overview of field trial analysis procedures
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Overview of field trial analysis procedures. National Research Coordinators Meeting Windsor, June 2008. Content of presentation. Purposes of field trial analysis Methodologies applied IRT Rasch model Factor analysis Criteria used Fit indices Item and scale statistics. - PowerPoint PPT PresentationTRANSCRIPT
Overview of field trial analysis procedures
National Research Coordinators Meeting Windsor, June 2008
NRCMeetingWindsor
June 2008
Content of presentation
• Purposes of field trial analysis• Methodologies applied
– IRT Rasch model– Factor analysis
• Criteria used– Fit indices– Item and scale statistics
NRCMeetingWindsor
June 2008
Purposes of field trial
• Test feasibility of construct measurement • Review scalability of item material• Check test and questionnaire length• Compare different formats (items with and
without “don’t know” category)• Inform on relationships between constructs
and variables• Compare results from on-line and paper
surveys
NRCMeetingWindsor
June 2008
Data included in analysis
• Data from 31 countries included in international analyses
• Instrument data from– Student test (98 cognitive items)– Student questionnaire– Teacher questionnaire– School questionnaire– Regional instruments (cognitive and
questionnaire data)
• Comparison of on-line and paper surveys (international option)
NRCMeetingWindsor
June 2008
Types of analysis
• Review of frequencies and means
• Review of correlations between variables and constructs
• Review of reliabilities and item-score correlations
• IRT (Rasch) Scaling results
• Exploratory and Confirmatory Factor Analysis
NRCMeetingWindsor
June 2008
Analysis reports
• Part 1 in NRC(June08)2.pdf– Analysis of cognitive test items– Analysis of student questionnaire data– Four appendix documents (a, b, c and d)
• Part 2 in NRC(June08)3.pdf– Analysis of teacher questionnaire data– Analysis of school questionnaire data– Two appendix documents (a and b)– Addition document on comparison of paper and
online mode (NRC(June08)3c.pdf)
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June 2008
Cognitive test data analysis
• Review of omitted, invalid and “not reached” responses
• Analysis of item difficulties, discrimination and Rasch model fit
• Differential item functioning– Gender groups– Countries
• Analysis of dimensionality• Trend item analysis
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June 2008
Not reached items (medians)
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The IRT “Rasch” Model
• Modelling probability of getting a correct response
• Modelling probability of getting an incorrect response
in
innii XP
exp1
exp)1(
)exp(1
1)0(
inniXP
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June 2008
IRT curves
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June 2008
MC Item statistics (example)
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June 2008
Example
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June 2008
IRT models for categorical data
• Extension of Rasch model with additional step parameters
• Partial credit model has different step parameters for each item
iim
h
k
kijin
x
kijin
x mxPii
,,1,0
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June 2008
Partial Credit Model – probabilities
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June 2008
Test item difficulties
and abilities
| | 2 | | X| | X|57 | XX| | XX| | XX|48 67 | XXX|23 | XXX| | XXXX|78 | XXXXX|31 76 | 1 XXXXX|45 80 | XXXXXXX|17 41 42 72 97 | XXXXXX|12 | XXXXXX|59 68 73 75 98 | XXXXXXX|61 77 79 83 91 | XXXXXXXX|8 11 60 90 | XXXXXXXXX|85 89 | XXXXXXXXXX|14 29 37 47 53 84 94 | XXXXXXXX|6 65 92 | XXXXXXXXX|27 63 70 88 | 0 XXXXXXXX|22 44 64 81 93 | XXXXXXXXX|2 7 9 32 50 71 | XXXXXXXXX|4 13 55 62 96 | XXXXXXXXX|5 15 20 24 | XXXXXXXX|16 25 26 30 58 | XXXXXXXX|18 46 49 51 52 82 86 | XXXXX|1 21 43 54 66 | XXXXX|3 19 28 34 35 74 | XXXXXX|40 56 | -1 XXXX|69 | XXX|10 95 | XXX|33 36 | XX| | X| | X| | X|38 87 | X|39 | | | | | -2 | | ==================================================================== Each 'X' represents 106.7 cases ====================================================================
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June 2008
Gender DIF
• Gender effect directly estimated with ACER ConQuest
• Reflects difference in logits if item parameters had been estimated separately for males and females
• Differences for combined effect > 0.3 flagged (effect * 2)– DPC item stats: separate effects reported
• Generally few cognitive test items had Gender DIF
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June 2008
Item-by-country interaction
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June 2008
Item dimensionality
• No clear pattern of dimensionality with regard to old CIVED and new ICCS items– High correlation between the two test
parts (0.87)
• High correlation for sub-dimensions– Cognitive dimensions: 0.89– Content dimensions: 0.93
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June 2008
Review of CIVED trend items
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June 2008
Coder reliability
0102030405060708090
100
IC2
PD
O1
IC2
BIO
1
IC2
MB
O1
IC2
ET
O1
IC2
VS
O1
IC2
RR
O1
IC2
WF
O1
IC2
WF
O2
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June 2008
Summary for test item analysis
• Very positive results regarding scalability of test items
• Support for uni-dimensionality of test items
• Few items to be deleted or modified
• Open-ended items performed generally well (except one item)
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June 2008
National reports
• Purpose: Checking of national item statistics and review of possible explanations
• Only for cognitive test items
• Graphical displays
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Item Stats in graphical
form
