# Multilevel modelling

## 13 important questions on Multilevel modelling

### What is the typical structure of levels of analyses in psychological statistics?

- Statistical data concern elements of a population (e.g. individual people)

- These individuals can be members of larger groups (e.g., different occupations)
- These groups can be members of even larger groups, etc.
- So populations are naturally organized mereologically (but not necessarily in just one way!!)

- The mereological relations are called
**nesting**; a lower level group is nested in a higher level group - the lower level is nested in the higher level. Subpopulations are nested in higher populations

### What is a typical example of not taking the nesting of your data into account?

- A simpson's paradox where the relationship between variables at a sample level is different from the relationship between the same variables for different subpopulations.

### What is the central idea of multilevel analysis?

- The central idea of multilevel analysis is that you make a model where you allow each subgroup to have their own intercept and their own slope.
- these parameters at the lower level are treated as variables at the next level.
- the slope and the intercept within a group are fixed values, but between groups (on a sample level) they are variables.

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### What is a level 1 predictor?

- A level 1 predictor is a variable that varies at the lowest level of analyses but is constant at level 2.
- e.g. A variable can have a different value for different people within a group, but is a constant between groups (the mean of the group can be compared to other groups)

### What is a level 2 predictor?

- A variable that varies at level 2, but is a constant at level 3 and within classes at level 1:
- e.g. Students within a class have the same value for the level 2 predictor. The level 2 predictor varies between classes. At level 3 it is a constant again.

### What is meant by qualitative differences between groups?

another example of simpson's paradox

### What are some examples of research questions for which multilevel modelling is a very subsequent (aansluitend) procedure?

- You can use multilevel to deal with excess dependency

- However in some cases multilevel may be theoretically indicated

- This is the case if:
- The research question operates at a specific level (e.g. you’re interested in trajectories of the individual person rather than the group mean)

- The research question is how the variance is distributed over the levels (e.g. how much is due to intra- vs interindividual effects?)

- The research question is whether there is or is not heterogeneity in or between levels (e.g. does the group model resemble the individual model?)

### What is a specific situation of excess dependency where multilevel models are needed?

- One situation in which multilevel models are typically needed is in modeling change over time

- The reason is that the repeated measurements of an individual are usually highly correlated
- the data within individuals is correlated much more than between individuals.

- In this case the time points are nested in the individual

- The individual differences in trajectories can be modeled as random effects in the parameters of the change model (e.g. intercepts and slopes)

- Covariates (e.g., background variables or interventions) can be added as predictors of these parameters

### What is the first step in growth curve modeling?

- Plot the data in a spaghetti plot to inspect your data
- also plot the individual trajectories split by groups to see whether there are differences between groups.
- Are the data roughly normally distributed ?
- do they vary around the mean?
- Do the individual growth trajectories look roughly linear?
- is the dat not parabolically curved or something.

- Are there large differences that you can visually pick up?

- See whether there is a need for multilevel models: compute the ICC and inspect the data to see whether there are really different trajectories (especially qualitative differences)

### How can you extend your model from the first growth model?

- Making a
**conditional growth**model b which expands from the first growth model. - This model assesses how the average outcome changes over time across all individuals and groups, accounting for both differences in intercepts and differences in slopes
- Level 1:

### How can you add an intervention as an experimental manipulation to a multilevel model?

- An intervention is a level 2 variable because within individuals over time the intervention is constant, but between individuals the intervention varies.
- we want to model as such that the intervention causes a difference in slopes and intercepts (why intercepts?)
- level 1: Yit = B0i + Bi1 * time + eij
- level 2:

Bi0 = y0 + y0*interventioni + u0j

Bi1 = y1 + y1 * intervention i + u1j - the intervention thus influences the mean of an individual and the slope of an individual.
- model <- lmer(Y ~ 1 + intervention*time + (1 + time | individual), REML = F, data = data)

### How can multilevel models and network models be used together?

- The slopes and intercepts can be seen as variables that people can differ on.
- They are basically latent variables that may be correlated

- You can examine the structure of these correlations through a network.
- or the correlations between values can be explained through a factor model where a latent variable accounts for the correlations.

### How can multilevel models be used in time-series data?

- Sometimes time series themselves have a nesting structure

- For instance, ESM assessments are nested in days

- The days are nested in parts of the week (e.g., weekdays/weekends)

- Or: the data are organized into episodes (e.g. depressed episode vs. healthy episode)

- In this case one can use a multilevel approach to accommodate that the different phases may feature different regimes

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