PLANNED MISSING DATA DESIGNS
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1 PLANNED MISSING DATA DESIGNS SRCD Developmental Methodology Conference Feb 9 202
2 PLANNED MISSING DATA DESIGNS In planned missing data designs, participants are randomly assigned to conditions in which they do not respond to all items, all measures, and/or all measurement occasions Why would you want to do this?. Long assessments can reduce data quality 2. Repeated assessments can induce practice effects 3. Collecting data can be time- and cost-intensive 4. Less taxing assessments may reduce unplanned missingness 2
3 PLANNED MISSING DATA DESIGNS Cross-Sectional Designs Multiple Matrix Sampling Three-Form Design (and Variations) Two-Method Measurement Longitudinal Designs Developmental Time-Lag Wave- to Age-based designs Monotonic Sample Reduction Growth-Curve Planned Missing 3
4 Participants MULTIPLE MATRIX SAMPLING Shoemaker (97) Test Items K N 4
5 Participants MULTIPLE MATRIX SAMPLING Test Items K N 5
6 Participants MULTIPLE MATRIX SAMPLING Test Items K N 6
7 MULTIPLE MATRIX SAMPLING Assumptions The K items are a random sample from a population of items (just as N participants are a random sample from a population) Limitations Properties of individual items or relations between items are not of interest Questions? 7
8 THREE-FORM DESIGN Form Common Set X Variable Set A Variable Set B Variable Set C ¼ of items ¼ of items ¼ of items missing 2 ¼ of items ¼ of items missing ¼ of items 3 ¼ of items missing ¼ of items ¼ of items Graham et al. (2006) Raghunathan & Grizzle (995) split questionnaire design Wacholder et al. (994) partial questionnaire design 8
9 THREE-FORM DESIGN What goes in the Common Set? Form Common Set X Variable Set A Variable Set B Variable Set C ¼ of items ¼ of items ¼ of items missing 2 ¼ of items ¼ of items missing ¼ of items 3 ¼ of items missing ¼ of items ¼ of items 9
10 THREE-FORM DESIGN What goes in the split sets? Form Common Set X Variable Set A Variable Set B Variable Set C ¼ of items ¼ of items ¼ of items missing 2 ¼ of items ¼ of items missing ¼ of items 3 ¼ of items missing ¼ of items ¼ of items 0
11 THREE-FORM DESIGN: EXAMPLE 2 questions made up of 7 3-question subtests Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others.
12 THREE-FORM DESIGN: EXAMPLE Common Set (X) Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others. 2
13 THREE-FORM DESIGN: EXAMPLE Common Set (X) Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others. 3
14 THREE-FORM DESIGN: EXAMPLE Set A Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others. 4
15 THREE-FORM DESIGN: EXAMPLE Set B Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others. 5
16 THREE-FORM DESIGN: EXAMPLE Set C Subtest Item Subtest Item Demographics Musical Taste Openness How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I have a vivid imagination. Extraversion Neuroticism Conscientiousness Agreeableness I start conversations. I am the life of the party. I am comfortable around people. I get stressed out easily. I get irritated easily. I have frequent mood swings. swings. I am always prepared. I like order. I pay attention to details. I am interested in people. I have a soft heart. I take time out for others. 6
