Methodology: Constructing a Socioeconomic Index for TIMSS Trend Analyses
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Abstract
To assess education system trends in the inequality of educational outcomes, a robust socioeconomic index for TIMSS trend analysis is needed. This chapter begins by outlining the TIMSS data and sample design, as well as changes in the sample design over time, with special emphasis on the aspects that are specifically related to family socioeconomic status and student achievement. To analyze trends over the entire 20 years of TIMSS data, the analysis was limited to education systems that participated in the first cycle in 1995, the most recent cycle in 2015, and at least one other administration in between. After assessing the completeness of the data, 13 educational systems were included in the study: Australia, Hong Kong, Hungary, Islamic Republic of Iran, Lithuania, New Zealand, Norway, Republic of Korea, Russian Federation, Singapore, Slovenia, Sweden, and the United States. Items used for constructing the SES index were the number of books at home, home possessions, and the highest level of education of either parent. Students in each educational system were grouped into high and lowSES groups based on the SES distribution for a given year. Constructing a consistent measure of SES across all TIMSS cycles is an important contribution to research that uses TIMSS for trend analyses. In addition to analyzing the achievement gaps over time, examining trends in performance among lowSES students in each education system provides additional information on how education systems are addressing the issues facing disadvantaged students.
Keywords
Index construction International largescale assessment Measures of educational inequality Multiple imputation Plausible values Socioeconomic status (SES) Trends in International Mathematics and Science Study (TIMSS)3.1 TIMSS Data and Sample Characteristics
We used the TIMSS grade eight publicuse data from 1995 through 2015 to establish how inequalities of education outcomes have changed between 1995 and 2015, and to assess whether education systems have managed to increase the performance of disadvantaged students. TIMSS has been conducted every four years since 1995 to monitor trends in mathematics and science performance of students across education systems. Every participating education system provides a representative sample of students by adopting a twostage random sample design. Typically, in each participating education system, a sample of schools is drawn at the first stage, and one or more intact classes of students from each of the sampled schools are selected at the second stage (LaRoche et al. 2016). Although most features have remained constant over the different TIMSS cycles, there have also been several significant changes in sample design, country participation, and questionnaire administration.
First, the target population has changed slightly. The first cycle of TIMSS in 1995 identified three target populations; one of them was students enrolled in the two adjacent grades, which maximized coverage of 13yearolds (Foy et al. 1996). At the time of testing, most students were either in the grade seven or grade eight. This practice was refined for the 1999 cycle of TIMSS, and resulted in only grade eight students being assessed. To maintain comparability, for our study, we therefore only included grade eight students for most education systems in the 1995 assessment in our trend analyses, which is in alignment with the practice outlined in the TIMSS 1999 international mathematics report (Mullis et al. 2000) and TIMSS 2015 international results in mathematics (Mullis et al. 2016, appendix A.1, at http://timssandpirls.bc.edu/timss2015/internationalresults/timss2015/mathematics/appendices/).^{1} Norway was the only exception, because Norway only included grade six and seven students in its 1995 sample. However, according to the TIMSS 2015 report, the sample of uppergrade students (grade seven) in Norway in 1995 was comparable to that in 2015 (see Mullis et al. 2016, appendix A.1). Therefore, in the case of Norway, we kept the sample of grade seven students in 1995 for trend comparison (Gonzalez and Miles 2001).^{2}
Second, although many education systems have participated in TIMSS over the last 20 years, not every education system participated in each cycle. To analyze trends over the entire 20 years of TIMSS data, we therefore limited our analysis to those education systems that participated in the first cycle in 1995, the most recent cycle in 2015, and at least one other intermediate administration cycle. This produced a potential sample of 18 education systems.^{3}
However, according to the 2015 TIMSS international results in mathematics (see Mullis et al. 2016, appendix A.1), many education systems’ previous data cannot be used for trend analysis to 2015. This is primarily due to improved translations or increased population coverage. For example, the data for Australia in 1999, Kuwait in 1995 and 2007, Canada in 1995 and 1999, Israel in 1995, 1999, 2003, and 2007, Slovenia in 1999, and Thailand in 1995 were not considered comparable to 2015 data. Therefore, four education systems (Canada, Israel, Kuwait, and Thailand) had to be excluded from the analyses because 1995 data cannot be used for trend analyses.

Australia, Hong Kong, Hungary, Islamic Republic of Iran, Lithuania, Republic of Korea, Russian Federation, Singapore, Slovenia, and the United States (education systems that participated in all six cycles); and

New Zealand (which participated in 1995, 1999, 2003, 2011, and 2015), Norway (which participated in 1995, 2003, 2007, 2011, and 2015), and Sweden (which participated in 1995, 2003, 2007, 2011, and 2015).
