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Concept
Ordered probit
Summary
In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, fair, good, excellent). Similarly, the widely used logit method also has a counterpart ordered logit. Ordered probit, like ordered logit, is a particular method of ordinal regression.
For example, in clinical research, 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.
Another example application are Likert-type items commonly employed in survey research, where respondents rate their agreement on an ordered scale (e.g., "Strongly disagree" to "Strongly agree"). The ordered probit model provides an appropriate fit to these data, preserving the ordering of response options while making no assumptions of the interval distances between options.
Suppose the underlying relationship to be characterized is
where is the exact but unobserved dependent variable (perhaps the exact level of improvement by the patient); 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 , we instead can only observe the categories of response:
Then the ordered probit technique will use the observations on , which are a form of censored data on , to fit the parameter vector .
The model cannot be consistently estimated using ordinary least squares; it is usually estimated using maximum likelihood. For details on how the equation is estimated, see the article Ordinal regression.
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Ontological neighbourhood
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Related concepts (5)
Linear regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
Ordered logit
In statistics, the ordered logit model (also ordered logistic regression or proportional odds model) is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. For example, if one question on a survey is to be answered by a choice among "poor", "fair", "good", "very good" and "excellent", and the purpose of the analysis is to see how well that response can be predicted by the responses to other questions, some of which may be quantitative, then ordered logistic regression may be used.
Generalized linear model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.