A stratified sample was drawn by country and school to obtain a balanced sample of p = 15 grade-4 students per school for each of four countries (The Netherlands (NL), Croatia (HR), Germany (DE), and Denmark (DK)) and two measurement occasions (2011, 2015). Achievement scores (first plausible value) of overall mathematics were considered. Performances of fourth and eight graders from more than 50 participating countries around the world can be found at (https://www.iea.nl/timss) The TIMSS achievement scale is centered at 500 and the standard deviation is equal to 100 scale score points. The TIMSS data set has a three-level structure, where students are nested within classrooms/schools, and the classrooms/schools are nested within countries. Only one classroom was sampled per school. Changes in the mathematics achievement can be investigated by examining the grouping of students in schools across countries. Changes in country-specific intraclass correlation coefficient from 2011 to 2015, representing heterogeneity in mathematic achievements within and between schools across years, can be tested. When detecting a decrease in average performance together with an increase of the intraclass correlation, a subset of schools performed worse. For a constant intraclass correlation across years the drop in performance applied to the entire population of schools. For different countries, changes in the intraclass correlation across years can be tested concurrently to examine also differences across countries.
data(timssICC)A data.frame with 16770 rows and 15 columns.
| math | numeric |
math score child |
| groupNL11 | numeric |
Indicator for child from NL in 2011 |
| groupNL15 | numeric |
Indicator for child from NL in 2015 |
| groupHR11 | numeric |
Indicator for child from HR in 2011 |
| groupHR15 | numeric |
Indicator for child from HR in 2015 |
| groupDE11 | numeric |
Indicator for child from DE in 2011 |
| groupDE15 | numeric |
Indicator for child from DE in 2015 |
| groupDR11 | numeric |
Indicator for child from DK in 2011 |
| groupDR15 | numeric |
Indicator for child from DK in 2015 |
| gender | numeric |
Female=0,Male=1 |
| weight | numeric |
Child sampling weight |
| yeargender | numeric |
Interaction for occassion and gender |
| lln | numeric |
total number of children in school-class |
| groupschool | factor |
Nested indicator for school in country |
Mulder, J. & Fox, J.-P. (2019). Bayes factor testing of multiple intraclass correlations. Bayesian Analysis. 14, 2, p. 521-552.