Transcript Introduction to Multilevel Analysis pptx (730kb)

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
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.
one
class
Student
student
student
Just another way to show the hierarchical
structure
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In the last figure there were two levels.
There is no reason why their can’t be 3 or 4 (Multi.)
ML models are also called
Mixed models
Multilevel linear models
Random effect models
3
Glossary of terms
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.
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ON ML MODELS
Basically ML models are regression models.
Well, we all know the basic OLS regression model.
yi  0  1 X i  ri
where
0
is the intercept ,
1
is the slope and
ri
is the residual.
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In regression we also make assumptions about the residuals.
For example, residuals are normally distributed,
with mean0 and variance
2
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
communities ?
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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.
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So now the our regression line for the ith person in the jth community is
yij   0 j  1 j X ij  ri j
Where
0 j
is the intercept for the jth community,
1 j
is the slope for the jth community, so on
So , if we randomly select communities and compute the
regression line for each community
-we can consider the intercept as a random variable
-we can consider the slope as a random variable
-Both the intercept and slope can then be predicted by other
properties of the communities
-8
ML models fit a regression model for each of the
 0 j .and .ij.
- called the Level – 2 regression model.
Level -2 regression models are expressed as
follows.
0 j   00   01W j  u
1 j   10   11W j  u
0j
1j
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