Fractional Logit Regression

Fractional logit regression models a proportion between 0 and 1, including exact 0 and 1, with a logistic mean function estimated by Bernoulli quasi-likelihood and robust standard errors.

분수 로짓 회귀는 0과 1을 포함한 비율 결과에 로지스틱 평균식을 베르누이 준우도로 적합하고 강건 표준오차로 추론하는 방법입니다.

My outcome is a share between 0 and 1 and some units have exactly 0 or 100 percent; how do I regress it?

0%나 100%인 사례가 섞인 비율 결과는 어떤 회귀로 분석해야 하나요?

Fractional logit regression, proposed by Papke and Wooldridge, fits a logistic mean function to a fractional outcome using the Bernoulli quasi-likelihood, so exact 0 and 1 values are allowed. Because only the mean model is assumed, inference uses heteroskedasticity-robust (sandwich) standard errors.

When to use Fractional Logit Regression

• The outcome is a proportion bounded by 0 and 1 and may include the endpoints
• You want consistent mean effects without assuming a full distribution
• You need average marginal effects on the proportion scale

When to use something else

• You need a full distribution for the proportion with a precision parameter; use beta regression instead
• The outcome is a count of successes out of known trials; use binary logistic regression instead

Assumptions and requirements

• The conditional mean of the outcome is the logistic function of a linear predictor
• Observations are independent
• The sample is large enough for robust standard errors

What the analysis reports

• Coefficients on the logit scale with HC1 robust standard errors
• Average marginal effects on the proportion scale
• Squared correlation between observed and fitted values
• Shares of exact 0 and 1 values

How to report it

A fractional logit model with robust standard errors showed that [predictor] increased [outcome], b = [value], SE = [value], z = [value], p = [value]; the average marginal effect was [value] percentage points.

Related methods

• Beta Regression
• Binary Logistic Regression

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