17 Form (XAB) Form 2 (XAC) Form 3 (XBC) How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? How old are you? Are you male or female? What is your occupation? What is your favorite genre of music? Do you like to listen to music while you work? Do you prefer music played loud or softly? I have a rich vocabulary. I have excellent ideas. I start conversations. I am the life of the party. I get stressed out easily. I get irritated easily. I am always prepared. I like order. I am interested in people. I have a soft heart. I have a rich vocabulary. I have a vivid imagination. I start conversations. I am comfortable around people. I get stressed out easily. I have frequent mood swings. I am always prepared. I pay attention to details. I am interested in people. I take time out for others. I have excellent ideas. I have a vivid imagination. I am the life of the party. I am comfortable around people. I get irritated easily. I have frequent mood swings. I like order. I pay attention to details. I have a soft heart. I take time out for others. 7
18 Participant Form Age Sex Occupation Genre Work Music Volume Open Open2 Open3 Extra Extra2 Extra3 Neuro Neuro2 Neuro3 Consc Consc2 Consc3 Agree Agree2 Agree3 7 F professor Classical N loud F musician Funk N soft M student Jazz N soft M server Metal N soft M chef Rock N soft F painter Pop Y loud F librarian Alt N loud F server Ska N soft M doctor Punk N loud F statistician Pop N loud F chef Rock Y loud M nurse Rock N soft M lawyer Jazz Y soft F accountant Metal N soft F secretary Alt N loud
19 Participant Form Age Sex Occupation Genre Work Music Volume Open Open2 Open3 Extra Extra2 Extra3 Neuro Neuro2 Neuro3 Consc Consc2 Consc3 Agree Agree2 Agree3 7 F professor Classical N loud F musician Funk N soft M student Jazz N soft M server Metal N soft M chef Rock N soft F painter Pop Y loud F librarian Alt N loud F server Ska N soft M doctor Punk N loud F statistician Pop N loud F chef Rock Y loud M nurse Rock N soft M lawyer Jazz Y soft F accountant Metal N soft F secretary Alt N loud
20 Participant Form Age Sex Occupation Genre Work Music Volume Open Open2 Open3 Extra Extra2 Extra3 Neuro Neuro2 Neuro3 Consc Consc2 Consc3 Agree Agree2 Agree3 7 F professor Classical N loud F musician Funk N soft M student Jazz N soft M server Metal N soft M chef Rock N soft F painter Pop Y loud F librarian Alt N loud F server Ska N soft M doctor Punk N loud F statistician Pop N loud F chef Rock Y loud M nurse Rock N soft M lawyer Jazz Y soft F accountant Metal N soft F secretary Alt N loud
21 Participant Form Age Sex Occupation Genre Work Music Volume Open Open2 Open3 Extra Extra2 Extra3 Neuro Neuro2 Neuro3 Consc Consc2 Consc3 Agree Agree2 Agree3 7 F professor Classical N loud F musician Funk N soft M student Jazz N soft M server Metal N soft M chef Rock N soft F painter Pop Y loud F librarian Alt N loud F server Ska N soft M doctor Punk N loud F statistician Pop N loud F chef Rock Y loud M nurse Rock N soft M lawyer Jazz Y soft F accountant Metal N soft F secretary Alt N loud
22 Participant Form Age Sex Occupation Genre Work Music Volume Open Open2 Open3 Extra Extra2 Extra3 Neuro Neuro2 Neuro3 Consc Consc2 Consc3 Agree Agree2 Agree3 7 F professor Classical N loud F musician Funk N soft M student Jazz N soft M server Metal N soft M chef Rock N soft F painter Pop Y loud F librarian Alt N loud F server Ska N soft M doctor Punk N loud F statistician Pop N loud F chef Rock Y loud M nurse Rock N soft M lawyer Jazz Y soft F accountant Metal N soft F secretary Alt N loud
23 THREE-FORM DESIGN Things to consider number of forms order of items 23
24 THREE-FORM DESIGN Summary Shorter questionnaire = higher-quality data Shorter questionnaire = less unplanned missing High correlations between item sets = high efficiency relative to a complete data design Questions? 24
25 TWO-METHOD MEASUREMENT Measure Gold standard highly valid (unbiased) measure of the construct under investigation Problem: Measure is time-consuming and/or costly to collect, so it is not feasible to collect from a large sample Measure 2 Practical inexpensive and/or quick to collect on a large sample Problem: Measure 2 is systematically biased so not ideal 25
