# 1 Multilevel modeling of educational longitudinal data with crossed random effects Minjeong Jeon Sophia Rabe-Hesketh University of California, Berkeley.

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1 Multilevel modeling of educational longitudinal data with crossed random effects Minjeong Jeon Sophia Rabe-Hesketh University of California, Berkeley 2008 Fall North American Stata Users Group meeting Nov. 13. 2008

Motivation: How to model this data? 2  Longitudinal cross-classified data  Longitudinal data -Repeated observations within students  Promotion to high school -First two years in middle school -Last two years in high school

Diagram: Longitudinal cross-classified data 3 T1,..T4: Time(wave), Stu: students MS: middle school, HS: high school Rasbash et al. (2005; 2008) Jeon & Rabe-Hesketh

Purpose of the study  Propose three modeling strategies crossed random effects  Estimate crossed random effects of middle school (MS) and high school (HS) xtmixed  By xtmixed in Stata ★ Key point ! MS and HS random effects change over time  Impacts of MS and HS random effects change over time 4

Data  Source:  Source: The Korea Youth Panel Survey (KYPS) (http://www.nypi.re.kr/panel/index.asp)  Prospective panel survey: (2003-2006 year)  Middle school 2 nd (8 th graders), Age(m) =13  Sample design: Stratified multi-year cluster sampling 5

More about the data 6  Summary statistics  Summary statistics: Number of schools & students

Data: Crossed structure 7  Cross-classification between MS and HS MS id HS id

More about the crossed structure 8  Number of high schools within middle school Number of MS per HS: 1~5 Number of HS per MS: 2~17

School area information 9 Maximum number of MS per area = 21 Maximum number of HS per area = 175  15 Areas that students do not “cross” when moving from MS to HS

Study variables 10

within-student, within-school variation Self esteem: within-student, within-school variation 11 N=31N=24 N=20N=7

12 Model specification: Model1  Trick 1

Model specification: Model1 13  Trick 2

Using a trick? 14  Exactly same results! (from model1)

Modeling strategies 15

Stata commands 16

Results: Random effects 17 Random intercept model  Random intercept model

Fixed effects 18  Increase over time  Decrease in the increase (From model 1)

Discussion  Use a trick computational efficiency  Use a trick for computational efficiency  to handle random slopes in cross-classified model  Need an easy way to handle random slopes in cross-classified model   Future work: Find weights empirically Find weights empirically 19

20 Thank you very much! Contact Minjeong Jeon (mjj@berkeley.edu) Sophia Rabe-Hesketh(sophiarh@berkeley.edu) Graduate School of Education University of California, Berkeley

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