exam {gammi} | R Documentation |
Cross-Classified Examination Data
Description
Scores on secondary school leaving examinations (response) and verbal reasoning scores in primary school (fixed effect) for 3435 students in Fife, Scotland. The students are cross-classified in 148 primary schools (random effect) and 19 secondary schools (random effect).
Usage
data("exam")
Format
A data frame with 3435 observations on the following 4 variables.
VRQ.score
Verbal Reasoning Quotient obtained in primary school (integer vector ranging from 70 to 140)
Exam.score
Leaving examination score obtained in secondary school (integer vector ranging from 1 to 10)
Primary.school
Primary school identifier (factor with 148 levels)
Secondary.school
Secondary school identifier (factor with 19 levels)
Details
The VRQ scores were obtained at age 12 (right before entering secondary school), and the Exam scores were obtained at age 16 (right before leaving secondary school). The VRQ scores are constructed to have a population mean of 100 and population standard deviation of 15. The goal is to predict the leaving Exam scores from the VRQ scores while accounting for the primary and secondary school cross-classifications.
Source
Data Obtainable from: https://www.bristol.ac.uk/cmm/team/hg/msm-3rd-ed/datasets.html
References
Goldstein, H. (2011). Multilevel Statistical Models, 4th Edition. Chapter 12: Cross-classified data structures (pages 243-254). doi:10.1002/9780470973394
Paterson, L. (1991). Socio-economic status and educational attainment: a multidimensional and multilevel study. Evaluation and Research in Education, 5, 97-121. doi:10.1080/09500799109533303
Examples
# load 'exam' help file
?exam
# load data
data(exam)
# header of data
head(exam)
# fit model
mod <- gammi(Exam.score ~ VRQ.score, data = exam,
random = ~ (1 | Primary.school) + (1 | Secondary.school))
# plot results
plot(mod)
# summarize results
summary(mod)
# variance parameters
mod$VarCorr