Ordered probit
Encyclopedia
In statistics
, ordered probit is a generalization of the popular probit
analysis to the case of more than two outcomes of an ordinal dependent variable. Similarly, the popular logit
method also has a counterpart ordered logit
.
Example: In the medical area, the effect a drug may have on a patient may be modeled with ordered probit regression. Independent variables may include the use or non-use of the drug as well as control variables such as age and details from medical history such as whether the patient suffers from high blood pressure, heart disease, etc. The dependent variable would be ranked from the following list: complete cure, relieve symptoms, no effect, deteriorate condition, death.
The model cannot be consistently estimated using ordinary least squares
; it is usually estimated using maximum likelihood
.
Suppose the underlying relationship to be characterized is
x' 
,
where y* is the exact but unobserved dependent variable (perhaps the exact level of improvement by the patient); x is the vector of independent variables, and
is the vector of regression coefficients which we wish to estimate. Further suppose that while we cannot observe y*, we instead can only observe the categories of response:
Then the ordered probit technique will use the observations on y, which are a form of censored data on y*, to fit the parameter vector
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, ordered probit is a generalization of the popular probit
Probit model
In statistics, a probit model is a type of regression where the dependent variable can only take two values, for example married or not married....
analysis to the case of more than two outcomes of an ordinal dependent variable. Similarly, the popular logit
Logit
The logit function is the inverse of the sigmoidal "logistic" function used in mathematics, especially in statistics.Log-odds and logit are synonyms.-Definition:The logit of a number p between 0 and 1 is given by the formula:...
method also has a counterpart ordered logit
Ordered logit
In statistics, the ordered logit model , is a regression model for ordinal dependent variables...
.
Example: In the medical area, the effect a drug may have on a patient may be modeled with ordered probit regression. Independent variables may include the use or non-use of the drug as well as control variables such as age and details from medical history such as whether the patient suffers from high blood pressure, heart disease, etc. The dependent variable would be ranked from the following list: complete cure, relieve symptoms, no effect, deteriorate condition, death.
The model cannot be consistently estimated using ordinary least squares
Ordinary least squares
In statistics, ordinary least squares or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear...
; it is usually estimated using maximum likelihood
Maximum likelihood
In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters....
.
Suppose the underlying relationship to be characterized is
x' ,where y* is the exact but unobserved dependent variable (perhaps the exact level of improvement by the patient); x is the vector of independent variables, and
is the vector of regression coefficients which we wish to estimate. Further suppose that while we cannot observe y*, we instead can only observe the categories of response:Then the ordered probit technique will use the observations on y, which are a form of censored data on y*, to fit the parameter vector
.