In multilevel modelling, what does it mean if the slope is fixed?

In multilevel modelling, what does it mean if the slope is fixed?

• A. The slope is fixed and does not vary across groups.
• B. The slope can vary across groups.
• C. The intercept is fixed and does not vary across groups.
• D. The model has no slope.

Answer: (A)

In multilevel modeling, fixed versus random describes whether a parameter can differ across higher-level groups. If the slope is fixed, the effect of the predictor on the outcome is the same for every group; there’s no group-to-group variation in the slope estimate. You can still have differences in starting points across groups (random intercepts), but the rate at which the outcome changes with the predictor is assumed constant across groups. To see this, imagine a two-level model where students are nested within schools. If the slope is fixed, the model says every school has the same increase in the outcome for each additional unit of the predictor, while each school might have its own baseline level (intercept) if those are allowed to vary. If the slope could vary by school, you’d include a random slope term, meaning some schools show a stronger or weaker effect of the predictor. So the statement that the slope is fixed means it does not vary across groups; the predictor’s effect is uniform across the groups being analyzed.

In multilevel modeling, fixed versus random describes whether a parameter can differ across higher-level groups. If the slope is fixed, the effect of the predictor on the outcome is the same for every group; there’s no group-to-group variation in the slope estimate. You can still have differences in starting points across groups (random intercepts), but the rate at which the outcome changes with the predictor is assumed constant across groups.

To see this, imagine a two-level model where students are nested within schools. If the slope is fixed, the model says every school has the same increase in the outcome for each additional unit of the predictor, while each school might have its own baseline level (intercept) if those are allowed to vary. If the slope could vary by school, you’d include a random slope term, meaning some schools show a stronger or weaker effect of the predictor.

So the statement that the slope is fixed means it does not vary across groups; the predictor’s effect is uniform across the groups being analyzed.