## Fixed Effects / Random Effects Models in Experimental Research

In design of experiments, data from a treatment group and control group is compared with ANOVA or a similar statistical tool. *Fixed effects* are variables that are **constant across individuals**. Some variables, like age, sex, or ethnicity, don’t change or change at a constant rate over time. These variables have **fixed effects**. Other variables are random and unpredictable— the **random effects**. In a fixed effects model, these random variables are treated as though they were non random, or fixed. A mixture between fixed effects and random effects model is called a **mixed effects model.**

Fixed effects models remove **omitted variable bias** by measuring changes within groups across time, usually by including dummy variables for the missing or unknown characteristics.

## Omitted Variable Bias

In research, one way to control for differences between subjects (i.e. to “fix” the effects) is to randomly assign the participants to treatment groups and control groups. For example, one difference could be age, but by randomly assigning participants you control for age across groups. In real life, it’s difficult or impossible to randomly assign participants (or treatments), so these variables (like age) must be measured instead. Ultimately, it’s not possible to control for *all *possible variables and research results can be contaminated with these hidden variables. This contamination of results is called **omitted variable bias**.

## Limitations of Fixed Effects Models

Fixed effects models do have some **limitations**. For example, they can’t control for variables that vary over time (like income level or employment status). However, these variables can be included in the model by including dummy variables for time or space units. This may seem like a good idea, but the more dummy variables you introduce, the more the “noise” in the model is controlled for; this could lead to over-dampening the model, reducing the useful as well as the useless information.

## References

Kreft, I., and De Leeuw, J. (1998). Introducing Multilevel Modeling. London: Sage. Retrieved November 17, 2017 from: http://gifi.stat.ucla.edu/janspubs/1998/books/kreft_deleeuw_B_98.pdf

LaMotte, L. R. (1983). Fixed-, random-, and mixed-effects models. In Encyclopedia of Statistical Sciences, ed. S. Kotz, N. L. Johnson, and C. B. Read, 137–141.

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