What are the consequences of rare events in logistic regression? - Cross Validated most recent 30 from stats.stackexchange.com 2019-08-20T01:34:44Z https://stats.stackexchange.com/feeds/question/307635 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/307635 8 What are the consequences of rare events in logistic regression? Great38 https://stats.stackexchange.com/users/122545 2017-10-12T18:00:27Z 2017-10-18T17:58:12Z <p>I know that sample size affects power in any statistical method. There are rules are thumb for how many samples a regression needs for each predictor. </p> <p>I also hear often that the number of samples in each category in the dependent variable of a logistic regression is important. Why is this?</p> <p><strong>What are the actual consequences to the logistic regression model when the number of samples in one of the categories is small (rare events)?</strong></p> <p>Are there rules of thumb that incorporate both the number of predictors and the number of samples in each level of the dependent variable? </p> https://stats.stackexchange.com/questions/307635/-/307642#307642 10 Answer by gung for What are the consequences of rare events in logistic regression? gung https://stats.stackexchange.com/users/7290 2017-10-12T18:27:00Z 2017-10-12T18:27:00Z <p>The standard rule of thumb for <em>linear</em> (OLS) regression is that you need at least \$10\$ data per variable or you will be 'approaching' <a href="https://stats.stackexchange.com/q/283/">saturation</a>. However, for logistic regression, the corresponding rule of thumb is that you want \$15\$ data <em>of the less commonly occurring category</em> for every variable. </p> <p>The issue here is that binary data just don't contain as much information as continuous data. Moreover, you can have perfect predictions with a lot of data, if you only have a couple of actual events. To make an example that is rather extreme, but should be immediately clear, consider a case where you have \$N = 300\$, and so tried to fit a model with \$30\$ predictors, but had only \$3\$ events. You simply can't even estimate the association between most of your \$X\$-variables and \$Y\$. </p>