Daniel Horn
A note on the importance of within country standardization when conducting multilevel analysis : an example of stratification and the educational inequality of opportunity

Most of the internationally comparable datasets are designed to be mean-comparable, i.e. the means (and high and low values, percentages…etc.) of the variables can be compared across countries. But it is less obvious that the standard deviations of the same variables are also comparable, or that the unit-movements (regression coefficients) are comparable at all. Thus when conducting multilevel analyses one must standardize the variables of interest within country in order for the regression coefficients to be comparable across countries; i.e. transfer the standard deviations to be the same in every country. Hence, the effort to obtain an additional unit on the variable becomes the same across countries. This paper uses a multilevel model on the PISA 2003 dataset to illustrate the size of the bias that occurs when one misses to standardize the variables. An example on the effects of stratifying educational institutions on the inequality of opportunity is presented.