# Mixed Effects Logistic Regression vs Logistic Regression

I'm conducting a study on how pregnancy weight gain affects risk of breast cancer and decided to go with a logistic regression model (outcome is yes/no for breast cancer) and my primary independent variable is categorical (<10lbs, 10-19 lbs, 30-39 lbs and >40 lbs each compared to the referent 20-29lbs). I've recently been told that mixed modeling may be a better alternative to account for random effects (which as I understand is basically variation between subjects if I treat that as a random effect for example).

My question is: are there any major drawbacks to using mixed-effects logistic regression? Is it a more complex model by any chance that I may not necessarily need? Could it inflate odds ratios?

In other words, how do I defend my use of logistic regression over mixed-effects logistic regression, if I can?

• Are there known causes of breast cancer that you have no data for? (eg, smoking & alcohol consumption) Jan 13, 2017 at 0:12
• I have data for most breast cancer risk factors and do plan on including them as covariates in my model. What are your thoughts? Jan 13, 2017 at 0:18
• What would your 'groups' of observations be in a mixed model? E.g. Do you have multiple measurements per subject? Jan 13, 2017 at 3:30
• Yes, pretty much. The way the data is set up is that the subjects are asked to fill out a questionnaire every 2 years and they're asked if they've been diagnosed with breast cancer, so I suppose those count as repeated measurements? Jan 13, 2017 at 4:10
• You started off on the wrong foot by classifying a continuous variable and pretending that subjects are homogeneous in the <10lbs and >40lbs groups. This will do more damage to the model than any benefit you will achieve by better modeling. Jan 14, 2017 at 14:49

## 1 Answer

There are different approaches of including random effects in your model (random slope model, random slope + intercept model, random intercept model). You can check for the magnitude of random effects using for example "induced correlation" (Zuur et al. 2008).

Based on its magnitude you can then justify whether to include the random effect in your model or not.

While there is no threshold (at least that I know of) at which to include or exclude a random effect in your model (talking about "induced correlation"), you can most often easily justify the exclusion of random effects with a value close to 0. Furthermore, you have a generalized comparison of the influences of your random effects.

In general, simple models are preferred over complex ones in statistical modelling.