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June 2008
National item fit and discrimination
International value
Summary of the national values(mean +/- 1STD)National value
[Item #]
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National Item difficulties and thresholds
International value
National value1. Summary of the
national values(mean +/- 1STD)
[Item #]
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June 2008
National item review list
[Item #1]
[Item #2]
[Item #3]
[Item #4]
[Item #5]
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June 2008
International Summary
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June 2008
Item statistics
• DPC provided NRCs with item statistics
• Review of – category frequencies– point biserials (correlations)– Rasch parameter and fit– Gender DIF information– Difficulty in percentage correct (national
and international)
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June 2008
Questionnaire item analysis
• Review of frequencies (including for omitted and invalid responses)
• Comparison of different formats (with and without “don’t know” categories)
• Analysis of scaling properties (reliabilities, Rasch modelling)
• Analysis of dimensionality• Analysis of relationships between
variables and constructs
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June 2008
Correlations
• Reporting of Pearson’s correlation coefficients
• Used to review whether expected relationships are found in data (e.g. correlations between indicators of social background)
• Correlation with test performance regularly reported for student scales
• Criteria (not “scientific”): – < 0.1 Not substantial– 0.1 – 0.2 Weak– 0.2 – 0.5 Moderate– > 0.5 Strong
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June 2008
Reliabilities
• Cronbach’s alpha coefficient– Is influenced by number of items!
• Item-by-total correlation
• Criteria– < 0.60 Poor– 0.60 – 0.70 Marginally satisfactory– > 0.70 Good
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June 2008
Example of scale information
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June 2008
Exploratory factor analysis
• Used for exploring dimensionality for sets of items
• VARIMAX rotation– Assumes factors to be uncorrelated
• PROMAX rotation– Assumes factors to be correlated
• Not always reported as it was used primarily in preliminary analysis steps
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June 2008
Confirmatory Factor Analysis
• Model estimation based on variances and covariances– LISREL and SAS CALIS estimates– Maximum Likelihood (items assumed to
be continuous)
• Analysis to confirm expected factor structure
• Model fit indices indicate whether the model “fits the data”
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June 2008
Example of CFA
VOTEPART1.00
POLPART1.00
INFPART1.00
I03A 0.26
I03B 0.25
I03C 0.59
I03D 0.59
I03E 0.32
I03F 0.45
I03G 0.45
I04C 0.53
I04D 0.54
I04E 0.41
I04F 0.45
I04G 0.45
Chi-Square=2788.41, df=51, P-value=0.00000, RMSEA=0.070
0.86
0.87
0.64
0.64
0.82
0.74
0.74
0.68
0.67
0.77
0.74
0.74
0.43
0.39
0.70
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June 2008
CFA by country
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June 2008
Fit indices
• RMSEA (Root mean squared error approximation)– > 0.10 Poor model fit of) – 0.10 – 0.05 Marginally satisfactory model fit– < 0.05 Close model fit
• RMR– > 0.10 Poor model fit– 0.10 – 0.05 Marginally satisfactory model fit– < 0.05 Close model fit
• CFI (Comparative fit index) and NNFI (Non-normed fit index)– < 0.70 Poor model fit– 0.80 - 0.90 Marginally satisfactory model fit– > .90 Close model fit
NRCMeetingWindsor
June 2008
IRT models for categorical items
• Partial credit model models the response probability for each depending on the latent trait – Item location parameter – Step parameter
iim
h
k
kijin
x
kijin
x mxPii
,,1,0
)(exp
)(exp)(
0 0
0
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June 2008
ACER ConQuest models
• ITEM+ITEM*STEP: Constrained model– Assumes all item parameters to be equal
across countries
• ITEM-CNT+ITEM*CNT+ITEM*STEP:Unconstrained model– Assumes item location parameters to be
different across countries
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June 2008
Item-by-country interaction
• Item-by-country interaction effects sum up to zero
• For review, the median of the absolute values was taken as an indicator of measurement invariance across countries
• Those values > 0.3 logits were interpreted as items with large item-by-country interaction
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June 2008
IRT result tables
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June 2008
Scope of analysis
• Given the narrow timeframe for analysis not all of these analyses were carried out for all instruments
• Reviews of frequencies, computation of scale reliabilities and exploratory factor analyses were done for all field trial instruments
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June 2008
Analysis of relationships between context variables
• Correlation of school, teacher and student data aggregated at the school level– Results show quite a few of the expected
relationships
• Single-level regression analysis for test performance and expected electoral participation– 25 percent of variance in test performance and
21 percent of variance in index of expected electoral participation explained by models
NRCMeetingWindsor
June 2008
General outcomes
• Good scaling properties for most items– Some constructs and items not retained due to
poor results
• Comparison of formats– No substantial differences in outcomes but large
differences in missing values– Proposal to omit “don’t know” categories
• Encouraging results for measurement of socio-economic student background– Proposal not to retain household possession
items
NRCMeetingWindsor
June 2008
Questions or comments?