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Journal Article•DOI•

A Partial Simulation Study of Phantom Effects in Multilevel Analysis of School Effects: The Case of School Socioeconomic Composition:

Hao Zhou1, Xin Ma1•
University of Kentucky1
01 Feb 2021-Sociological Methods & Research (SAGE PublicationsSage CA: Los Angeles, CA)-pp 004912412098619
TL;DR: This paper used hierarchical linear modeling (HLM) to estimate the effects of socioeconomic status (SES) on academic achievement at different levels of an educational system and found that if a prior acad...
Abstract: 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 acad...

Summary (4 min read)

Jump to: [1.2 Phantom Effects] – [1.3 Contextual Effects] – [1.4 Purpose of Research] – [1.5.1 Informing Policy Change] – [1.5.2 Promoting Pioneer Research] – [2.2 School socioeconomic composition] – [2.3 Effects of School SES on Academic Achievement] – [2.5 Phantom effects of School SES] – [3.5 Partial Simulation] – [3.6 Working with Plausible Values in Partial Simulation] – [4.1 The Null Model] – [4.2 The Absolute Effects Models] – [4.3 The Relative Effects Models] – [5.3 Implications for Empirical Research] – [5.4 Implications for Policy and Practice] – [5.6 Suggestions for Further Research] and [5.7 Conclusion]

1.2 Phantom Effects

  • Phantom effects can also occur at other levels of an educational system.
  • At the student level, in the absence of SES, the racial-ethnic background often indicates statistically significant effects on academic achievement of students; however, in the presence of SES, such significant effects often disappear, which makes the racial-ethnic effects phantom effects.
  • With a focus on school SES, the present study investigates school contextual effects as a potential source of phantom effects in the school effectiveness research literature.

1.3 Contextual Effects

  • At the level 2, school SES was the mean SES for each school.
  • A two-level random intercept HLM was applied.
  • The results showed that after controlling for student's prior academic achievement, school SES effect disappeared in both cases (i.e., SES_1 and SES_2).
  • The effects of school SES were phantom effects.

1.4 Purpose of Research

  • The purpose of the present study is to examine the extent to which the effects.
  • The combination of empirical answers to both questions will provide evidence to address the issue of the extent to which the effects of school SES on science achievement of students are phantom effects.

1.5.1 Informing Policy Change

  • As argued earlier, many researchers have shown that school SES largely affects students ' academic achievement (e.g., OECD, 2015) .
  • The phenomenon of phantom effects associated with school SES may threaten the credibility of claims like this.
  • To some degree, education policymakers may have been misinformed on research evidence due to the complexity concerning school contextual effects, especially school SES.
  • This study aims to provide empirical evidence on whether phantom effects of school SES on students' academic achievement exist and, if yes, the extent to which school SES produces phantom effects on students' academic achievement.
  • The significance of this study is that it may promote policy change through a revisiting of educational policies and practices concerning school SES.

1.5.2 Promoting Pioneer Research

  • Among many important school characteristics, school socioeconomic status (SES)-a school background variable-plays a critical role in many educational policies and practices.
  • In New Zealand and the United Kingdom, schools adopt a funding model that provides similar resources to all schools and provides additional funding to schools with high needs (e.g. rural school, high percentage of students from low SES, etc.) (Perry and McConney, 2010) .
  • In the United States, policymakers issued different polices aimed to adjust school SES for better distribution of educational resources, such as magnet schools and school assignment policy.
  • The present study considers this important school characteristic.

2.2 School socioeconomic composition

  • At school level, school SES related with student academic achievement (e.g., Ma, 2010) .
  • School SES is often measured in two ways, either as the proportion of students enrolled in a reduced-price or free lunch program (Sirin 2005).
  • In general, School SES is dependent upon student SES.

2.3 Effects of School SES on Academic Achievement

  • If the coefficient is positive, school SES improves student academic achievement.
  • If the coefficient is negative, school SES hinders student academic achievement.
  • All studies referenced earlier showed evidence to support that students in high SES schools performed better than students in low SES schools.
  • Some of them, however, indicated that the effects of school SES can be conditional.
  • Lam and Lau's study (2014) , after controlling school size on school's level, showed that the school SES effects disappeared.