Samples for each education system in each TIMSS assessment year
Education system  Sample characteristics  TIMSS cycle  

1995  1999  2003  2007  2011  2015  
Australia  Overall student sample  12,852  4032  4791  4069  7556  10,338 
Grade level(s) used for trend analysis  G8  n/c  G8  G8  G8  G8  
Number of students in trend sample  7392  n/c  4791  4069  7556  10,338  
Hong Kong  Overall student sample  6752  5179  4972  3470  4015  4155 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  3339  5179  4972  3470  4015  4155  
Hungary  Overall student sample  5978  3183  3302  4111  5178  4893 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  2912  3183  3302  4111  5178  4893  
Islamic Republic of Iran  Overall student sample  7429  5301  4942  3981  6029  6130 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  3694  5301  4942  3981  6029  6130  
Lithuania  Overall student sample  5056  2361  4964  3991  4747  4347 
Grade level(s) used for trend analysis  G8  G9  G8  G8  G8  G8  
Number of students in trend sample  2525  2361  4964  3991  4747  2933  
New Zealand  Overall student sample  6867  3613  3801  n/a  5336  8142 
Grade level(s) used for trend analysis  G9  G9  G8  n/a  G9  G9  
Number of students in trend sample  3683  3613  3801  n/a  5336  8142  
Norway  Overall student sample  5736  n/a  4133  4627  3862  4795 
Grade level(s) used for trend analysis  G7  n/a  G8  G8  G8  G8  
Number of students in trend sample  3267  n/a  4133  4627  3862  4795  
Republic of Korea  Overall student sample  5827  6114  5309  4240  5166  5309 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  2920  6114  5309  4240  5166  5309  
Russian Federation  Overall student sample  8160  4332  4667  4472  4893  4780 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  4022  4332  4667  4472  4893  4780  
Singapore  Overall student sample  8285  4966  6018  4599  5927  6116 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  4644  4966  6018  4599  5927  6116  
Slovenia  Overall student sample  5606  3109  3578  4043  4415  4257 
Grade level(s) used for trend analysis  G7  n/c  G7 and G8  G8  G8  G8  
Number of students in trend sample  2898  n/c  3578  4043  4415  4257  
Sweden  Overall student sample  8855  n/a  4256  5215  5573  4090 
Grade level(s) used for trend analysis  G8  n/a  G8  G8  G8  G8  
Number of students in trend sample  1949  n/a  4256  5215  5573  4090  
United States  Overall student sample  10,973  9072  8912  7377  10,477  10,221 
Grade level(s) used for trend analysis  G8  G8  G8  G8  G8  G8  
Number of students in trend sample  7087  9072  8912  7377  10,477  10,221 
Finally, for trend analysis, several adjustments were made to follow the approach used by Mullis et al. (2016). First, IEA has a policy that students should not fall under the minimum average age of 13.5 years (for grade eight) at the time of testing (see Mullis et al. 2016, appendix C.10). Therefore, New Zealand assessed students in grade nine across multiple cycles. The results for grade nine students in 1995, 1999, 2011, and 2015 are deemed comparable to those for grade eight students who participated in 2003 in New Zealand. Second, although Slovenia assessed grade eight students in 1995, the results for grade eight students in 1995 are not deemed comparable to those in other cycles. Therefore, data for grade seven students in 1995 is used for trend analysis. Third, in Lithuania, the results for students assessed in Polish or Russian in 2015 are deemed not comparable to previous cycles. Therefore, trend results only include students assessed in Lithuanian and do not include students assessed in Polish or Russian in 2015.
3.2 Construction of a Proxy Measure for Socioeconomic Status
To address the research questions, we first needed to construct a comparable proxy measure for socioeconomic status across the different TIMSS administration cycles. The TIMSS home educational resources (HER) index measures important aspects of SES, but it is not applicable for trend comparisons across all cycles for several reasons.
First and foremost, the HER index was constructed by different measurement methods in different cycles. In 1995 and 1999, the HER index was a simple combination of several background variables, including the number of books at home, number of home possessions, and parents’ education, which were combined into three levels: high, medium, and low. For example, students at the high level were those with more than 100 books in the home, all three educational possessions (computer, study desk, and dictionary), and at least one collegeeducated parent. This index made interpretation easy since each category had its own corresponding characteristics. However, since 2011, the HER index has been constructed using IRT scaling methodology (Martin et al. 2011), which allows for the analysis of more finegrained differences in home educational resources between students, and enables forward comparability for future administrations even if the components of the index should change in the future. The current form of the HER is, however, not comparable to the earlier index. In addition to that, in 2003 and 2007, no HER index was constructed for TIMSS.
