# 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.