Multilevel modelling - reading
5 important questions on Multilevel modelling - reading
What is a way to recognize level 1 and level 2 variables?
- Level 1 variables are variables that vary at this level. These are variables that are often measured within an individual at different time points.
- level 2 variables are often grouping variables that vary between individuals and not within individuals e.g. Treatment, gender, etc.
The book gives an example where music performance anxiety is an outcome variable and instrument type and playing in a large ensamble vs playing solo are predictors. What would be a multilevel structure of models in this situation?
- At the level of the individual, instrument is not varying but solo vs band is varying from performance to performance. This makes instrument a level 2 variables (only varies between individuals) and band a level 1 variable.
- for each individual separate, we can fit a regression that predicts mpa from playing in a band or not: mpa = a + b1 * band + e
These are level one models - each individual has it's own intercept and coefficient. These coefficients however, can be modeled with music instrument as a level 2 predictor.
ai = a0 + a1 * instrument + ui
bi = B0 + B1 * instrument + vi
These are level two models
In the example given, which parameters or variables denote the fixed effects?
- The fixed effects are the parameters in the level two models:
- ai = a0 + a1 * instrument + ui
- bi = B0 + B1 * instrument + vi
- a0, a1, b0 and b1 denote the fixed effects. They model the parameters in the level 1 models as variables.
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When we want to start modeling our data from the example described, what would be our first steps?
- Creating a baseline model: the unconditional means model or random intercepts model.
- In this model, there are no predictors at either level; rather, the purpose of the unconditional means model is to assess the amount of variation at each level—to compare variability within subject to variability between subjects.
- the formulas are:
mpa = ai + e
ai = a0 + ui - mpa is modeled as the intercept (mean) of an individual. The intercept of an individual is modeled as the sample mean.
- each subject’s intercept is assumed to be a random value from a normal distribution centered at α0
What is a possible next step from your random intercepts model?
- Adding a level 1 predictor to create a random slopes and random intercepts model.
- mpa = ai + bi * band + ei
- ai = a0+ ui
- bi = B0 + vi
- in this model, it is assumed that different individuals have different starting values of mpa and that the effect of band is different for each individual.
- α0 is then the true mean performance anxiety level for Solos and Small Ensembles, and β0 is the true mean difference in performance anxiety for Large Ensembles compared to other performance types.
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