Home possession items by TIMSS cycle
Item  TIMSS cycle  

1995  1999  2003  2007  2011  2015  
Common items  Computer  Computer  Computer  Computer  Computer  Computer/tablet 
Study desk  Study desk  Study desk  Study desk  Study desk  Study desk  
Yearspecific items  Dictionary  Dictionary  Dictionary  Dictionary  n/a  n/a 
Calculator  Calculator  Calculator  Calculator  n/a  n/a  
n/a  n/a  n/a  Internet connection  Internet connection  Internet connection  
n/a  n/a  n/a  n/a  Own room  Own room  
n/a  n/a  n/a  n/a  Books of your own  n/a  
n/a  n/a  n/a  n/a  n/a  Own mobile phone  
n/a  n/a  n/a  n/a  n/a  Gaming system 
It was clear that constructing a consistent measure of SES that can be applied across all TIMSS cycles would be of immense value to researchers who wished to use TIMSS for trend analyses. We therefore developed a modified version of the HER index to address this issue. Our SES measure, which we here term SES*, does not represent the full SES construct as usually defined by parental education, family income, and parental occupation.^{4} While the construction of such an index serves a specific purpose in this study, we believe that the SES* index that is proposed here is sufficiently closely related to the later IRTscaled HER versions to yield highly relevant and valid results. This index can thus also be beneficially applied to other future studies that intend to use the SES* variable for analysis over multiple administrations.^{5}
3.2.1 Components of the SES* Measure
Our SES* measure, which as mentioned in the introduction is a modified version of the HER index, is constructed using three common components across the six cycles of TIMSS. These components include (1) number of books at home, (2) number of home possessions, and (3) the highest level of education of either parent.
Number of Books at Home
The information is derived from the student questionnaire asking how many books students have at home. There are five categories, coded (0) to (4): (0) 0 to 10 books; (1) 11 to 25 books; (2) 26 to 100 books; (3) 101 to 200 books; and (4) more than 200 books.
Number of Home Possessions
This information comes from questions asking students whether they have each of a list of items at home. Since there are only two common items (computer and study desk) across all cycles, the total number of home possessions ranges from 0 to 2. One caveat needs to be mentioned for 2015. The question regarding having a computer at home was changed to two variables: one asking if a student owns a computer or tablet at home and the other one asking if a student shares a computer or tablet with others at home. We coded a positive response to either of these questions as a “1”. Despite the addition of tablet in 2015, the correlations of the other SES* components with the computer/tablet variable were comparable with those found in 2011 (computer alone), with the scoring of either response as a “1”. We therefore believe that the addition of tablet in 2015 did not substantially change the construct being measured, and that the SES* index remains consistent over time.
Highest Level of Education of Either Parent
This is a derived variable constructed from both the father’s and mother’s highest educational levels. The categories of the source variables were grouped into five levels in line with the 1995 survey, coded as follows: (0) less than lower secondary; (1) completed lower secondary; (2) completed upper secondary; (3) postsecondary nontertiary education; and (4) completed university or higher. “I don’t know” responses were treated as missing.
3.2.2 Multiple Imputation of Missing Values
The main components of the SES* index have different degrees of missingness. Of specific concern is parental education, which on average has missing values of around 20%, depending on administration year and education system. Since dropping such a large part of the sample would undermine the generalizability of the findings, especially when the students with missing values tended to come from lower ability levels, multiple imputation was used for all missing values of the SES* index components. Instead of imputing the “highest level of parental education” variable directly, we imputed father’s and mother’s education separately, compared them after imputation, and then generated the highest level of parental education for the SES* index. We imputed the missing values of SES* index variables five times using multiple imputation chained equations before constructing the SES* index. Imputation using chained equations is known for its flexibility in handling different types of variables (for example binary, categorical, and continuous; Hughes et al. 2014), with our variables of interests being mostly categorical. The imputation is achieved by using the observed values for a given individual and the observed relations in the data for other participants (Schafer and Graham 2002).
In addition, since TIMSS data include multiple education systems across multiple years, we decided to impute the missing data for each year first and only then create a database of all years. The advantage of this approach was that we maximally used available information for a given year since the questionnaires have been modified over time and thus available relevant variables differ by year. In the imputation model, we included all analytic variables that were included in our final analysis, other common home possession items available for all education systems in each year, plausible values of achievement score, and other related variables (such as language spoken at home). After imputation, the correlation between these variables in each year was compared between the original dataset and the imputed dataset, and the results suggested the imputation preserved the overall relationship among variables very well. The student sampling weight was taken into account in the imputation model, as shown in a case study of conducting multiple imputation for missing data in TIMSS (Bouhlila and Sellaouti 2013).
