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Multilevel modelling

Q: 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:

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.

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?

When the nature of the relationship between variables differ between groups as opposed to the situation where the relationship is the same but the strength is different (quantitative differences)
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

The question on the page originate from the summary of the following study material:

BDS: psychometrics

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Multilevel modelling

13 important questions on Multilevel modelling

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

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

What is the central idea of multilevel analysis?

What is a level 1 predictor?

What is a level 2 predictor?

What is meant by qualitative differences between groups?

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

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

What is the first step in growth curve modeling?

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

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

How can multilevel models and network models be used together?

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

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