Overview of Main Survey Data Analysis and

Scaling

National Research Coordinators Meeting Madrid, February 2010

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February 2010

Content of presentation

• Scaling and analysis of test items

• Scaling and analysis of questionnaire items

• Data analysis for the reporting of ICCS data

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February 2010

Steps in analysis

• Preliminary analysis of first data sets received– Review at JMC data analysis meeting in

Hamburg in July 2009

• Analysis of clean and uncleaned data sets from almost all participating countries– Review at PAC meeting in Tallinn (Oct 2009)

and JMC data analysis meeting in Hamburg in early December 2009

• Final scaling and analysis with clean data from all 38 countries

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February 2010

Test item analysis

• Review of missing data

• Analysis of item dimensionality

• Review of item statistics (international)

• Analysis of differential item functioning by gender

• Analysis of item-by-country interaction– Measurement equivalence

• Item adjudication

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Scaling model

• Rasch one-parameter model

• Pi() is the probability for person n to score 1 on item i

n is the estimated ability of person n and i

P

i

n i

n i

( )exp

exp

1

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Probability curves

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1

-4 -3 -2 -1 0 1 2 3 4

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Partial credit model

• For open-ended items (and questionnaire items) with more than two categories the Partial Credit model was used:

• Here, tij denotes an additional step parameter

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Threshold curves

THETA

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babi

lity

1.0

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Strongly Agree Agree Disagree Strongly disagree

1

2 3

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THETA

4.003.002.001.00.00-1.00-2.00-3.00-4.00

Pro

babi

lity

1.0

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2 3

Strongly Agree Agree Disagree Strongly disagree

Response probabilities

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Missing data issues

• Different categories of missing data

• Omitted responses– Somewhat higher percentages for open

response items

• Invalid responses– Generally very low percentages

• Not reached responses– Omitted items at end of test booklets– Generally low, in few countries more

considerable

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Not reached % by region

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Test characteristics

• Test items were generally a little easier than the average student abilities (pooled across countries)

• Test reliability was 0.84 (similar to CIVED assessment)

• Very high latent correlations between possible sub-dimensions– Decision not to pursue sub-scales

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Mapping of test items to

abilities

| | X| 2 X| XX| XX| XX|14 XX| XXX|25 XXXX| XXXXX| 1 XXXXX| XXXXXXX| XXXXX| XXXXXX|5 37 XXXXXXX|46 75 XXXXXXXX|2 4 49 56 74 XXXXXXXXX|51 71 XXXXXXXXXX|6 9 28 0 XXXXXXXX|55 59 77 XXXXXXXXX|10 32 34 68 XXXXXXXX|19 27 44 XXXXXXXXX|20 30 33 36 65 72 XXXXXXXXX|26 40 41 50 53 57 58 61 70 XXXXXXXXX|11 16 18 21 23 31 64 66 69 XXXXXXXX|12 17 35 76 78 XXXXXXXX|29 XXXXX|3 38 43 47 63 -1 XXXXX|7 13 15 22 48 62 67 79 XXXXX|1 52 54 XXXX|42 60 73 XXX|24 39 XXX| XX|45 X| X| -2 X| X| |8 | | |

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Review of item scaling properties

• Most items had excellent scaling properties– Weighted mean square item fit– Item-total correlation– Item characteristic curves

• Only on test item (CI2HRM2) was omitted from scaling

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February 2010

Item statistics

Item 37 ------- item:37 (CI2HRM2) Cases for this item 7574 Item-Rest Cor. 0.09 Item Threshold(s): -0.37 Weighted MNSQ 1.23 Item Delta(s): -0.37 ------------------------------------------------------------------------------ Label Score Count % of tot Pt Bis t (p) PV1Avg:1 PV1 SD:1 ------------------------------------------------------------------------------ 1 0.00 222 2.93 -0.15 -13.31(.000) -0.78 0.85 2 1.00 4401 58.11 0.09 7.44(.000) 0.12 0.90 3 0.00 449 5.93 -0.12 -10.71(.000) -0.43 0.83 4 0.00 2392 31.58 0.05 4.23(.000) 0.00 0.86 7 0.00 45 0.59 -0.07 -5.92(.000) -0.97 1.08 9 0.00 65 0.86 -0.06 -4.80(.000) -0.52 0.73 ==============================================================================

