# Tobit model

**TobitTobit regressionGeneralized Tobit**

In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way.wikipedia

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### James Tobin

**Tobin, JamesJ. TobinTobin**

The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods.

He also proposed an econometric model for censored dependent variables, the well-known Tobit model.

### Censoring (statistics)

**censoringcensoredcensored data**

In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way.

An earlier model for censored regression, the Tobit model, was proposed by James Tobin in 1958.

### Heckman correction

**Heckit modelHeckman selection correctionHeckman selection model**

The Heckman selection model falls into the Type II tobit, which is sometimes called Heckit after James Heckman.

The resulting likelihood function is mathematically similar to the Tobit model for censored dependent variables, a connection first drawn by James Heckman in 1976.

### Censored regression model

**Censoredcensored regressionCensoring**

The tobit model is a special case of a censored regression model, because the latent variable y_i^* cannot always be observed while the independent variable x_i is observable.

A commonly used likelihood-based model to accommodate to a censored sample is the Tobit model, but quantile and nonparametric estimators have also been developed.

### Truncated normal hurdle model

In econometrics, the truncated normal hurdle model is a variant of the Tobit model and was first proposed by Cragg in 1971.

### Limited dependent variable

**two possible outcomes**

### Rectifier (neural networks)

**rectified linear unitReLUrectifier**

### Probit model

**probit regressionprobitBayesian probit regression**

### Regression analysis

**regressionmultiple regressionregression model**

In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way.

### Dependent and independent variables

**dependent variableindependent variableexplanatory variable**

In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way.

### Arthur Goldberger

**Arthur S. GoldbergerArthur Stanley GoldbergerGoldberger**

The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods.

### Zero-inflated model

**Zero Inflatedzero-inflatedzero-inflated Poisson**

The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods.

### Truncation (statistics)

**truncationtruncatedstatistical truncation**

Because Tobin's method can be easily extended to handle truncated and other non-randomly selected samples, some authors adopt a broader definition of the tobit model that includes these cases.

### Likelihood function

**likelihoodlikelihood ratiolog-likelihood**

Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold.

### Sampling probability

**first-order inclusion probabilityinclusion probability**

Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold.

### Latent variable

**latent variableslatenthidden variables**

Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold.

### Integral

**integrationintegral calculusdefinite integral**

For any limit observation, it is the cumulative density, i.e. the integral below zero of the appropriate density function.

### Cumulative distribution function

**distribution functionCDFcumulative probability distribution function**

Next, let \Phi be the standard normal cumulative distribution function and \varphi to be the standard normal probability density function.

### Probability density function

**probability densitydensity functiondensity**

Next, let \Phi be the standard normal cumulative distribution function and \varphi to be the standard normal probability density function. For a sample that, as in Tobin's original case, was censored from below at zero, the sampling probability for each non-limit observation is simply height of the appropriate density function.

### Stationary point

**stationarystationary pointsextremal**

For the truncated (tobit II) model, Orme showed that while the log-likelihood is not globally concave, it is concave at any stationary point under the above transformation.

### Least squares

**least-squaresmethod of least squaresleast squares method**

If the relationship parameter \beta is estimated by regressing the observed y_i on x_i, the resulting ordinary least squares regression estimator is inconsistent.

### Consistency (statistics)

**consistentconsistencyinconsistent**

If the relationship parameter \beta is estimated by regressing the observed y_i on x_i, the resulting ordinary least squares regression estimator is inconsistent.

### Takeshi Amemiya

**AmemiyaAmemiya, Takeshi**

Takeshi Amemiya (1973) has proven that the maximum likelihood estimator suggested by Tobin for this model is consistent.

### Maximum likelihood estimation

**maximum likelihoodmaximum likelihood estimatormaximum likelihood estimate**

Takeshi Amemiya (1973) has proven that the maximum likelihood estimator suggested by Tobin for this model is consistent. The log-likelihood is stated above is not globally concave, which complicates the maximum likelihood estimation.

### Linear regression

**regression coefficientmultiple linear regressionregression**

The \beta coefficient should not be interpreted as the effect of x_i on y_i, as one would with a linear regression model; this is a common error.