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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

[...]

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.
References
More filters
Journal Article•DOI•
Phantom effects in school composition research: consequences of failure to control biases due to measurement error in traditional multilevel models

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Ioulia Televantou1, Herbert W. Marsh2, Leonidas Kyriakides3, Benjamin Nagengast4, John M. Fletcher1, Lars-Erik Malmberg1 •
University of Oxford1, University of Western Sydney2, University of Cyprus3, University of Tübingen4
21 Jan 2015-School Effectiveness and School Improvement
TL;DR: In this paper, a large sample of English primary students in Cyprus in years 1 and 4, revealed a significantly negative compositional effect associated with school-average achievement that became more negative after controlling for measurement error.
Abstract: The main objective of this study was to quantify the impact of failing to account for measurement error on school compositional effects. Multilevel structural equation models were incorporated to control for measurement error and/or sampling error. Study 1, a large sample of English primary students in Years 1 and 4, revealed a significantly negative compositional effect associated with school-average achievement that became more negative after controlling for measurement error. Study 2, a large study of Cypriot primary students in Year 4, showed a small, positive but statistically significant compositional effect that became non-significant after controlling for measurement error. Our findings have important methodological, substantive, and theoretical implications for on-going debates on the school compositional effects on students’ outcomes, because nearly all previous research has been based on traditional approaches to multilevel models, which are positively biased, due to the failure to control for ...

53 citations

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

  • ...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)....

    [...]

  • ...students’ academic achievement might be biased by this omission (Marks, 2015; Pokropek, 2015; Televantou et al. 2015)....

    [...]

  • ...In light of the findings in this study and evidences from other researchers (e.g., Marks, 2015; Televantou et al. 2015), it is noteworthy that for the contextual HLM model, missing information at the first level may attenuate the school (and student)...

    [...]

  • ...The effect of school level SES on students’ academic achievement might be biased by this omission (Marks, 2015; Pokropek, 2015; Televantou et al. 2015)....

    [...]

  • ...5.3 Implications for Empirical Research In light of the findings in this study and evidences from other researchers (e.g., Marks, 2015; Televantou et al. 2015), it is noteworthy that for the contextual HLM model, missing information at the first level may attenuate the school (and student) 49 SES…...

    [...]

Journal Article•DOI•
Socioeconomic Status, Self-Efficacy, and Mathematics Achievement in Australia: A Secondary Analysis.

[...]

Andrew McConney1, Laura B. Perry1•
Murdoch University1
28 Apr 2010-Educational Research for Policy and Practice
TL;DR: This article found that increases in school socioeconomic status are consistently associated with substantial increases in achievement in mathematics and this phenomenon holds for all groups, regardless of their individual SES, and that the association of school SES with maths achievement persists even when subject-specific self-efficacy is taken into account.
Abstract: Previous studies have shown that both student and school socioeconomic status (SES) are strongly associated with student outcomes, but less is known about how these relationships may vary for different students, schools and nations. In this study we use a large international dataset to examine how student SES, school SES and self-efficacy are associated with mathematics performance among 15-year-old students in Australia. We found that increases in school SES are consistently associated with substantial increases in achievement in mathematics and this phenomenon holds for all groups, regardless of their individual SES. Furthermore, our findings show that the association of school SES with maths achievement persists even when subject-specific self-efficacy is taken into account. However, our findings also suggest modest differences among student groups disaggregated by these factors. In particular, the association between maths achievement and school SES appears moderately stronger for students with higher levels of self-efficacy compared with their peers with lower self-efficacy. Furthermore, among students with similar levels of self-efficacy, the association between maths achievement and school SES tends to be stronger for lower SES students than for their more privileged peers. From these findings, we highlight the importance of the Australian case for comparable systems of education, and provide a discussion of policy implications and strategies for mitigating the influence of school socioeconomic composition on academic achievement more generally.

50 citations

Journal Article•DOI•
Examining Factors Affecting Science Achievement of Hong Kong in PISA 2006 Using Hierarchical Linear Modeling

[...]

Terence Yuk Ping Lam1, Kwok-chi Lau1•
The Chinese University of Hong Kong1
08 Aug 2014-International Journal of Science Education
TL;DR: This article used hierarchical linear modeling to examine the influence of a range of factors on the science performances of Hong Kong students in PISA 2006 and found that student backgrounds as male, at higher grade levels, and born in mainland (when in the same grade) are associated with better science performance.
Abstract: This study uses hierarchical linear modeling to examine the influence of a range of factors on the science performances of Hong Kong students in PISA 2006. Hong Kong has been consistently ranked highly in international science assessments, such as Programme for International Student Assessment and Trends in International Mathematics and Science Study; therefore, an exploration of the factors that affect science performances of Hong Kong students can give a lens to examine how science education can be improved in Hong Kong and other countries. The analyses reveal that student backgrounds as male, at higher grade levels, and born in mainland (when in the same grade) are associated with better science performance. Among the attitudinal factors, enjoyment of science and self-efficacy in science play important roles in scientific achievements. Most of the parental factors, on the other hand, are not having significant impacts on achievement after student attitudes are taken into account, with only parents’ val...

50 citations

Journal Article•DOI•
Phantom Effects in Multilevel Compositional Analysis Problems and Solutions

[...]

Artur Pokropek
01 Nov 2015-Sociological Methods & Research
TL;DR: Examples using data from the Trends in International Mathematics and Science Study are shown to present the behavior of the tested models in real-data situations and indicate the consequences of ignoring the problem of reliability.
Abstract: This article combines statistical and applied research perspective showing problems that might arise when measurement error in multilevel compositional effects analysis is ignored. This article focuses on data where independent variables are constructed measures. Simulation studies are conducted evaluating methods that could overcome the measurement error problems. These methods are a multilevel regression model with reliability correction, a multilevel model with plausible values, and a multilevel latent regression model (doubly latent model). While the latter one performs best, all models have their advantages and disadvantages. Examples using data from the Trends in International Mathematics and Science Study are shown to present the behavior of the tested models in real-data situations and indicate the consequences of ignoring the problem of reliability.

30 citations

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

  • ...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)....

    [...]

  • ...Pokropek (2015) provides only limited information to answer some of the questions, but more comprehensive studies should be conducted....

    [...]

  • ...students’ academic achievement might be biased by this omission (Marks, 2015; Pokropek, 2015; Televantou et al. 2015)....

    [...]

  • ...The effect of school level SES on students’ academic achievement might be biased by this omission (Marks, 2015; Pokropek, 2015; Televantou et al. 2015)....

    [...]

  • ...52 after correcting measurement error based on a different correction method, how does school SES change? Pokropek (2015) examined three approaches to correct...

    [...]

Journal Article•DOI•
Transforming the Idea into Action: Policies and Practices to Enhance School Effectiveness

[...]

Linda Coyle1, Ann E. Witcher1•
University of Central Arkansas1
01 Jan 1992-Urban Education
TL;DR: The characteristics of effective schools can now be summarized as mentioned in this paper and the characteristics of "effective" schools can be found in a survey of the most effective schools in the world, including:
Abstract: The characteristics of \"effective\" schools can now be summarized

25 citations

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