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Multilevel modeling Multilevel modeling

of educational longitudinal data of educational longitudinal data

with crossed random effects with crossed random effects

Minjeong JeonSophia Rabe-Hesketh

University of California, Berkeley

2008 Fall North American Stata Users Group meeting

Nov. 13. 2008

Motivation: How to model this Motivation: How to model this data?data?

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Middle School

Hish

School

Student

time1 time3time2 time4

Longitudinal cross-classified Longitudinal cross-classified data data

Longitudinal data -Repeated observations within students

Promotion to high school-First two years in middle school-Last two years in high school

Diagram: Diagram: Longitudinal cross-classified Longitudinal cross-classified data data

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T1,..T4: Time(wave), Stu: students

MS: middle school , HS: high school

MS HS

Stu

Time

Rasbash et al. (2005; 2008)

MS HS

Stu

T1 T2 T3 T4

MS HS

Stu

T1 T2 T3 T4

Jeon &Rabe-Hesketh

<1>

<2>

<3>

Purpose of the studyPurpose of the study

Propose three modeling strategies Propose three modeling strategies Estimate crossed random effects crossed random effects of

middle school (MS) and high school (HS) By xtmixedxtmixed in Stata

★★Key point !Key point ! Impacts of MS and HS random effects MS and HS random effects

change over time change over time

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DataData

Source: Source: The Korea Youth Panel Survey (KYPS) (http://www.nypi.re.kr/panel/index.asp)

Prospective panel survey: (2003-2006 year)

Middle school 2nd(8th graders), Age(m) =13

Sample design: Stratified multi-year cluster

sampling

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More about the dataMore about the data

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Summary statisticsSummary statistics: Number of schools & students

Data: Crossed structureData: Crossed structure

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Cross-classification between MS Cross-classification between MS and HSand HSMS idMS id

HS idHS id

More about the crossed More about the crossed structure structure

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Number of high schools within middle school Number of high schools within middle school

Number of MS

per HS:1~5

Number of HS

per MS:2~17

School area informationSchool area information

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Maximum number of MS per area = 21

Maximum number of HS per area = 175

15 Areas that students do not “cross” when moving 15 Areas that students do not “cross” when moving from MS to HS from MS to HS

Study variablesStudy variables

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Self esteem: within-student, within-school within-student, within-school variation variation

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N=31 N=24

N=20 N=7

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Model specification: Model1Model specification: Model1

MS HS

Stu

T1 T2 T3 T4

Trick 1Trick 1

Model specification: Model1Model specification: Model1

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Trick 2Trick 2

Using a trick? Using a trick?

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Exactly same results!

(from model1)

Modeling strategiesModeling strategies

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Stata commandsStata commands

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Results: Random effectsResults: Random effects

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Random intercept Random intercept model model

FixedFixed effectseffects

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Increase over time

Decrease in the increase

(From model 1)

DiscussionDiscussion

Use a trick Use a trick for computational computational efficiency efficiency

Need an easy way to handle to handle random slopes in cross-classified random slopes in cross-classified modelmodel

Future work:

Find weights empirically Find weights empirically 19

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Thank you very much!Thank you very much!

ContactContactMinjeong Jeon (mjj@berkeley.edu)

Sophia Rabe-Hesketh(sophiarh@berkeley.edu)

Graduate School of Education

University of California, Berkeley