Multilevel Modeling: Issues and Applications

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Multi-level Modeling Issues and Applications
Sam Field Rob Crosnoe Population Research
Center April 15, 2004 sfield_at_mail.la.utexas.edu
, crosnoe_at_mail.la.utexas.edu
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Outline

• Introduction
• Multi-level Data
• Multi-Models
• Uses of multi-level models
• Applications

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Conceptual Issues

• human beings are social animals that create,
  and are subsequently effected by, modes of social
  organization that can vary across time and
  space. (Teachman and Crowder, 2002).

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Conceptual Issues

• Individuals (i (1,2,3,n))
• Modes of Social Organization (j (1,2,3,p))
• Communities (cities, towns, neighborhoods, etc.)
• Formal Organizations (schools, businesses, etc.).
• Social networks (peer groups)
• Primary Institutions (family)

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Conceptual Issues

• Lets assume for now that human beings are
  primarily effected by social context (rather then
  creating it).
• Men make their own history, but they don not
  make it just as they please they do not make it
  under circumstances chosen by themselves, but
  under circumstances directly found, given and
  transmitted from the past. The tradition of all
  dead generations weighs like a nightmare on the
  brain of the living Karl Marx, The Eighteenth
  Brumaire.

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In other words
Social Context
How do we examine the impacts of social context
empirically?
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Multi-level Data
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Multi-level Data
data delinquency do school 1 to
35 num_students ranpoi(0,12) do student
1 to num_students delinquency
2rannor(0) output end end run
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The Multi-level Model

• Individuals (i (1,2,3,n))
• Modes of Social Organization (j (1,2,3,p))

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The Multi-level Model (Multiple Equations)
random intercept
random slope
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Random Effects Models
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The Multi-level Model (Single Equation)
Level 1 Covariate
Level 2 Covariate
Cross-level interaction
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Simulated Example
Religious Homogeneity in School
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School Level
data delinquency do school 1 to
100 num_students ranpoi(0,9) t00
1.5 t01 -.08 t10 -.5 t11 -.03 w
ranuni(0)100 u0j sqrt(1.5)rannor(0) u1j
sqrt(.5)rannor(0) b0j t00 t01w
u0j b1j t10 t11w u1j
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Student Level
do student 1 to num_students x
rannor(0) rij sqrt(3)rannor(0)
delinquency b0j b1jx rij
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Data
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Three Uses of Multi-level Models

• Improved estimation of individual effects
• School specific slopes and intercepts.
• Modeling cross-level effects.
• Partitioning variance-covariance components.