3.2.3 The SES* Index
SES* index construction
SES* component  Categories  Score 

Highest level of parental education  Less than lower secondary education  0 
Completed lower secondary education  1  
Completed upper secondary education  2  
Postsecondary, nontertiary education  3  
Completed university or higher  4  
Home possessions  None  0 
Computer/tablet  1 home possession  1 
Study desk  2 home possessions  2 
Number of books at home  0–10 books  0 
11–25 books  1  
26–100 books  2  
101–200 books  3  
More than 200 books  4 
3.2.4 Defining High and LowSES* Groups
To calculate the achievement gap between students with high and lowSES* backgrounds over time, we first needed to define the criterion or cutoff points corresponding to high and lowSES* backgrounds. Among the different approaches for establishing cutoffs, the main choices are either (a) using common cutoffs across educational systems and years, or (b) defining education systemspecific lowSES* versus highSES* groups based on the distribution of the SES* index for a given year.
Common CutOffs
Common cutoffs by overall distribution of SES* index (cumulative proportion)
SES* index  Average percentage cutoff  Australia (1995) percentage cutoff  Islamic Republic of Iran (1995) percentage cutoff 

0  3  3  22 
1  7  4  44 
2  13  6  63 
3  21  10  76 
4  31  18  84 
5  42  30  91 
6  56  46  95 
7  68  60  97 
8  81  74  99 
9  91  87  100 
10  100  100  100 
Thus, common cutoffs tend to generate unbalanced groups in certain education systems since individual education systems’ specific situations are not taken into account. While these may be the actual percentages for high and lowSES* students across educational systems, SES* is a relative concept when viewed within an educational system. That is, what is perceived as high or low SES* is society dependent. And it is the perception which is important, because what is perceived to be real is real in its consequences. Therefore, we decided to establish education system specific cutoffs for each year. Given each education system’s distribution of SES* in each year, we used quartiles as cutoffs; students in the bottom quartile were considered low SES*, while students in the top quartile were considered high SES* (see the Appendix for a sensitivity analysis using quintiles versus quartiles and additional information). This approach generated better grouping results because it takes local context into consideration.
Weighted distribution of SES* index for Australia, 1995
SES*  Proportion (%)  Cumulative proportion (%) 

0  0  0 
1  1  1 
2  2  3 
3  4  6 
4  8  15 
5  13  27 
6  16  43 
7  15  59 
8  14  73 
9  13  86 
10  14  100 
To address this issue, we decided to randomly split the sample of students at the cutoff point below or above the 25th and 75th percentiles and then combine it with a random subsample from the adjacent group, resulting in top and bottom categories containing 25% of students. Again, using Australia in 1995 as our example, to obtain the bottom quartile, we needed another 10% of students in addition to those having 0 to 4 points on the SES* index. Therefore, we randomly selected a subsample of the Australian students who participated in 1995 and who scored five SES* index points to create a sample comprising 25% of students as the bottom SES* category (another way to consider this is that if 27% of students are at index point five, then the sample contains 2 % more students than needed for the bottom quartile, so 2% of students, in absolute terms, have to be randomly excluded from the fivepoint subsample). Applying the same strategy to every individual education system and year guaranteed that the bottom and topquartile SES* groups always represented exactly 25% of students from a given education system in any given year.
3.3 Analytic Approach
3.3.1 Plausible Values and Imputed Datasets
One significant analytic challenge underlying this work was how to simultaneously use the existing five plausible values of achievement scores while incorporating results from the multiple imputation procedure for the missing values of SES* background variables. One approach might be to conduct nested multiple imputation, in which the plausible values imputation is nested within the background variable imputation (Weirich et al. 2014). However, that would have required an extra step back to item responses, and the imputation model would highly depend on the final analytic model, meaning that other studies using this SES* index would have to create their own models. More importantly, the TIMSS & PIRLS International Study Center had clearly stated that principal components for a large number of student background variables were included as conditioning variables to improve the reliability of the estimated student proficiency scores (Foy and Yin 2016). It is reasonable to believe that the components in our SES* index, which are very important student background variables, were included in the TIMSS conditioning models for proficiency estimation. Therefore, we used the existing plausible values of achievement scores in TIMSS to impute missing values in the SES* component variables, together with other relevant variables, resulting in five imputed datasets.
