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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.
The general formula for G is G = 2 ∑ i O i ⋅ ln ( O i E i ) , {\displaystyle G=2\sum _{i}{O_{i}\cdot \ln \left({\frac {O_{i}}{E_{i}}}\right)},} where O i {\textstyle O_{i}} and E i {\textstyle E_{i}} are the same as for the chi-square test, ln {\textstyle \ln } denotes the natural logarithm , and the sum is taken over all non-empty bins.
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]
Examples ANOVA, ANCOVA, linear regression: linear regression, logistic regression, Poisson regression, gamma regression, [7] general linear model Extensions and related methods MANOVA, MANCOVA, linear mixed model: generalized linear mixed model (GLMM), generalized estimating equations (GEE) R package and function lm() in stats package (base R)
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
Himmelblau's function-- Hindley–Milner type system-- Hindmarsh–Rose model-- Hindu–Arabic numeral system-- Hindu units of time-- Hindustani numerals-- Hinge theorem-- Hinged dissection-- Hippopede-- Hiptmair–Xu preconditioner-- Hironaka decomposition-- Hironaka's example-- Hiroshima Mathematical Journal-- Hiroyuki Goto-- Hirsch ...