BackgroundLarge-scale cross-national studies designed to measure student achievement use different social, cultural, economic and other background variables to explain observed differences in that achievement. Prior to their inclusion into a prediction model, these variables are commonly scaled into latent background indices. To allow cross-national comparisons of the latent indices, measurement invariance is assumed. However, it is unclear whether the assumption of measurement invariance has some influence on the results of the prediction model, thus challenging the reliability and validity of cross-national comparisons of predicted results.MethodsTo establish the effect size attributed to different degrees of measurement invariance, we rescaled the ‘home resource for learning index’ (HRL) for the 37 countries ($$n=166,709$$n=166,709 students) that participated in the IEA’s combined ‘Progress in International Reading Literacy Study’ (PIRLS) and ‘Trends in International Mathematics and Science Study’ (TIMSS) assessments of 2011. We used (a) two different measurement models [one-parameter model (1PL) and two-parameter model (2PL)] with (b) two different degrees of measurement invariance, resulting in four different models. We introduced the different HRL indices as predictors in a generalized linear mixed model (GLMM) with mathematics achievement as the dependent variable. We then compared three outcomes across countries and by scaling model: (1) the differing fit-values of the measurement models, (2) the estimated discrimination parameters, and (3) the estimated regression coefficients.ResultsThe least restrictive measurement model fitted the data best, and the degree of assumed measurement invariance of the HRL indices influenced the random effects of the GLMM in all but one country. For one-third of the countries, the fixed effects of the GLMM also related to the degree of assumed measurement invariance.ConclusionThe results support the use of country-specific measurement models for scaling the HRL index. In general, equating procedures could be used for cross-national comparisons of the latent indices when country-specific measurement models are fitted. Cross-national comparisons of the coefficients of the GLMM should take into account the applied measurement model for scaling the HRL indices. This process could be achieved by, for example, adjusting the standard errors of the coefficients.

中文翻译：

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假设国际比较教育成就研究中背景指标的测量不变性：对成就差异的解释的挑战

背景技术旨在衡量学生成绩的大规模跨国研究使用不同的社会，文化，经济和其他背景变量来解释所观察到的成绩差异。在将它们包含到预测模型中之前，通常将这些变量缩放为潜在的背景索引。为了对潜在指数进行跨国比较，假设测量不变性。然而，尚不清楚测量不变性的假设是否会对预测模型的结果产生某些影响，从而挑战了跨国比较预测结果的可靠性和有效性。我们重新调整了37个国家/地区的“学习的家庭资源指数”（HRL）（$$ n = 166,709 $$ n = 166，709名学生）参加了IEA在2011年进行的“国际阅读素养研究进展”（PIRLS）和“国际数学和科学研究趋势”（TIMSS）评估的合并评估。我们使用了（a）两种不同的测量模型[一个参数（1PL）和两参数模型（2PL）]（b）两个不同程度的测量不变性，得到四个不同的模型。我们在数学成就作为因变量的广义线性混合模型（GLMM）中引入了不同的HRL指标作为预测变量。然后我们通过比例模型比较了各国之间的三个结果：（1）度量模型的拟合值不同;（2）估计的歧视参数;（3）估计的回归系数。最好，HRL指标的假设测量不变性程度影响了除一个国家以外的所有国家GLMM的随机效应。对于三分之一的国家，GLMM的固定效应还与假定的测量不变性程度有关。结论结论支持使用特定国家的测量模型来缩放HRL指数。一般而言，当采用特定于国家的度量模型时，可以使用等值程序进行潜在指数的跨国比较。GLMM系数的跨国比较应考虑到用于缩放HRL指数的测量模型。该过程可以通过例如调整系数的标准误差来实现。