1 / 44

Introduction to Multilevel Analysis - PowerPoint PPT Presentation

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' Introduction to Multilevel Analysis' - gyala

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Introduction to Multilevel Analysis

Presented

by

Vijay Pillai

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

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

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.

4

Basically ML models are regression models.

Well, we all know the basic OLS regression model.

where

is the intercept ,

is the slope and

is the residual.

5

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

communities ?

6

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.

7

Where

is the intercept for the jth community,

• 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 community is

- called the Level – 2 regression model.

Level -2 regression models are expressed as follows.

Slide 25 community is