A fixed effects model is a type of statistical model that is used to estimate the effect of one or more categorical variables on a continuous outcome variable, while controlling for other variables. In a fixed effects model, the categorical variables are assumed to be fixed and not a random sample from a larger population. Therefore, the model is able to estimate the effect of these variables on the outcome variable, while controlling for any other variables that may be influencing the outcome.

On the other hand, a random effects model is a type of statistical model that is used to estimate the effect of one or more categorical variables on a continuous outcome variable, while also accounting for the fact that the categorical variables are a random sample from a larger population. In a random effects model, the effect of the categorical variables is allowed to vary across the levels of the variable.

The main difference between a fixed effects and a random effects model is that a fixed effects model assumes that the categorical variables are fixed, while a random effects model allows for the effect of the categorical variables to vary across the levels of the variable. This means that a random effects model allows for the possibility that the effect of a variable may be different in different groups or levels of the variable.

In general, fixed effects models are appropriate when the goal is to estimate the average effect of a variable within a group, while random effects models are more appropriate when the goal is to estimate the overall effect of a variable across multiple groups.

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