2.5 Phantom effects of School SES

  • The first method is that MLM includes variables that highly correlated with students' present academic achievement (Harker & Tymms, 2004) .
  • The above illustration pertains to this approach.
  • In other words, the effects of school SES are phantom effects because the model cannot adequately control for measurement errors.
  • There are few empirical studies to support this view.
  • Showed the same pattern as taking Year 5 student achievement as prior ability.

3.5 Partial Simulation

  • Simulated data would then work with actual data to address a statistical issue, thus named partial simulation.
  • The partial simulation procedure can generate a random variable with a defined correlation to an existing variable.
  • Once these prior measures of science achievement were generated, a separate multilevel analysis was performed with models that were discussed in the previous section.
  • As a result, 10 sets of multilevel analyses were conducted for each of the ten correlation conditions.

3.6 Working with Plausible Values in Partial Simulation

  • A short discussion on the variables employed at the student level and at the school level is in order before the modeling activities.
  • In addition, 26percent of the students are native, and 81 percent of the students speak English at home.
  • At the school level, the average school size is 1,251 students with a standard deviation of 887 students Meanwhile, 38 percent of the schools are located in city areas, 49 percent of the schools are located in town areas, and 13 percent of the schools are located in rural areas.
  • The average school SES is .07 with a standard deviation of .54.
  • Disciplinary climate is an index, and the average disciplinary climate is 0.28 with a standard deviation of 0.38.

4.1 The Null Model

  • The null model (see Chapter 3) provides the background for all the subsequent analyses.
  • The results of the null model show that the average science achievement of U.S. students is 494 points.
  • Therefore, according to the PISA science scale (M = 500, SD = 100), U.S. students scored a little lower than the international average.
  • The variance in science achievement at the student level is 7727.50, and variance in science achievement at the school level is 1876.65.
  • Intra-class correlation is approximately 0.20, which indicates that 20 percent of the total variance in science achievement is due to the school level.

4.2 The Absolute Effects Models

  • It is important to emphasize that, although all effects are statistically significant at the alpha level of .05 in Table 4 .2, some effects have rather small effect sizes.
  • If 25 percent of a SD can be considered practically important (e.g., Cohen, 1988) , then phantom effects of school SES appear when a prior measure has a correlation of .65 (even .55) with the present measure.
  • Compared with the base model, student SES effects and school SES effects in the model with .75 correlation between prior and present measures are decreased by 51 percent and 53 percent respectively.

4.3 The Relative Effects Models

  • As discussed in Chapter 3, the relative effects models examine student SES effects and school SES effects in the presence of student and school background variables (at student and school levels).
  • Meanwhile, with the increasing correlation between prior science achievement and present science achievement, the association between student SES and student science achievement decreases dramatically as well.
  • In the relative model, all effects associated with student SES are below .25 SD.
  • Phantom effects of student SES disappear when a prior science achievement reaches .35 (even .25) in correlation to present science achievement measurement.

5.3 Implications for Empirical Research

  • This study also offers a way to help create prior academic achievement measures when they are not available for data analysis.
  • Researchers are encouraged to conduct a thorough literature review to locate possible correlations between prior academic achievement measures and current academic achievement measures.
  • When these correlations are known, this study developed a procedure (in the programming language of R) to create prior academic achievement measurements, which will help researchers conduct data analysis based on correctly specified models.

5.4 Implications for Policy and Practice

  • The effectiveness of these policy practices is open to question based on the evidence in this and other studies.
  • The association between school SES and student academic achievement may be attenuated by misspecified contextual models.
  • In other words, student SES and school SES may not have as strong effects on student academic achievement as previous studies indicated, if the school contextual models are correctly specified.
  • In order to make appropriate policies, policymakers may want to encourage (e.g., fund) research projects that gather appropriate evidence with a fuller data collection from students and schools, particularly including prior student academic achievement measures.

5.6 Suggestions for Further Research

  • On the other hand, the approach that focuses on potential measurement errors may also be explored further.
  • Measurement error and model specification are often tangled up with each other to produce effects on parameter estimation.
  • Based on simulation study, the author gave a thumbs-up rule for applying each approach.
  • Pokropek (2015) provides only limited information to answer some of the questions, but more comprehensive studies should be conducted.

