Tobit Regression Model

Tobit regression is a censored regression model that estimates the relationship between predictors and a latent continuous outcome observed only above or below a threshold, often zero.

토빗 회귀분석은 결과변수가 0과 같은 임계값 이상 또는 이하에서만 관측되는 경우 잠재 연속변수와 예측변수의 관계를 추정하는 중도절단 회귀모형이다.

How do I run a regression when many outcome values pile up at zero or at a limit?

결과변수 값이 0이나 특정 한계값에 많이 몰려 있을 때 어떻게 회귀분석하나요?

The Tobit model treats a limited outcome as a censored version of a latent normally distributed variable and estimates coefficients by maximum likelihood. It fits outcomes such as expenditures, hours worked, or efficiency scores that cluster at a lower or upper bound because of censoring.

When to use Tobit Regression Model

• Outcome has a mass point at zero with continuous positive values, such as spending
• Measurements are capped at a known upper or lower limit
• Survey or administrative variables top-coded or bottom-coded at a known value, such as income above a reporting cap

When to use something else

• The zeros reflect a separate participation decision with different drivers: use a hurdle (Cragg) model or Heckman selection model
• The outcome is a proportion between 0 and 1 without censoring: use fractional or beta regression

Assumptions and requirements

• A latent continuous outcome underlies the observed censored values
• Normally distributed and homoscedastic latent errors
• Known censoring point(s)
• The same process drives both whether an observation is censored and its value

What the analysis reports

• Coefficients on the latent variable with standard errors
• Marginal effects on the observed and uncensored outcome
• Sigma (error scale) estimate
• Number of left- and right-censored observations
• Log-likelihood and pseudo R²

How to report it

A Tobit model left-censored at zero showed that [predictor] increased latent [outcome], b = [value], SE = [value], p = [value]; the marginal effect on observed [outcome] was [value].

Related methods

• Heckman Two Stage Selection Model
• Hurdle Model
• Censored Quantile Regression

Run Tobit Regression Model on Quorant