Multilevel modeling of educational longitudinal data with crossed

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 1

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

Diagram: Longitudinal cross-classified data <1> <2> <3> Rasbash et al. (2005; 2008) Jeon & Rabe-Hesketh T 1, . . T 4: Time(wave), Stu: students MS: middle school , HS: high school 3

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

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

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

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

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

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

Study variables 10

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

Model specification: Model 1 Trick 1 12

Model specification: Model 1 Trick 2 13

Using a trick? Ø Exactly same results! (from model 1) 14

Modeling strategies 15

Stata commands 16

Results: Random effects v Random intercept model 17

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

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

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