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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 goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question.
In statistics, the logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables. In regression analysis, logistic regression [1] (or logit regression) estimates the
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.
In linear regression, the squared multiple correlation, R 2 is used to assess goodness of fit as it represents the proportion of variance in the criterion that is explained by the predictors. [1] In logistic regression analysis, there is no agreed upon analogous measure, but there are several competing measures each with limitations. [1] [2]
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.
Statistical analysis using logistic regression of Grade on GPA, Tuce and Psi was conducted in SPSS using Stepwise Logistic Regression. In the output, the "block" line relates to Chi-Square test on the set of independent variables that are tested and included in the model fitting.