is a count of successes out of a known number of trials; use binary logistic regression instead

Assumptions and requirements

• The outcome follows a beta distribution conditional on predictors
• The logit of the mean is linear in the predictors
• Observations are independent
• Values lie strictly inside (0, 1); exact 0s and 1s are compressed with the Smithson-Verkuilen transformation

What the analysis reports

• Mean-model coefficients on the logit scale with odds ratios
• Precision parameter φ
• Pseudo R², log-likelihood and AIC
• Pearson residual summary

How to report it

A beta regression with a logit link showed that [predictor] was associated with a higher mean [outcome], b = [value], SE = [value], z = [value], p = [value] (precision φ = [value], pseudo R² = [value]).

Related methods

• Fractional Logit Regression
• Binary Logistic Regression
• Tobit Regression Model

Run Beta Regression on Quorant