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Mixed-effects models are any regression models that have both independent variables that are fixed (fixed) and random (random) (see table below). In software programs, this is most often found within something called “Generalized Linear Mixed Model (GLMM)”. In GLMM, one often includes combinations of fixed and random variables in one of the various linear regressions. Multilevel analyses basically always use GLMM when calculating inferential statistics.
| Feature | Fixed effect | Random effect |
|---|---|---|
| Focus | Estimate the contribution that each level of the factor (or group membership) provides. This is often an effect size (sometimes with an associated p-value). | Estimate, and above all adjust for, the variance that different factors contribute. These are variables that introduce ‘noise’ in our dataset. |
| Selection | All levels of the factors / all groups that one wants to make a statement about are represented. When it comes to levels of measured values, it does not matter if individual levels that lie between what has been observed are missing. (for example, most included patients in a study had a systolic blood pressure between 110-170 mmHg, but no patient had the exact measured value 132, this is not a problem). | The levels of the factors are a sample from a larger population where there may be levels of factors (or groups) that lie outside our observations. |
| Aim | Look for relationships or compare groups with each other. One can make a statement about the individual contribution from each observed value / each included group. | Observations should normally be independent of each other. When this is not the case, one must control for it. Often, this dependence is because the observations are at multiple levels. For example, several observations may be nested within a patient, and in turn, several patients are nested within a clinic. We use the random variable both to adjust for this and to get an estimate of the magnitude of the “noise”. |
| Generalization | Slutsatser gäller endast för de nivåer av Conclusions only apply to the levels of the factors that have been observed (for the groups that were included). | One can only comment on what the random variable as a whole contributes in terms of variance. One cannot comment on the individual contribution from each level of a variable (for each and every one of all relevant groups). |
| Example | A variable of interest or a group membership. Examples of variables can be blood pressure, blood sugar, body weight, sex, age, choice of treatment, etc. | Patient, participant, school, place, etc |