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The '''Hosmer–Lemeshow test''' is a [[statistical test]] for [[goodness of fit]] for [[logistic regression]] models. It is used frequently in [[Predictive analytics|risk prediction]] models. The test assesses whether or not the observed event rates match expected event rates in subgroups of the model population. The Hosmer–Lemeshow test specifically identifies subgroups as the [[decile]]s of fitted risk values. Models for which expected and observed event rates in subgroups are similar are called well calibrated.
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The Hosmer–Lemeshow test statistic is given by:
 
:<math> H = \sum_{g=1}^{G} \frac{(O_g - E_g)^2}{N_g \pi_g (1-\pi_g)} .\,\!</math>
 
Here ''O<sub>g</sub>'', ''E<sub>g</sub>'', ''N<sub>g</sub>'', and ''π<sub>g</sub>'' denote the observed events, expected events, observations, predicted risk for the ''g''<sup>th</sup> risk decile group, and ''G'' is the number of groups. The test statistic asymptotically follows a [[chi-squared distribution|<math>\chi^2</math> distribution]] with ''G''−2 degrees of freedom. The number of risk groups may be adjusted depending on how many fitted risks are determined by the model. This helps to avoid singular decile groups.
 
==References==
{{Reflist}}
* {{cite book |last=Hosmer |first=David W. |last2=Lemeshow |first2=Stanley |year=2000 |title=Applied Logistic Regression |location=New York |publisher=Wiley |isbn=0-471-61553-6 }}
* {{cite book | author=Agresti, Alan| authorlink = Alan Agresti| title=Categorical Data Analysis| location= Hoboken | publisher=John Wiley and Sons| year=2002 | isbn=0-471-36093-7}}
 
{{DEFAULTSORT:Hosmer-Lemeshow test}}
[[Category:Statistical tests]]
[[Category:Regression analysis]]

Latest revision as of 23:00, 21 November 2014



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