26 TWO-METHOD MEASUREMENT e.g., measuring stress Measure = collect spit samples, measure cortisol Measure 2 = survey querying stressful thoughts e.g., measuring intelligence Measure = WAIS IQ scale Measure 2 = multiple choice IQ test e.g., measuring smoking Measure = carbon monoxide measure Measure 2 = self-report 26
27 TWO-METHOD MEASUREMENT How it works ALL participants receive Measure 2 (the cheap one) A subset of participants also receive Measure (the gold standard) Using both measures (on a subset of participants) enables us to estimate and remove the bias from the inexpensive measure (for all participants) using a latent variable model 27
28 TWO-METHOD MEASUREMENT Example Does child s level of classroom attention in Grade predict math ability in Grade 3? Attention Measures ) Direct Classroom Assessment (2 items, N = 60) 2) Teacher Report (2 items, N = 200) Math Ability Measure, item (test score, N = 200) 28
29 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 29
30 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 30
31 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 3
32 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 32
33 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 33
34 Attention (Grade ) Math Score (Grade 3) TR TR2 DA DA 2 Teacher Report Teacher Report 2 Direct Assessment Direct Assessment 2 Math Score (Grade 3) (N = 200) (N = 200) (N = 60) (N = 60) (N = 200) Teacher Bias 2 bias 34
35 TWO-METHOD MEASUREMENT Assumptions: expensive measure is unbiased (i.e., valid) inexpensive measure is systematically biased both measures access the same construct 35
36 TWO-METHOD MEASUREMENT Holding cost constant, as N total increases, N expensive decreases As N total increases, SEs begin to decrease (power increases); as N total continues to increase, SEs increase again 36 from Graham et al. (2006)
37 TWO-METHOD MEASUREMENT Find the sweet spot! true-score reliability (expensive) true-score reliability (cheap) bias cheap only cheap only cheap only cheap only neither 37 from Graham et al. (2006)
38 TWO-METHOD MEASUREMENT Summary Rather than face a choice between high power/low validity vs. low power/high validity, 2-method measurement can result in high power/high validity This design is only possible when there are two suitable measures for the construct of interest Questions? 38
39 DEVELOPMENTAL TIME-LAG MODEL Use 2-time point data with variable time-lags to measure a growth trajectory + practice effects (McArdle & Woodcock, 997) 39
40 Age Time student T T ;6 5; ;3 4;9 4;6 4; 5;7 5;2 5;4 5;8 4; 5;0 5;4 5;0 5;3 5;8 40
41 T0 T T2 T3 T4 T5 T6 4
42 Y I B G A P t t t Intercept T0 T T2 T3 T4 T5 T6 42
43 Linear growth Y I B G A P t t t Intercept Growth T0 T T2 T3 T4 T5 T6 43
44 Constant Practice Effect Y I B G A P t t t Intercept Growth Practice T0 T T2 T3 T4 T5 T6 44
45 YT0 I YT I G P YT2 I 2G P Y I 3G P T3 45
46 Linear growth; Exponential practice decline Intercept Growth Practice T0 T T2 T3 T4 T5 T6 46
47 DEVELOPMENTAL TIME-LAG MODEL Summary 2 measured time points are formatted according to time-lag This formatting allows a growth-curve to be fit, measuring growth and practice effects Questions? 47
48 WAVE- TO AGE-BASED DATA The idea of reformatting data to answer a different question is not limited to time-lag designs Wave-based data collection (e.g., data collected at Grade -3) can be transformed into age-based data with missingness 48
49 49 K 2 grade student ;6-4; 5;0-5;5 5;6-5; age 6;0-6;5 6;6-6; 7;0-7;5 7;6-7; 5;6 5;3 4;9 4;6 4; 5;7 5;2 5;4 6;7 6;0 5; 5;5 5;9 6;7 6; 6;5 7;4 6;0 7;3 6;0 7;5 6;4 7;3 7;6
50 Out of 3 waves, create 7 waves of data with high missingness Allows for more fine-tuned agespecific growth modeling 4;6-4; 4;9 4;6 5;0-5;5 5;3 5;5 5;6-5; 5;6 5; age 6;0-6;5 6;0 6;4 6;6-6; 6;7 6;0 7;0-7;5 7;3 7;4 7;6-7; Even high amounts of missing data are not typically a problem for estimation 4; 5;2 5;4 5;9 5;7 6; 6;5 6;0 6;7 7;5 7;3 7;6 50
