Hierarchical linear modeling (HLM) is often used to estimate the effects of socioeconomic status (SES) on academic achievement at different levels of an educational system. However, if a prior academic achievement measure is missing in a HLM model, biased estimates may occur on the effects of student SES and school SES. Phantom effects describe the phenomenon in which the effects of student SES and school SES disappear once prior academic achievement is added to the model. In the present analysis, partial simulation (i.e., simulated data are used together with real-world data) was employed to examine the phantom effects of student SES and school SES on science achievement, using the national sample of the United States from the 2015 Programme for International Student Assessment. The results showed that the phantom effects of student SES and school SES are rather real. The stronger the correlation between prior science achievement and (present) science achievement, the greater the chance that the phantom effects occur.

分层线性建模（HLM）通常用于估计教育系统不同级别的社会经济地位（SES）对学业成绩的影响。但是，如果HLM模型中缺少先前的学业成就测度，则对学生SES和学校SES的影响可能会产生偏差的估计。幻影效应描述了一旦将先前的学业成绩添加到模型后，学生SES和学校SES的影响就会消失的现象。在当前的分析中，使用部分模拟（即模拟数据与实际数据一起使用），使用来自2015年计划的美国国家样本，研究了学生SES和学校SES对科学成就的幻影效果用于国际学生评估。结果表明，学生SES和学校SES的幻像效果是相当真实的。在先科学成就和（现在）科学成就之间的相关性越强，幻影效应发生的机会就越大。