Schmid Comparative Migration Studies (2020) 8:25 Western settler states – the United States, Canada, Australia, and New Zealand. This leads to 713 country-year observations. Part of the analysis will sub-divide the timespan from 1980 to 2010 into three geopolitical periods to detect changes over time. They roughly correspond to the three decades. The 1980–1991 period marks the final years of the Cold War. After the collapse of the Soviet Union, the world has become fundamentally different. Globalisation picked up speed and the USA sat at the top of the liberal world order during the 1992– 2001 period. The world changed again in fundamental ways after 9/11. Especially the latter event is often assumed to be important for (changing) immigration and citizenship policies. In line with the concept specification outlined in the first part of this article, the measurement of IRO covers the policy fields of labour immigration, family reunification, and asylum. There are two components for each field: entry and stay. Entry requirements define the criteria that immigrants need to fulfil to be able to enter a host country (called eligibility and conditions in IMPIC). Conditions for stay define the security of status and the possibilities for long-term settlement associated with a specific entry permit (called security of status in IMPIC; for details see Bjerre et al. 2016). This leads to a total of six policy components. Based on the conceptualisation of CRI above, CITRIX is composed of four policy components. These are (1) the strength of jus soli; (2) residence duration requirements; (3) the toleration of multiple citizenship; and (4) further naturalisation requirements, namely language tests and citizenship tests as well as economic and criminal record requirements. The first is measured as years and then rescaled from 0 to 100 with 100 indicating the least amount of years required in the sample. For the others the threepoint 0–50-100 MIPEX scales are applied, though for one jus soli indicator the scale is refined and for the dual citizenship component it is rearranged. More details as well as validity tests of CITRIX can be found in Additional file 1. In Additional file 1, I also offer some reflections on building indices of immigration policies, elaborating on how the country-year methodology used to measure immigration regimes qualifies the analysis, and how it compares to other approaches in the literature. The IMPIC components are coded with an ordinal restrictiveness scale from 0 to 1, using theoretical minima and maxima (Helbling et al. 2017, p. 89). A score of 1 indicates maximum restrictiveness. I reverse the scales and linearly transform them so that 0 represents the empirical minimum and 100 the empirical maximum. Except for the residence duration requirement, the data of CITRIX are also ordinal. Also, there 0 represents the empirical minimum and 100 the empirical maximum. Given the ordinal scaling, I use categorical instead of standard principal component analysis (CATPCA; Meulman and Heiser 2005) to analyse the dimensionality of the data. This method can accommodate variables that are scaled at various levels (residence duration is deemed numeric) with the aim of modelling non-linear relationships. The output of CATPCA is similar to standard PCA – it can be interpreted in the same way (Linting et al. 2007, pp. 27–8). For the empirical analysis, the 713 country-year observations are pooled. This means that each indicator in each country and year is correlated with the indicator in that country in the previous year. Whether this autocorrelation poses a problem for principal component analysis has been contested. Jolliffe (2002, p. 299) argues that this problem poses no serious threat if the main goal of PCA is descriptive. This applies to my Page 11 of 20