The value-added model: Multilevel Model

Currently available information for value-added measurement

• End of P6 AAI• End of S5 HKCEE• End of S7 HKALE

S1-S5

S6-S7

Control Variables in Multilevel Model

• Gender• Academic ability• Average academic ability• All Girls• All Boys• Number of different schools attended (for S1-S5 cohort only)• Change of schools at S3-S4 (for S1-S5 cohort only)

Student exam score

= Student predicted score + School residual +

School differential effect + Student residual

measure of school effectiveness

Compute School Value-added using Multilevel Model

yij = b00 + b1x1ij + … bnxnij + (u0j + u1jx1ij + eij)

Student exam scoreStudent predicted score

School residual

school differential effect

student residual

Compute School Value-added using Multilevel Model

Multilevel model provides the most statistically valid way of measuring school value-added estimate

Multilevel model takes into account complex interrelationships among the factors affecting student performance

Validity of Value-added

No. of Candidates 10 15 20 25 30 35 40 45 50 60 70 80 90 100

HKCEE .66 .74 .79 .82 .85 .87 .88 .89 .90 .92 .93 .94 .94 .95 HKALE .61 .70 .75 .79 .82 .84 .86 .87 .88 .90 .91 .92 .93 .94

Average reliabilities across subjects for different values of number of candidates in 1999

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 20 40 60 80 100 120

Number of Candidates

Rel

iabi

lity

Chinese

Biology

Reliability of Value-added

Value-added will not be provided for subjects with less than 10 students taking the examination in the school

Value-added may not be provided for subjects with the low level of precision by the value-added model, for example, EPA, Social Studies, Human Biology, Commerce, Visual Arts, Music.

To ensure reliable value-added

To ensure reliable value-added estimates

Confidence intervals are reported for all value-added estimates, indicating the degree of certainty surrounding each estimate

Limitation of value-added

It only reflects the academic performance of students.

It doesn't provide the absolute performance of students.

It doesn't provide the reasons behind the value-added performance.