Editing Regression analysis (section)

===Limited dependent variables===

[[Limited dependent variable]]s, which are response variables that are [[categorical variable|categorical]] or constrained to fall only in a certain range, often arise in [[econometrics]].

The response variable may be non-continuous ("limited" to lie on some subset of the real line). For binary (zero or one) variables, if analysis proceeds with least-squares linear regression, the model is called the [[linear probability model]]. Nonlinear models for binary dependent variables include the [[probit model|probit]] and [[logistic regression|logit model]]. The [[multivariate probit]] model is a standard method of estimating a joint relationship between several binary dependent variables and some independent variables. For [[categorical variable]]s with more than two values there is the [[multinomial logit]]. For [[ordinal variable]]s with more than two values, there are the [[ordered logit]] and [[ordered probit]] models. [[Censored regression model]]s may be used when the dependent variable is only sometimes observed, and [[Heckman correction]] type models may be used when the sample is not randomly selected from the population of interest. 

An alternative to such procedures is linear regression based on [[polychoric correlation]] (or polyserial correlations) between the categorical variables. Such procedures differ in the assumptions made about the distribution of the variables in the population. If the variable is positive with low values and represents the repetition of the occurrence of an event, then count models like the [[Poisson regression]] or the [[negative binomial]] model may be used.