# Standardize betas in logistic regression

I want to compare beta weights across different logistic regression models (one per subject) and therefore standardize beta weights. I would use t-scores and then test t-scores from different models against zero to estimate whether there is an significant effect across subjects. However, I recently saw one line of code where betas are standardized by (??) beta=beta./sqrt(sum(beta^2)). Can anyone explain to me why you would standardize that way and what are the advantages compared to t-scores?

Thanks! Laurie

• What exactly do you want to compare and why? Could you give us examples? – Tim Apr 23 '19 at 16:22
• Sure--for example, I want to assess the influence of task difficulty on response (right button yes/no) in the context of other variables. For each subject I would get a beta vector ( one weight for each factor) which I want to average across subjects. However I want to standardize betas before averaging or further testing. Usually I use average t-score but I don`t understand whats the reasoning behind the above described approach? – Laurie Apr 23 '19 at 18:15
• Why separate model per subject rather then random effects model? – Tim Apr 23 '19 at 18:17
• Sounds intresting, thanks! I will definitely try that! But do you have any thoughts on my previous question? – Laurie Apr 23 '19 at 18:25

## 1 Answer

Instead of estimating separate models per each student and then trying to make the parameters comparable, better use a single mixed-effects model for all students (see other questions tagged as ). In such model you would use random slopes for students, where the slopes would follow common distribution. By doing this, the only thing that you'd need to test is if their common distribution is centred at zero. Moreover, if this is a test data and you want to study things like task difficulty, then this sounds like a problem for Item Response Theory model and such models can be treated as a special case of mixed-effects logistic regression models. If it is a single test taken by different students and you want to study the properties of the test that are common for all the students, then this is another argument for using a single model.

• Hi Tim, thanks for your answer. However, since I want to correlate model variables with other factors on a group level (eg. hormonal coneventrations) I need one estimate of the influence of task difficulty on choice per subject and cannot provide one estimate across subjects and trials, right? – Laurie Apr 25 '19 at 8:59
• @Laurie I'm not sure if I follow you. – Tim Apr 25 '19 at 9:52
• Maybe I got something wrong here. In my understanding using a single mixed model would result in one estimate of the influence of task difficulty on choice across subjects ( so one weight for all subjects). However, I would like to correlate the weights that I obtained for each subject (in this case 25 describing the individual influence of task difficulty on choice ) with other parameters which I have only measured on the group level (for instance one specific hormonal concentrations). Adding those to the model does not make sense since they do not change across trials, right? – Laurie Apr 25 '19 at 16:20
• @Laurie no. One estimate would be a global fixed effects model. In mixed effects model you would have separate effects per each subject, but under assumption that they all follow common distribution (you seem to be interested exactly in this distribution). – Tim Apr 25 '19 at 16:32
• @Laurie adding this in the model would be the usual way to go. – Tim Mar 4 '20 at 8:57