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Item characteristic curves

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Scoring reliabilities - 1

• Open-ended items were scored according to international scoring guidelines

• Double-scoring of sub-samples

• On average, percentages of scorer agreement ranged between 84 and 92 across participating countries

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Scoring reliabilities - 2

• Only items accepted where scorer agreement was 70% or more

• Data for items where this criterion was not met were not included in scaling

• In two countries open-ended items were consistently easier than other items– Omitted from scaling and database

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February 2010

Gender DIF

• DIF estimates reflect the differences between item difficulties for males and females of equal ability – This may cause bias in favour of one

group

• Generally, only few items with gender DIF were found

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Cross-national measurement equivalence

• Occurrence of item-by-country interaction– Items relatively much harder in some

countries but much easier in others

• In ICCS, national item calibrations were compared with those for the international calibration sample

• Standard errors were adjusted for sample design effects and multiple comparisons

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Example for CI2HRM2

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Item-by-country interaction

• Generally, items tended to behave in a similar way

• Number of items with parameter variance– Sometimes due to translation errors– Often due to other factors (national context,

curricula)

• Occurrence of some parameter variation across countries – Similar results as in other cross-national

studies

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February 2010

Item adjudication

• Based on results from scaling analysis (item statistics, item curves, item-by-country interaction etc.)

• International item adjudication– Omission of CI2HRM2 from scaling

• National item adjudication– Re-verification for items with larger

discrepancies in item difficulty– Omission of item for national scaling with

translation or scoring issues

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Calibration of items

• Based on international calibration sample with 500 randomly selected students from each of the 36 participating countries that met sampling requirements

• ACER ConQuest was used for estimation

• Booklet effects adjusted by including booklet as a facet in the scaling model

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Scaling methodology

• Plausible values were generated as student ability estimates– More information at workshop!

• Dummy indicators for classroom and all student level variables (international and regional) were included in the conditioning model

• Scale scores set to international metric with mean of 500 and SD of 100 for equally weighted countries

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Estimation of changes in cognitive knowledge - 1

• 17 test items from CIVED included as intact cluster

• 17 countries with comparable data– Three countries with grade 9 in CIVED

and additional grade 9 samples in ICCS

• Small number of items in some countries had to be discarded due to translation errors or differences between ICCS and CIVED

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Estimation of changes in cognitive knowledge - 2

• Comparison of item parameters showed high similarity (correlation of 0.95)

• Slight positioning effect due to different test designs– CIVED: One booklet– ICCS: CIVED link cluster in each of the

three positions• CIVED items at beginning slightly easier, at

end slightly harder than in ICCS

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Estimation of changes in cognitive knowledge - 3

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Estimation of changes in cognitive knowledge - 4

• Framework broadened since CIVED– Re-scaling CIVED data to equate with

ICCS not appropriate

• Selection of CIVED items not representative for overall CIVED test– Equating link items with CIVED scale (or

sub-scale) also not appropriate

• Solution: Establish new comparison scale based only on 17 link items

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Estimation of changes in cognitive knowledge - 5

• Concurrent calibration of item parameters based on calibration samples with 34 samples from 17 countries (CIVED and ICCS)

• Establishing a metric with a mean of 500 and SD of 100 for equally weighted 17 CIVED countries

• For results in tables, weighted likelihood estimates were used– Usually unbiased for country averages

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Questionnaire item analysis

• Missing data issues

• Item dimensionality and scaling review

• Item/scale adjudication

• Scaling procedures

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Missing data - 1

• On average about 3 percent of students have missing scale scores– Only in two countries there are

percentages of 18 and 12 percent

• Teacher survey data relatively low missing percentages were found (about 2 percent)

