Latent variable or achievement-tailored composite?: The home resources for learning (HRL) index in TIMSS and PIRLS

Background variables in international large-scale assessments are often combined into indices for statistical analyses. Using the Home Resources for Learning (HRL) index as an example, we draw from the Cowan et al. (2012) report on socio-economic status (SES) to consider parallel ways of defining HRL composites, and show how the choice among alternatives has the potential to affect estimation of cross-country HRL–achievement relationships. Prior studies have emphasized HRL indicator variables as reflective indicators of a latent HRL construct, and address cross-country measurement differences through latent variable partial-invariance models [e.g., Wendt et al. (2017); Jusufi et al. (2026)]. However, the latent variable logic commonly applied to constructs like HRL and the accompanying perspectives of measurement invariance that ensure can be questioned (Welzel and Inglehart, 2016). In this paper, rather than adopting a strong stand regarding which approach is best, we explore empirically the implications of adopting latent variable weights as opposed to achievement-tailored weights as a basis for improving cross-country comparability in HRL. Our empirical analyses using structural equation modeling demonstrate disproportionality between latent variable HRL indicator loadings and the corresponding predictive effects of the HRL indicator variables on achievement, suggesting a potential for differences between latent variable versus achievement-tailored composite approaches. Overall, parent–reported books in the home predicts achievement more strongly, and parental occupation less strongly, than is implied by their respective loadings on an HRL latent variable. While overall the implications of these effects appear small, they impact the estimated strength of HRL-achievement relationships in certain individual countries (systems).