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Biostat 201: Winter 10

Biostat 201: Winter 10. Lab Session 3 - Supplement. Assignment 3 - Supplement. Multilevel Example. This slide presentation is an adapted example from UCLA’s Academic Technology Services. http://www.ats.ucla.edu/stat/sas/seminars/sas_mlm/mlm_sas_seminar.htm. The Data.

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Biostat 201: Winter 10

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  1. Biostat 201: Winter 10 Lab Session 3 - Supplement

  2. Assignment 3 - Supplement

  3. Multilevel Example • This slide presentation is an adapted example from UCLA’s Academic Technology Services. • http://www.ats.ucla.edu/stat/sas/seminars/sas_mlm/mlm_sas_seminar.htm

  4. The Data • 7,185 students in 160 schools • Student-level data (level 1): • mathach: student’s math achievement score • ses: student’s socio-economic status (SES) • School-level data (level 2): • school: school ID number • meanses: mean SES of students in that school • sector: 0=public school, 1=catholic school • Note: ses and meanses have been “centered”

  5. Importing the Data • SAS • libname src "C:\Desktop"; • data lab3; set src.hsb12;run; • STATA • cd "C:\Desktop" • insheet using hsb12.csv

  6. Fixed Effects ANOVA • Q: Is there a difference in math achievement scores in schools 1224, 1288, and 1296? • Note: We are interested in only these three schools. • Study design: We randomly sample students within each of these three schools.

  7. Parameterization • Student i in school j • Yij=b0j+sij • School j • b0j =a0j • Combined • School 1: Y=a01+eij • School 2: Y=a02+eij • School 3: Y=a03+eij • Y=b0+b1(school1)+b2(school2)+eij

  8. Code • SAS • proc mixed data=lab3; class school; model mathach = school / s; where school in ("1224","1288","1296");run; • STATA • gen school1=0 if (school==1224 | school==1288 | school==1296) • gen school2=0 if (school==1224 | school==1288 | school==1296) • replace school1=1 if (school==1224 & school1==0) • replace school2=1 if (school==1288 & school2==0) • reg mathach school1 school2 if (school==1224 | school==1288 | school==1296)

  9. Conclusion • Because p=0.0023 for “school”, we conclude that, statistically, the math achievement scores of these three schools are different.

  10. Random Intercept • Q: What is the average math achievement score in schools in California? • Study design: We randomly sample schools in California, then randomly sample the students within each of these schools. • Note: Suppose that the schools in our dataset have been randomly sampled from the schools in California.

  11. Parameterization • Student i in school j • Yij=b0j+eij • A student’s score is the school’s score + the student’s deviation • School j • b0j =a00+t0j • The school’s score is the global score + the school’s deviation • Combined • Yij=(a00+t0j) +eij

  12. Code • SAS • proc mixed data=lab3; class school; model mathach = / s cl; random intercept / sub=school;run; • STATA • xtmixed matchach || school:

  13. Conclusion • We conclude that the average math achievement score of schools in California is 12.64. • The variance between schools is estimated to be 8.61. • The variance between students (or within schools) is estimated to be 39.15.

  14. Random Intercept With a Level 2 Effect • Q: What is the average math achievement score in schools in California adjusting for the school’s SES? • Study design: We randomly sample schools in California, then randomly sample the students within each of these schools. • Note: Suppose that the schools in our dataset have been randomly sampled from the schools in California.

  15. Parameterization • Student i in school j • Yij=b0j+eij • A student’s score is the school’s score + the student’s deviation • School j • b0j =a00+a01(meanses)+t0j • A school’s score is the global score + the school SES effect + the school’s deviation • Combined • Yij=(a00+t0j) +a01(meanses)+eij

  16. Code • SAS • proc mixed data=lab3; class school; model mathach = meanses / s cl ddfm=bw; random intercept / sub=school;run; • STATA • xtmixed mathach meanses || school:

  17. Conclusion • The adjusted average math achievement score of schools in California is 12.65. • A school’s centered SES is positively associated with its match achievement scores (p<0.0001). [can also interpret the slope] • The variance between schools is estimated to be 2.64. • The variance between students is estimated to be 39.16.

  18. Random Intercept With a Level 1 Effect • Q: What is the average math achievement score in schools in California adjusting for the student’s SES? • Study design: We randomly sample schools in California, then randomly sample the students within each of these schools. • Note: Suppose that the schools in our dataset have been randomly sampled from the schools in California.

  19. Parameterization • Student i in school j • Yij=b0j+b1j(cses)+eij • A student’s score is the school’s score + the “school specific” student SES effect + the student’s deviation • School j • b0j =a00+t0j • A school’s score is the global score + the school’s deviation • b1j =a10+t1j • The “school specific” student SES effect is the global student SES effect + the “school specific” student SES effect deviation • Combined • Yij=(a00+t0j) +(a10+t1j)(cses)+eij

  20. First, some data stuff… • The variable “cses” isn’t in our dataset. We have to calculate it • cses = ses – meanses • This gives us the student’s SES in regards to the school’s centered SES. • SAS • data lab3; set lab3; cses = ses - meanses;run; • STATA • gen cses = ses - meanses

  21. Code • SAS • proc mixed data=lab3 covtest; class school; model mathach = cses / s ddfm=bw; random intercept cses / sub=school type=un;run; • STATA • xtmixed mathach cses || school:cses, covariance(unstructured)

  22. Conclusion • The adjusted average math achievement score of schools in California is 12.65. • The student’s SES effect is estimated to be 2.19. • The variance between schools is estimated to be 8.68. • The variance between students is estimated to be 36.70. • The variance of the student SES effect is estimated to be 0.69.

  23. Random Intercept With a Level 1 and 2 Effects • Q: What is the average math achievement scores in schools in California adjusting for the student’s SES and the school’s sector? • Study design: We randomly sample schools in California, then randomly sample the students within each of these schools. • Note: Suppose that the schools in our dataset have been randomly sampled from the schools in California.

  24. Parameterization • Student i in school j • Yij=b0j+b1j(cses)+eij • A student’s score is the school’s score + the “school specific” student SES effect + the student’s deviation • School j • b0j =a00+a01(sector)+t0j • A school’s score is the global score + the sector effect + the school’s deviation • b1j =a10+a11(sector)+t1j • The “school specific” student SES effect is the global student SES effect + the sector effect + the school’s sector effect deviation • Combined • Yij=b0j+b1j(cses)+sijYij=[a00+a01(sector)+t0j]+[a10+a11(sector)+t1j](cses)+eij • Yij=a00+a01(sector)+t0j+a10(cses)+a11(cses*sector)+t1j(cses)+eij • Yij=(a00+t0j)+a01(sector) +(a10+t1j)(cses)+a11(cses*sector)+eij

  25. Code • SAS • proc mixed data=lab3 covtest; class school; model mathach = sector cses cses*sector / s cl ddfm=bw; random intercept cses / sub=school type=un;run; • STATA • gen cses_sector = cses*sector • xtmixed mathach sector cses cses*sector || school:cses, covariance(unstructured)

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