5.7 Conclusion

  • The result of this study can be summarized by several important points.
  • First, based on partial simulation procedure, phantom effects of school SES and student SES are real.
  • The stronger the correlation between prior science achievement measure and present science achievement measure, the greater the decrease in both student SES effects and school SES effects.
  • Third, the procedure of partial simulation provides a new angle to conduct theoretical studies (full simulation), which is entirely based on ideal assumption.
  • Finally, the procedure of partial simulation offers researchers a way to create prior student academic achievement measures when they are not available for data analysis.

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A PARTIAL SIMULATION STUDY OF PHANTOM EFFECTS IN MULTILEVEL
ANALYSIS OF SCHOOL EFFECTS: THE CASE OF SCHOOL SOCIOECONOMIC
COMPOSITION
________________________________________
DISSERTATION
________________________________________
A dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy in the
College of Education
at the University of Kentucky
By
Hao Zhou
Lexington, Kentucky
Director: Dr. Xin Ma, Professor of Quantitative and Psychometric Methods
Lexington, Kentucky
2019
Copyright © Hao Zhou 2019
ABSTRACT OF DISSERTATION
A PARTIAL SIMULATION STUDY OF PHANTOM EFFECTS IN MULTILEVEL
ANALYSIS OF SCHOOL EFFECTS: THE CASE OF SCHOOL SOCIOECONOMIC
COMPOSITION
Socioeconomic status (SES) affects students’ academic achievement at different
levels of an educational system. However, misspecified Hierarchical Linear Model (HLM)
may bias school SES estimation. In this study, a partial simulation study was conducted
to examine how misspecified HLM model bias school and student SES estimation.
The result of this study can be summarized by four important points. First, based
on partial simulation procedure, phantom effects of school SES and student SES are real.
Second, characteristics of phantom effects are generalized. The stronger the correlation
between prior science achievement measure and present science achievement measure,
the greater the decrease in both student SES effects and school SES effects. Third, the
procedure of partial simulation provides a new angle to conduct theoretical studies (full
simulation), which is entirely based on ideal assumption. Finally, the procedure of partial
simulation offers researchers a way to create prior student academic achievement
measures when they are not available for data analysis.
KEYWORDS: Partial Simulation Study, School SES Effect, Student SES Effect
Hao Zhou
(Name of Student)
04/26/2019
Date
A PARTIAL SIMULATION STUDY OF PHANTOM EFFECTS IN MULTILEVEL
ANALYSIS OF SCHOOL EFFECTS: THE CASE OF SCHOOL SOCIOECONOMIC
COMPOSITION
By
Hao Zhou
Dr. Xin Ma
Director of Dissertation
Dr. Margaret Bausch
Director of Graduate Studies
04/26/2019
Date
Citations
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Journal Article•DOI•
Inadequacies in the SES–Achievement model: Evidence from PISA and other studies

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01 Oct 2021-Revista De Educacion
TL;DR: Marks et al. as mentioned in this paper found that SES has only moderate effects on student achievement, and its effects are especially weak when considering prior achievement, an important and relevant predictor.
Abstract: Correspondence Gary N. Marks, Social and Political Sciences, University of Melbourne, Parkville 3052, Victoria, Australia. Emails: gmarks@unimelb.edu.au; garymarks2030@gmail.com Abstract Students’ socioeconomic status (SES) is central to much research and policy deliberation on educational inequalities. However, the SES model is under severe stress for several reasons. SES is an illdefined concept, unlike parental education or family income. SES measures are frequently based on proxy reports from students; these are generally unreliable, sometimes endogenous to student achievement, only low to moderately intercorrelated, and exhibit low comparability across countries and over time. There are many explanations for SES inequalities in education, none of which achieves consensus among research and policy communities. SES has only moderate effects on student achievement, and its effects are especially weak when considering prior achievement, an important and relevant predictor. SES effects are substantially reduced when considering parent ability, which is causally prior to family SES. The alternative cognitive ability/genetic transmission model has far greater explanatory power; it provides logical and compelling explanations for a wide range of empirical findings from student achievement studies. The inadequacies of the SES model are hindering knowledge accumulation about student performance and the development of successful policies.