• Very low percentages of missing data in school questionnaire

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Missing data - 2

• Concerns about missing data for socio-economic indicators– Highest parental occupation: 5%– Highest parental education: 3%– Books at home: 1%

• However, in a few countries higher percentages of missing data were found (up to 15% for parental education)

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Analysis of item dimensionality

• Exploratory and confirmatory factor analyses showed generally very similar results to those from the field trial

• These analyses will be described in detail in the ICCS technical report

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Scaling analysis

• Scale reliabilities (Cronbach’s alpha)– Over 0.7 satisfactory internal consistency

• Item-total correlations:– Useful for reviewing translation errors

• Scaling with IRT Partial Credit Model– Item fit– Category characteristic curves

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Item and scale adjudication

• Only three scales with median scale reliabilities below 0.7– Democratic value beliefs, civic

participation in community and at school

• Adjudication for student, teacher, school and each regional questionnaire

• Some items were removed from scale

• In some cases, single-item reporting

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Scaling procedures - 1

• IRT scaling with Partial Credit Model

• So-called weighted likelihood estimates as scale scores

• International metric with mean of 50 and a standard deviation of 10

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Scaling procedures - 2

• Item parameter calibration with ACER ConQuest

• Calibration samples:– 500 students per country– 250 teachers per country– All school data with equal weights for

each country

• Only data from countries that met sampling requirements (categories 1 or 2) included in calibration

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Questionnaire scales

• Advantages of IRT scales– Inclusion of students with at least two

item responses per scale– Possibility to describe scale

• From IRT Partial Credit Model it is possible to map scale scores to expected item responses

• Item maps will be provided in appendix to international report

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Example of item map

Item

Item #1

Item #2

Item#3

Example of how to interpret the item-by-score map#1:

#2:

#3:

#4:

#5:

A respondent with score 60 has more than 50 probability to strongly agree with items 1 and at least agree with items 2 and 3

A respondent with score 40 has more than 50 % probability to strongly agree with items 1, 2 and 3

Example of item-by-score map

A respondent with score 30 has more than 50% probability to strongly agree with all three items

A respondent with score 40 has more than 50% probability to at least disagree with items 1 and 2 but to disagree with item 3

A respondent with score 50 has more than 50% probability to at least agree with items 1 and at least disagree with items 2 and 3

20 30 40 50 60 70 80

Scores

Strongly disagree Disagree Agree Strongly agree

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Data analysis for reporting

• Estimation of sampling variance

• Estimation of measurement variance

• Reporting of differences

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Estimation of sampling variance

• Data from cluster samples are not simple random samples– Standard formula for estimating sampling

error not appropriate

• Jackknife repeated replication technique used for ICCS

• IDB Analyser, WESVAR or SPSS/SAS macros may be used for applying this methodology

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Estimation of measurement variance

• Using plausible values allows estimating the measurement error– The variation between the five PVs can

be used for estimation

• IDB Analyser, WESVAR or SPSS macros (ACER replicates module) include features to do this

• More information will be provided at the training workshop on Wednesday

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Reporting of differences - 1

• The following types of significance tests will be reported:– For differences in population estimates between

countries– For differences between a country and the

international – in population estimates between subgroups within

countries.– For differences between population estimates in

ICCS and in CIVED (trend estimation)

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Reporting of differences - 2

• Adjustment for multiple comparisons with Dunn-Bonferroni method– increasing critical value (p> .05) from

1.96 to 3.189

• SE for differences between samples

• Estimation of SE for sub-group differences with JRR

22_ jiijdif SESESE

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Reporting of differences - 3

• For the SE of trend differences it is important to take the equating error into account

• The estimation of SE for differences between CIVED and ICCS can be computed as

• The equating error in the international metric is 3.31

222_ EqErrSESESE jiijdifCIVEDICCS

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Multivariate analysis

• Multiple regression models were used for the tables in draft Chapter 7– Bivariate regression– Multiple regression

• Multi-level models were used for the analysis in draft Chapter 8– Students nested within classrooms– Classrooms mostly equivalent to schools

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Questions or comments?