Search results
Results From The WOW.Com Content Network
Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation (see comparison). In machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.
Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences. For example, the Trauma and Injury Severity Score (), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. [6]
The resulting model is known as logistic regression (or multinomial logistic regression in the case that K-way rather than binary values are being predicted). For the Bernoulli and binomial distributions, the parameter is a single probability, indicating the likelihood of occurrence of a single event.
The logit in logistic regression is a special case of a link function in a generalized linear model: it is the canonical link function for the Bernoulli distribution. More abstractly, the logit is the natural parameter for the binomial distribution; see Exponential family § Binomial distribution.
The simplest direct probabilistic model is the logit model, which models the log-odds as a linear function of the explanatory variable or variables. The logit model is "simplest" in the sense of generalized linear models (GLIM): the log-odds are the natural parameter for the exponential family of the Bernoulli distribution, and thus it is the simplest to use for computations.
As the logistic distribution, which can be solved analytically, is similar to the normal distribution, it can be used instead. The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution.
The Hosmer–Lemeshow test is a statistical test for goodness of fit and calibration for logistic regression models. It is used frequently in risk prediction models. The test assesses whether or not the observed event rates match expected event rates in subgroups of the model population.
For example, a researcher is building a linear regression model using a dataset that contains 1000 patients (). If the researcher decides that five observations are needed to precisely define a straight line ( m {\displaystyle m} ), then the maximum number of independent variables ( n {\displaystyle n} ) the model can support is 4, because