After imputation, one possibility for using the imputed SES* variable was to average the SES* values among the five imputed datasets and thus generate a single SES* index score for each student. To validate this approach, we randomly selected 10% of cases in each country, replaced the existing value of parental education with “missing”, imputed the pseudomissing values using the same imputation model, and then compared the imputed values with actual values. However, the validation results were not satisfactory, since a simple average of the five imputed values presented a quite different distribution from the actual values because it overlooked the variance between the imputed values. Therefore, we decided not to average the imputed values for SES* but to treat the five imputed SES* values as plausible values (Kevin Macdonald, personal communication, 10 March 2018) and conduct analyses with the PV module in Stata 14 software (Macdonald 2008). This approach allowed us to simultaneously use the five plausible values of the TIMSS achievement scores and the five imputed values for the SES* index in the analyses for this report.
3.3.2 Measuring Educational Inequality
Ferreira and Gignoux (2011) described methods for measuring both inequality in achievement (which they saw as being expressed simply by the degree of variability in the outcome measure), and inequality in opportunity (they proposed a meaningful summary statistic for this would be the amount of variance explained obtained from an OLS regression of students’ test scores on a vector C of individual circumstances). Another approach was used by Green et al. (2015) in an application using international adult skills surveys. Their measure was a “social origins gradient” representing the point difference in scores that can be predicted for an individual when the education level of his or her parent(s) is increased from the bottom unit to the top unit (for example from “less than high school” to “college education”).
We opted for yet another different approach, one that we believe is better suited for trend analysis of educational inequality. To answer the first research question, “How has the inequality of education outcomes due to family socioeconomic status changed for different education systems between 1995 and 2015”, we calculated the achievement gap over time between students in low and highSES* groups in terms of the average TIMSS achievement score. The larger the gap, the larger the role of SES* in determining educational outcomes.
While seeing trends in the SES achievement gaps is important, they can hide important changes over time. For example, there might be no change in the size of the SES* gap over time because neither group has changed over time, and, in another case, the SES* gap may not change because both the lower and upper groups have changed in the same direction over time. Because gaps can close or widen for different reasons, it is also important to examine how the most disadvantaged students are doing over time, as proposed by our second research question, “To what extent have education systems managed to increase the academic performance of disadvantaged students between 1995 and 2015?” To address this, we analyzed the trend in performance among lowSES* students in each education system from 1995 to 2015. Specifically, we tracked the percentage of lowSES* students who performed at or above the TIMSS international intermediate benchmark (that is, 475 points) for each education system over time.
3.3.3 CountryLevel Indicators in the Educational Systems and the Macroeconomic Context
Sources for countrylevel economic indicators
Indicator  Source  Link 

GDP per person (current US$)  The World Bank Open Data  
The World Factbook 2018. Washington, DC: Central Intelligence Agency  https://www.cia.gov/library/publications/theworldfactbook/index.html  
Total percent of government expenditure on education  The World Bank Open Data  
The UNESCO Institute for Statistics  
Total percent of GDP spent on education  The World Bank Open Data  
The UNESCO Institute for Statistics  
Gini index  The World Bank Open Data  
The World Factbook 2018. Washington, DC: Central Intelligence Agency  https://www.cia.gov/library/publications/theworldfactbook/rankorder/2172rank.html  
The OECD Income Distribution Database  
Top 10% share pretax national income  The World Inequality Database 
Footnotes
 1.
In the TIMSS 1999 international mathematics report Mullis et al. (2000) examined trends in mathematics achievement between 1995 and 1999. The 1995 average scale score was calculated for grade eight students only in Exhibit 1.3 (see pp. 34–36).
 2.
According to the TIMSS 1999 user guide for the international database, the TIMSS 1999 target grade was the upper grade of the TIMSS 1995 population 2 and was expected to be the grade eight in most countries. However, for Norway, it was the seventh grade (see Exhibit 5.2 Grades tested in TIMSS 1995Population 2). Please refer to https://timss.bc.edu/timss1999i/data/bm2_userguide.pdf
 3.
The potential sample included (1) 11 education systems that participated in all six cycles: Australia, Hong Kong, Hungary, Islamic Republic of Iran, Israel, Republic of Korea, Lithuania, Russian Federation, Singapore, Slovenia, the United States, and (2) seven education systems that participated in both 1995 and 2015 and in at least one other administration: England, New Zealand, Norway, Sweden, Thailand, Canada, and Kuwait.
 4.
An asterisk is added to denote the conceptual difference (Please refer to Chap. 1 for more details).
 5.
Ideally, a scaled HER index could be constructed for prior years so that analysis with this index would be possible across all TIMSS administrations. However, this exceeds the scope of this research project.
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