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Larry J. Grabau, Lesley Eblie Trudel, X Ma
27 May 2022-International journal of science education
TL;DR: This paper found that disciplinary climate was more often associated with science dispositions (epistemology, enjoyment, interest, instrumental, self-efficacy activities) in U.S. science classrooms, but an emphasis on teaching support in Canadian science classrooms.
Abstract: ABSTRACT While the United States (U.S.) and Canada share features in their secondary education systems (e.g. proportion of immigrants), these nations have differences (e.g. linguistic ). Given the primacy of Canada over the U.S. vis-à-vis science literacy [as measured by the Programme International for Student Assessment (PISA)], underlying differences in science dispositions and school climate variables could exist. The PISA 2015 science-focused dataset, including 5712 students in 172 schools in the U.S. and 20,058 students in 645 schools in Canada, was modelled via multilevel methods to assess associations among science dispositions (epistemology, enjoyment, interest, instrumental, self-efficacy activities) and science literacy. Associations of school climate variables of instructional leadership, disciplinary climate and teaching support (the latter two in the context of science classes) with the above measures were evaluated. Disciplinary climate was more often associated with science dispositions (as outcome measures) in the U.S., while teaching support was most often associated with these measures for Canada. Disciplinary climate was associated with science literacy (as an outcome measure) in the U.S.; in contrast, no school climate measures were associated with science literacy in Canada. These results support an emphasis on disciplinary climate in U.S. science classrooms, but an emphasis on teaching support in Canadian science classrooms.

1 citations

Journal Article•DOI•
Meta-analytical insights on school SES effects

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Cheng Yong Tan, Xiaoou Hong, Lin Gao, Qiongjiang Song
17 Mar 2023-Educational Review
TL;DR: This article used meta-analysis to synthesize findings involving 480 effect sizes from 97 studies (dated 2000-2020) to provide insights on associations between school socioeconomic status (SES) and student learning outcomes; schools' percentage of ethnic minority students and students' prior ability; and school processes in K-12 schools.
Abstract: The present study uses meta-analysis to synthesise findings involving 480 effect sizes from 97 studies (dated 2000-2020) to provide insights on associations between school socioeconomic status (SES) and (a) student learning outcomes; (b) schools’ percentage of ethnic minority students and students’ prior ability; and (c) school processes in K-12 schools. It makes three contributions to the school SES scholarship. First, it elucidates the magnitude (r = .58) and nature of school SES effects (e.g. larger effect sizes for achievement (vis-à-vis attainment) outcomes). Second, it clarifies the conceptual meaning of school SES, namely that school SES is less associated with school processes than it is with schools’ percentage of ethnic minority students or students’ prior ability. Third, the study shows that school SES is more strongly associated with specific school processes (school leadership and climate, teacher capacity, parental involvement benefiting student learning) than others (instructional programmes, educational resources).
Journal Article•DOI•
How much is too much time spent on homework: an exploratory study based on a Bayesian multilevel piecewise model with a random change point

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Hao Zhou, Yueyang Shao
09 May 2023-Educational studies
TL;DR: This article applied multilevel piecewise linear regression with a random effects model under a Bayesian estimation framework to a total of 5,072 7th grade students in 35 schools to search for an optimum time in terms of the effect of homework time on student academic achievement.
Abstract: In this study, we applied multilevel piecewise linear regression with a random-effects model under a Bayesian estimation framework to a total of 5,072 7th grade students in 35 schools to search for an optimum time in terms of the effect of homework time on student academic achievement. First, we found a nonlinear relationship between time spent on homework and student academic achievement. Second, we found an optimum duration of homework with two rather distinguishing phenomena of patterns while controlling only student socioeconomic status (SES) and gender. The optimum time spent on homework is 1.77 hours. However, after further controlling students’ prior academic achievement, the optimum time disappeared. We discuss possible explanations for the disappearance of the optimum time and the implications for further research directions.
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01 Jan 2010-Educational Research Review
TL;DR: This article found that the compositional effect that researchers find is strongly related to how they measure SES and to their model choice, and that composition measured at cohort/school level is associated with smaller effects than composition at class level.

