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Can somebody please explain the difference between a mixed model and linear regression analysis? (I have very limited knowledge of statistics.)

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A mixed effects model has both random and fixed effects while a standard linear regression model has only fixed effects.

Consider a case where you have data on several children where you have their age and height at different time points and you want to use age to predict height. If you are willing to assume that all the children have the same slope and intercept relating age to height then you can fit a regular linear model with age as the predictor and height as the response. You could also fit a fixed effects model including an id term for each child that would effectively fit a separate intercept (or slope and intercept if you include the interaction) for each child.

A mixed effects model will let you fit an average intercept and slope as fixed effects, but then you can also include a random intercept (and random slope if desired) that models the possibility of differences between the children in a different way than the fully fixed effects model. To fully appreciate the advantages takes more than what could be included in an answer here, you really should read up on the topic in a textbook or take a class that talks about mixed effects models.

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    $\begingroup$ Thank you Greg. Do you recommend any book on mixed modeling techniques for someone like me with limited statistical knowledge $\endgroup$ – Esita Jan 12 '15 at 18:14
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In my opinion, Linear models and linear mixed effects models in R: Tutorial in two parts by Bodo Winter is a good starting point for a person without strong background in statistics.

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