Multilevel Models Flashcards
Why multilevel models?
They are very popular and will appear more and more of the articles you read - ideally suited for a variety of research designs
What is wrong if everyone scores the same on a quiz?
No way to predict / explain the scores - if there is no variance, can’t explain why people have scored in a certain way
Do people vary?
Usually people vary in their scores
some higher, some slower
more extreme values are infrequent
What is the point of explaining variance?
Want to know why the scores vary in the way that they do - to explain when or why scores are higher or lower
Want to explain the variance in the outcome: the outcome is what we are interested in explaining
What is variance partitioned into?
SST - total variance
SSM - improvement due to model
SSR - error in the model
want to make our model as big as we can so explain more SSM and as least SSR
the variation can explain is due to predictors, the variance our predictors can’t explain is unexplained residual variance or error
What is the equation for the linear model and what does each part mean?
y = b0 + b1 x1 + e
y = outcome/dependent variable - what we want to predict
b0 = the intercept, the value of y when x is 0
b1 = the estimate or parameter or slope - relationship between x and y
e = some degree of error
Together, the intercept and slope can describe any straight line - useful for linear model
What is the problem with hierarchical data?
It breaks the assumption of independent of errors - there are pre existing differences which have been created by the environment. For example, differences in the predictor (classroom tested in) and the teacher that has taught them, one might encourage spelling more - shows it would be influenced by the teaching The children in each class have scores that are related to each other because of a common factor - only matters if it directly related to the variable being measured
What is hierarchical data?
When the scores naturally fall into groups or clusters that share common influences / contexts - pre existing sub groups or structures within the data
for example, classroom and school - natural grouping which already exist when you do a test
What does crossed participants and items refer too?
All participants see all words and all words see all the participants - each participant and each condition is a group
What are examples of hierarchical data?
NSS scores across different universities
Mortality rates across different departments in different hospitals
Lexical decision reaction times across participants and words
Why can’t we use a regular linear model?
Because we would have to average across levels, so we would lose a lot of the individual data - but all this information is very useful
How do we account for hierarchical data?
Multilevel models
What do multilevel do?
Account for data wth multiple levels - same equation as the linear model but with new random elements
What is a fixed effect?
The predictor - think there is a fixed impact of something on your outcome
We hypothesise it has the same impact no matter what level a child is in
What is a random effect?
The hierarchical effect - basically means, a different slope/intercept for each group in the model
What do random variables represent?
The groups in the hierarchy - have to code each variable
Why do you add random variables?
To model the underlying hierarchical structure of the data - can apply to intercepts, slopes or both - explains more of the variance
What are random intercepts?
Each level has its own intercept estimated by the model around the overall intercept for the predictor - let them vary randomly
baseline score is different, expands the beta0, higher intercept for some levels
What are random slopes?
Each level of the variable has its own slope estimated by the model around the overall slope for the predictor - allows the relationship between the predictor and outcome b1 to be different for each level
same intercept, different slopes - but this doesn’t fit the data well
Why do we want both random slopes and intercepts?
Because it allows the linear model to be adapted for each sub group - each group has a slope and an interval
the overall relationship is the fixed effects
What do you look at once accounted for random effects?
Whether you still have an overall effect of the predictor on the outcome - allows a better fit for the data
What are the benefits of multilevel models?
Captures the existing relationship between people or groups that would otherwise be unexplained variation - by accounting of the variation due to shared context, get a clearer picture of the fixed effects
Explicitly models for the structure of hierarchical data
You can add random intercepts and slopes to any type of linear model - all it does is add in these variables
What is our overall goal?
To explain the variance, particularly in the outcome
What elements are included within a multilevel model?
Multilevel models include random elements to model this hierarchy
Random effects: allow each level of the random variable (e.g. each classroom in a school) to have its own intercept or slope or both
Fixed effects: an effect assumed to be consistent across different groups/contexts – previously simply called predictors or covariates