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Richard Harker, Peter Tymms
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Abstract: This article explores the concept of compositional effects in school effect studies, their generation and some of the difficulties that arise in their interpretation. Some basic issues are addressed using data from a New Zealand study of secondary schools, and further illustration of some of the “pitfalls” is provided from an English study of primary school performance indicators. The importance of model specification, predictor reliability, and cautious interpretation are highlighted.

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Journal Article•DOI•
A 2 x 2 Taxonomy of Multilevel Latent Contextual Models :Accuracy-Bias Trade-Offs in Full and Partial Error Correction Models

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Oliver Lüdtke1, Herbert W. Marsh2, Alexander Robitzsch, Ulrich Trautwein3•
Humboldt University of Berlin1, University of Oxford2, University of Tübingen3
25 Jul 2011-Psychological Methods
TL;DR: It is shown mathematically and with simulated data that the uncorrected and partial correction approaches can result in substantially biased estimates of contextual effects, depending on the number of L1 individuals per group, the numbers of groups, the intraclass correlation, thenumber of indicators, and the size of the factor loadings.
Abstract: In multilevel modeling, group-level variables (L2) for assessing contextual effects are frequently generated by aggregating variables from a lower level (L1). A major problem of contextual analyses in the social sciences is that there is no error-free measurement of constructs. In the present article, 2 types of error occurring in multilevel data when estimating contextual effects are distinguished: unreliability that is due to measurement error and unreliability that is due to sampling error. The fact that studies may or may not correct for these 2 types of error can be translated into a 2 × 2 taxonomy of multilevel latent contextual models comprising 4 approaches: an uncorrected approach, partial correction approaches correcting for either measurement or sampling error (but not both), and a full correction approach that adjusts for both sources of error. It is shown mathematically and with simulated data that the uncorrected and partial correction approaches can result in substantially biased estimates of contextual effects, depending on the number of L1 individuals per group, the number of groups, the intraclass correlation, the number of indicators, and the size of the factor loadings. However, the simulation study also shows that partial correction approaches can outperform full correction approaches when the data provide only limited information in terms of the L2 construct (i.e., small number of groups, low intraclass correlation). A real-data application from educational psychology is used to illustrate the different approaches.

206 citations

"A Partial Simulation Study of Phant..." refers methods in this paper

  • ...Although not specific to the effects of school SES, Lüdtke et al. (2011) later performed two simulation studies based on multilevel latent contextual models and suggested that the DL model has some potential to provide accurate estimation for the level 2 variables aggregated from the first level....

    [...]

  • ...effects of school SES, Lüdtke et al. (2011) later performed two simulation studies based on multilevel latent contextual models and suggested that the DL model has some potential to provide accurate estimation for the level 2 variables aggregated...

    [...]

  • ...The second method applies the doubly-latent model (DL) (Lüdtke et al., 2011)....

    [...]

  • ...Scholars argued that the DL model may reduce the bias of parameters’ estimation on second level so as to make the effects of school SES disappear (Lüdtke et al., 2011; Marsh.et al., 2009; Televantou et al., 2015; Pokropek,2015)....

    [...]

Journal Article•DOI•
School Composition and Contextual Effects on Student Outcomes

[...]

J. Douglas Willms1•
University of New Brunswick1
01 Apr 2010-Teachers College Record
TL;DR: This paper found that there is a significant relationship between literacy skills and socioeconomic status (SES), and also showed that school literacy skills are correlated with socioeconomic status, and that literacy skills can improve socioeconomic status.
Abstract: BackgroundFindings from several international studies have shown that there is a significant relationship between literacy skills and socioeconomic status (SES). Research has also shown that school...

198 citations

"A Partial Simulation Study of Phant..." refers background or methods in this paper

  • ...Willms (2010) examined science literacy scores by applying a three-level model....

    [...]

  • ...When the outcome was science, ICC varied between 23 percent and 37 percent (Willms, 2010; Sun et al.2012; Lam & Lau, 2014)....

    [...]

  • ...Willms (2010) showed a similar case where after controlling school contextual factors (quality of instruction, science time and school resource) at school level, the effects of school SES decreased....

    [...]

  • ...School socioeconomic composition is, perhaps, the most popular school contextual variable and school SES has been declared to have a large and persistent effect on students’ academic achievement (Perry & McConney, 2010; Willms, 2010)....

    [...]

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