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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.
Logistic regression; ... square test uses a measure of goodness of fit which is the sum of differences ... 1981 edition of the popular statistics textbook by Robert ...
For logistic regression, the measure of goodness-of-fit is the likelihood function L, or its logarithm, the log-likelihood ℓ. The likelihood function L is analogous to the in the linear regression case, except that the likelihood is maximized rather than minimized.
The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.
For very small samples the multinomial test for goodness of fit, and Fisher's exact test for contingency tables, or even Bayesian hypothesis selection are preferable to the G-test. [2] McDonald recommends to always use an exact test (exact test of goodness-of-fit, Fisher's exact test) if the total sample size is less than 1 000 .
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.
Once a regression model has been constructed, it may be important to confirm the goodness of fit of the model and the statistical significance of the estimated parameters. Commonly used checks of goodness of fit include the R-squared , analyses of the pattern of residuals and hypothesis testing.
Pearson's chi-squared test or Pearson's test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates , likelihood ratio , portmanteau test in time series , etc.) – statistical ...