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Example 1
Testing Higher-Level Main Effect
Question Is alcohol use among young men less
common in neighborhoods with high degrees of
neighbor cohesion?   Procedure Look for main
effect of neighborhood cohesion (nh2bonds) on
individual alcohol use (alcuse), taking into
account the nested nature of the data to produce
robust standard errors.
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Step 1 Run Unconditional Model and Calculate
Intra-Class Correlation
  Code proc mixed datanhooddata noclprint
class nhoodid weight wghtvar model
alcuse /s random intercept /typeun
subnhoodid run   Output Covariance
Parameter Estimates Cov Parm Subject
Estimate UN(1,1) nhoodid
0.1458 Residual 2.3898   ICC
.15/2.39.15 .06
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Step 2 Estimate Higher-Level Effect
Code proc mixed datanhooddata noclprint
class nhoodid weight wghtvar model
alcuse agew1 white ses hispanic asian nh2bonds
/s random intercept /typeun subnhoodid
run   Output Fit Statistics -2 Res Log
Likelihood 39610.2 AIC (smaller is
better) 39614.2 AICC (smaller is better)
39614.2 BIC (smaller is better)
39618.8  
Standard Effect Estimate Error
DF t Value Pr gt t Intercept -3.3680
0.2737 73 -12.31 lt.0001 AGEW1
0.1934 0.01323 9027 14.62
lt.0001 white 0.2902 0.05103 9027
5.69 lt.0001 hispanic 0.3373
0.07008 9027 4.81 lt.0001 asian
-0.3590 0.09413 9027 -3.81
0.0001 ses 0.01153 0.01456 9027
0.79 0.4287 misalc 0.8540
0.1115 9027 7.66 lt.0001 nh2bonds
0.1106 0.03527 9027 3.14
0.0017  
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Example 1 (cont.)
Testing Higher-Level Moderating Effect
Question Are SES differences in alcohol use less
pronounced in neighborhoods with a high degree of
cohesion?   Procedure Look at whether the main
effect of individual SES on individual alcohol
use varies significantly across neighborhoods in
the data (random slope) and then whether this
significant neighborhood by neighborhood
variation is explained by neighborhood cohesion
(cross-level interaction).
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Step 1 Test for Random Slope
  Code proc mixed datanhooddata noclprint
class nhoodid weight wghtvar model
alcuse agew1 white ses hispanic asian nh2bonds
/s random intercept /typeun subcommon
run   proc mixed datanhooddata noclprint
class nhoodid weight wghtvar model
alcuse agew1 white ses hispanic asian nh2bonds
/s random intercept ses /typeun
subcommon run
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Output   Covariance Parameter Estimates Cov Parm
Subject Estimate UN(1,1) nhoodid
0.2671 UN(2,1) nhoodid -0.06397 UN(2,2)
nhoodid 0.01835 Residual
2.2884   Check for significant decrease in 2
Res Log Likelihood 39610.2 (no RS) - 39553.3
(with RS) 56.9/2df, p lt .001
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Step 2 Estimate Cross-Level Interaction to
Explain Random Slope
proc mixed datanhooddata noclprint class
nhoodid weight wghtvar model alcuse
agew1 white ses hispanic asian nh2bonds
sesnh2bonds /s random
intercept ses /typeun subcommon
run   Check whether adding this cross-level
interaction explain the random slope (e.g., does
it become non-significant?
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Example 2
Question Does student failure lead to greater
levels of delinquency in high school? If so, are
there school contexts that can block this from
happening?
Step 1 Test main effect of individual failure on
individual delinquency No school variables
included but still estimate a random intercept to
account for nested nature of the data.   proc
mixed dataschdata noclprint class schid
weight wghtvar model delinq agew1
white ses fail /s random intercept /typeun
subschid run   Fail has significant
effect on delinq ICC .11/2.11.11 .05
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Step 2 Add School Variables
Code proc mixed dataschdata noclprint
class schid weight wghtvar model
delinq agew1 white ses fail press private /s
random intercept /typeun subschid   Output
Standard Effect
Estimate Error DF t Value Pr gt
t Intercept -3.0824 0.2792 73
-11.04 lt.0001 white 0.1599
0.03232 9028 4.95 lt.0001 AGEW1
0.1827 0.01326 9028 13.78
lt.0001 SES 0.02718 0.01462 9028
1.86 0.0631 w1fail 0.3168
0.03560 9028 8.90 lt.0001 press
-0.8647 0.1162 9028 -7.44
lt.0001 private -0.1176 0.03686 9028
-3.19 0.0014
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Step 3 Test for Random Slope
proc mixed dataschdata noclprint class
schid weight wghtvar model delinq
agew1 white ses fail smallsc press private /s
random intercept fail /typeun
subschid   39584.7 - 39551.7 33.0/2df, p lt
.001
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Step 4 Estimate Cross-Level Interactions
Code proc mixed dataschdata noclprint
class schid weight wghtvar model
delinq agew1 white ses fail smallsc press
private pressfail
privatefail /s random intercept fail
/typeun subschid   Output
Standard Effect Estimate Error
DF t Value Pr gt t   Intercept
-3.0908 0.2805 73 -11.02
lt.0001 white -0.1615 0.03227 8954
-5.00 lt.0001 AGEW1 0.1840
0.01324 8954 13.90 lt.0001 apare
0.03054 0.01461 8954 2.09
0.0366 w1fail 0.2800 0.3004 72
0.93 0.3545 press 0.8916
0.1177 8954 7.57 lt.0001 privat
0.1020 0.03769 8954 2.71
0.0068 w1failpress -0.08711 0.1898 8954
-0.46 0.6462 w1failprivate 0.04203
0.021 8954 0.72 0.0500