Linear Mixed Models

Question 1

Linear Mixed Model

Answer 1

Allow the study of the relationship between a continuous dependent variable (response) and one or more independent variables (factors or covariates)

Question 2

LMM cater for data that are not independent

Answer 2

LMM aka
multilevel models
Hierarchical linear models
Random Effects models
Nested models

Question 3

LMM assume residuals are normally distributed but may not be independent or have constant variance

Answer 3

LMM flexibly represent the covariance structure induced by the grouping of the data

Question 4

Covariance Structure

Answer 4

Units are correlated

Question 5

LMM can be used to analyse different types of data

Answer 5

Longitudinal data
repeated measures
multilevel data
clustered data
block designs

Question 6

Clustered data is

Answer 6

observations made on subjects within the same group e.g., students within classrooms within schools
This also be known as multilevel data

Question 7

Longitudinal or repeated measures

Answer 7

multiple observations made on the same subject over time, e.g., blood pressure measured for each patient each month for 6 months

Question 8

LMM

Answer 8

Defined: the model is linear in the parameters and the covariates involve a mix of fixed and random effects

Question 9

Fixed Effects

Answer 9

The factor or cluster effects (Beta i) are specific to the clusters in the study, e.g., Beta i only estimated for doctors practicing at Wollongong hospital.

Question 10

Random Effects

Answer 10

The factor levels in the study are randomly selected from a population of all possible factor levels

Question 11

When to use Random Effects

Answer 11

When we want to make conclusions about a wider population of clusters (not just about the tmt effect)
When the no. of observations per cluster vary, particularly when there are small numbers of observations in some clusters
When tmts and covariates applied differently in different clusters e.g., students within schools