Wk 12 - Multi-level modelling Flashcards
When is multi-level modelling useful? (x3, plus eg x3)
When data organised hierarchically
To see what levels of are drive effects
And if there’s interactions across levels
Patients sampled from different clinics
Students sampled from different schools
Multiple measurements taken from different individuals
What is introduced by a hierarchical data structure? (x1)
Which can… (x2)
Dependencies at lower levels of organisation = problems for traditional analysis methods
Produce spurious patterns at highest level of aggregation
Disguise meaningful variation at lower levels
How are variables organised in multi-level modelling? (x1)
Those at lower levels are nested within (grouped by) higher level variables
How can we identify the level of a unit of analysis in multi-level modelling? (x1)
Eg (x3)
By how frequently they provide a measure of the outcome variable
Individual student scores - Level 1
Teacher scores - Level 2
School district - Level 3
Why would our assumptions be wrong if we only based them on Level 1 (eg, student scores) of a hierarchical data structure? (x4)
Level 1 observations aren’t independent -
*Are related to higher levels
This inflates Type 1 error (false claims of effect)
May cause missed patterns (driven by other higher variables)
Why would our assumptions be wrong if we only based them on Level 2 (eg, teacher) of a hierarchical data structure? (x3)
Similar as if only look at Level 1, but also
Start losing power
Because averaging across Level 1 (students) reduces sample size
Why would our assumptions be wrong if we only based them on Level 3 (eg, school district) of a hierarchical data structure? (x1)
Increasing severity of issues as exclusively analysing Level 1 or 2
How is multi-level modelling similar to linear regression? (x1)
y’ = linear combo of predictor variables, weighted by different coefficients
How is multi-level modelling different to linear regression? (x3)
In linear, parameters (coefficients, intercepts) fixed across all cells
Multi-, they differ
*Different equations apply to different groups
What are the 4 assumptions of multi-level modelling? (x1, x2, x1, x3)
Lower-level variables nested within higher
Data aren’t independent - influenced by higher levels
Outcome variable measured at lowest level (eg test scores)
Outcome scores vary between units of each level
*eg, mean class scores of different teachers
*Or schools with different teachers
What is the general procedure for multi-level modelling? (x2, x2, x3, x1)
Stage 1: Analyse diffs in outcome means across highest level of analysis
*Ignoring all predictors
Stage 2: Add effects of Level 1 variables
*Do these predict outcome?
Stage 3: Add Level 2/interactions
*Do L2 predict outomes?
*Do any effects depend on other variables
And so on…
What is included in the Stage 1 model of multi-level model? (x1,)
Which gives… (x1)
No predictors, just intercepts
A ‘baseline’ null model used for comparison
What is included in the Stage 2 model of multi-level model? (x1)
Which involves… (x2)
And gives… (x1)
Level 1 predictors
* Fit separate regression lines for each * Then average the parameters to find effect line
‘Compromise model’ that ignores L2 variables (and higher)
What is included in the Stage 3 model of multi-level model? (x1)
Which involves…(x2)
Level 2 predictors
* Add new predictor to 'compromise' model * Try to predict slopes intercepts of each L1 group based on L2
How is regression model fit evaluated in multi-level modelling? (x3)
At each stage of analysis:
Model Likelihood = -2 x log likelihood
Used to compute change in fit, as per diff in chi-square of model selection with AIC
