# 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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