Multilevel Modeling
Using HLM and MLwiN
Xiao Chen
UCLA
Academic Technology Services
Hierarchical Data Structure
Organizational studies

Students nested in schools and variables are
measured at both student level and school level
Repeated measures

Multiple observations are collected over time on
each person
Doubly nested

Multiple observations are nested in individuals
and individuals are nested within organizations
Statistical Treatment of Clustered Data
Aggregation
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Moving variables from student level to school level
Shift of meaning
Ecological fallacy
Relationships observed for groups necessarily hold for
individuals

Neglecting the original data structure
Disaggregation
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Moving variables from school level to student level
Both macro level and micro level variables exist in the
model
Data has only micro level variables
What can Multilevel Modeling do?
Improving estimation of effects within
individual units
Hypotheses testing about cross-level
effects
Partitioning of variance and covariance
components among levels
Overview of HLM and MLwiN
HLM
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Under development
since mid 1980’s
First window version
came out in 1997
Version 6 in
September 2004
Run on Windows
95/98/NT/Me/2000/XP
Minimum 2 MB of
RAM and 2 MB of disk
space
MLwiN
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Based on MLn
First released in 1997
Version 2 in 2004
Run on Windows
95/98/NT/Me/2000/XP
32 Mb of Ram or more
A hard disk with at
least 20MB of
available space
Continued
HLM
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Graphical interface
Continuous outcome
Binary, count outcome
Multivariate outcome
variables
Cross-classified data
Sample weights
Number of levels: 3
MLwiN

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Graphical interface
Continuous outcome
Binary, count outcome
Multivariate outcome
variables
Cross-classified data
Sample weights
Number of levels: can
be many (default is 5)
Data Format for Multilevel Analysis
Inputting Data
HLM

Use a level-1 data set and
a level-2 data set for
creating an .mdm file
(mdmt stands for multivariate data
matrix)
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Read SAS, SPSS, STATA
and SYSTAT files directly
Built-in Stat/transfer for
many different data types
Use mdm file for
computation, very efficient
Use raw data sets for
graphics
MLwiN
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One single file
ASCII file
Native MLwiN format
(.ws extension)
Stata2mlwin program
for stata users
Set-up the size of
worksheet (memory
control)
Data Management
HLM

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Length of a variable name
is 8
No data management
Predictor variables can be
either grand-mean
centered or group-mean
centered
Cross-level interaction is
naturally built
Summary statistics created
when .mdm file is created
MLwiN
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Can create new variables
Categorical variables can
be dummied automatically
Summary statistics
Cross-level interaction
variable has to be created
before building up a model
HLM: Multilevel Model Approach
MLwiN: Mixed Model Approach
Output From HLM
Output from MLwiN
Graphics for Exploring Data: HLM
(Data-based graphs): line plots, scatter plots, and box plots
27.49
SECTOR = 0
SECTOR = 1
12.19
4.54
26.38
-3.12
SECTOR = 0
SECTOR = 1
0
12.00
18.73
MATHACH
MATHACH
19.84
11.08
3.43
-4.22
-1.82
-0.94
-0.07
SES
0.80
1.67
Graphs for Exploring the Model: HLM
(Model-based graphs)
20.89
MEANSES: low er
MEANSES: mid 50%
MEANSES: upper
13.85
10.33
6.82
0
3.00
6.00
9.00
21.40
12.00
MEANSES: low er ha
MEANSES: upper ha
17.46
MATHACH
INTERCEPT
17.37
13.53
9.59
5.65
-3.00
-1.66
-0.32
SES
1.03
Graphics for Exploring Data: MLwiN
Graphs for Exploring the Model: MLwiN
(Model-based graphs)
Reference and Site(s)
Ming Yang, Review of HLM 5.04 for Windows:
http://multilevel.ioe.ac.uk/softrev/reviewhlm5.pdf
Andy Jones, A review of random effects models in
MLwiN (version 2.0):
http://multilevel.ioe.ac.uk/softrev/reviewmlwin.pdf
MLwiN 2 user’s manual:
http://multilevel.ioe.ac.uk/download/userman20.pdf
Goldstein, Tutorial in Biostatistics Multilevel modeling of
medical data
http://media.wiley.com/product_data/excerpt/08/0470023
7/0470023708.pdf
Singer and Willett: Applied Longitudinal Data Analysis:
Modeling Change and Event Occurrence:
http://gseacademic.harvard.edu/~alda/
http://www.ats.ucla.edu/stat/