Introduction to Multilevel Analysis. Presented by Vijay Pillai. A GENERAL INTRODUCTION In Hierarchical data one unit is nested with in the other unit. These units are also called levels Level -1 represents the smallest unit of measurement Eg.: students
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In Hierarchical data one unit is nested with in the other unit.
These units are also called levels
Level -1 represents the smallest unit of measurement Eg.: students
Level -2 represents a larger unit of measurement Eg.: Class
The level -1 units are said to be nested within level -2 units
Probably, the most common educational example is when the
two different units are classes and students.
There is no reason why their can’t be 3 or 4 (Multi.)
ML models are also called
Multilevel linear models
Random effect models
Multilevel data –Data that have some intergroup membership
Fixed effect: A condition in which the levels of a factor
include all levels of interest to the researcher
Random effect: A condition in which the levels of a factor
represents a random sample of all possible levels.
Basically ML models are regression models.
Well, we all know the basic OLS regression model.
is the intercept ,
is the slope and
is the residual.
For example, residuals are normally distributed,
with mean0 and variance
no multi collinearity, etc
Of course, this model works well, when we have
a homogeneous population- such as a single community.
But what if we have observations from multiple
Each community then has its own regression line (with a intercept and a slope),
Now , the population we have may longer be homogenous.
We need a notation to indicate which community we are talking about
We will use a new subscript j to indicate which community we are talking about
We will have a total of j communities in our sample.
is the intercept for the jth community,
ML models fit a regression model for each of the community is
- called the Level – 2 regression model.
Level -2 regression models are expressed as follows.
Slide 25 community is