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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.
N = the sample size The resulting value can be compared with a chi-square distribution to determine the goodness of fit. The chi-square distribution has ( k − c ) degrees of freedom , where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the ...
7.2.3 Hosmer–Lemeshow test. ... Download QR code; Print/export Download as PDF; ... sample standard deviation of the y k data points.
Hosmer–Lemeshow test, a quality of fit statistic that can be used for binary data; Pearson's chi-squared test, an alternative quality of fit statistic for generalized linear models for count data; Peirce's criterion, a rule for eliminating outliers from data sets
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The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable.
In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution.If Y is a random variable with a normal distribution, and t is the standard logistic function, then X = t(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed.
[15] [5] For example, asking whether R = 1 is the same as asking whether log R = 0; but the Wald statistic for R = 1 is not the same as the Wald statistic for log R = 0 (because there is in general no neat relationship between the standard errors of R and log R, so it needs to be approximated). [16]