# What are the consequences of not including random effects in a linear model when they should be added?

I am dealing with repeated measures data in which there is clearly reason to incorporate random effects to account for each subject having multiple measurements.

A mixed effects model using random intercepts fits my data nicely. I also ran the same model but without the random intercept, thereby making it a standard linear regression. I realized that the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however, the Beta coefficients are rather different between these two models.

In general, considering that I am interested in making population level predictions, is the negative consequence of failing to include random intercepts when appropriate that the parameter (Beta) estimates and their associated confidence intervals will be biased?

My understanding is that failure to include random intercepts will cause issues for the assumption of independence of observations in standard multiple regression.

• Does this partially answer the question? stats.stackexchange.com/questions/48720/… – swmo Mar 9 '17 at 13:39
• When you say "without random effect", you mean you are using fixed effects for each subject or that you are not using subject ids at all? – amoeba Mar 9 '17 at 14:20
• I mean that I am not using subject ids at all. e.g. y ~ blah + (1/subject) vs. y ~ blah – Ghislain d'Entremont Mar 9 '17 at 15:14
• Well, imagine that effect of subject is HUGE and the effect of blah is tiny. By not including subject into the model you will not notice any effect of blah. – amoeba Mar 9 '17 at 15:43