51 MONOTONIC SAMPLE REDUCTION Sometimes used in large datasets (e.g., Early Childhood Longitudinal Study) to reduce costs At each wave, a randomly-selected subgroup of the original sample is observed again The remainder of the original participants do not need to be kept track of, dramatically reducing costs Group Time Time 2 Time 3 Time 4 Time 5 x x x x x 2 x x x x -- 3 x x x x x x
52 MONOTONIC SAMPLE REDUCTION Advantages: Cost reduction A lot of power to estimate effects at earlier waves Disadvantages: Very little power to estimate effects dependent on the last wave of data, e.g., growth curve models (may be missing 80% of data) It is important to be able to estimate attrition rates before beginning data collection 52
53 GROWTH-CURVE PLANNED MISSING With a particular analysis in mind, missingness may be tailored to maximize power In growth-curve designs, the most important parameters are the growth parameters (e.g., estimate the steepness and the shape of the curve) Estimation precision depends heavily on the first and last time points A planned missing design can take advantage of this by putting missingness in the middle 53
54 GROWTH-CURVE PLANNED MISSING Participants are randomly assigned to be missing one measurement occasion (Graham, Taylor & Cumsille, 200) Group Time Time 2 Time 3 Time 4 Time 5 x x x x x 2 x x x x -- 3 x x x -- x 4 x x -- x x 5 x -- x x x 6 -- x x x x 54
55 GROWTH-CURVE MODELS Group Time Time 2 Time 3 Time 4 Time 5 x x x x x 2 x x x x x -- x -- 4 x -- x x x x x -- 6 x x x 7 x -- x -- x 8 -- x x -- x 9 x x x 0 -- x -- x x x x x 55
56 GROWTH-CURVE MODELS Group Time Time 2 Time 3 Time 4 Time 5 x x x x x 2 x x x x x -- x -- 4 x -- x x x x x -- 6 x x x 7 x -- x -- x 8 -- x x -- x 9 x x x 0 -- x -- x x x x x 56
57 57
58 PLANNED MISSING DESIGNS: SUMMARY Purposeful missing data can address several issue in study design Cost of data collection Participant burden/fatigue Practice effects Participant dropout Rearranging data can turn one complete design into a more nuanced missing data design Developmental time-lag designs Wave-missing into age-missing 58
59 REFERENCES Enders, C. K. (200). Applied missing data analysis. New York: Guilford Press. Graham, J. W., Hofer, S. M., & Piccinin, A. M. (994). Analysis with Missing Data in Drug Prevention Research. In L. M. Collins & L. Seitz (Eds.), National Institute on Drug Abuse Research Monograph Series (pp. 3-62). Washington, DC: National Institute on Drug Abuse. Graham, J. W., Hofer, S. M., & MacKinnon, D. P. (996). Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures. Multivariate Behavioral Research, 3, Graham, J. W., Taylor, B. J., Olchowski, A. E., & Cumsille, P. E. (2006). Planned missing data designs in psychological research. Psychological Methods,, Graham, J. W., Taylor, B. J.,& Cumsille, P. E. (200). Planned missing data designs in the analysis of change. In L. M. Collins &A.G. Sayer (Eds.), New methods for the analysis of change (pp ). Washington, D.C.: American Psychological Association. McArdle, J. J. & Woodcock, R. W. (997). Expanding test -retest designs to include developmental time-lag components. Psychological Methods, 2, Raghunathan, T. E., & Grizzle, J. E. (995). A split questionnaire survey design. Journal of the American Statistical Association, 90, Shoemaker, D. M. (97). Principles and procedures of multiple matrix sampling. Southwest regional library technical report 34. Wacholder, S., Carroll, R. J., Pee, D., & Gail, M. H. (994). The partial questionnaire design for case-control studies. Statistics in Medicine, 3,
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