John Cursio

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1. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Latent Trait Shared Parameter Mixed-Models for Missing Ecological Momentary Assessment Data John F. Cursio, PhD jcursio@uchicago.edu University of Chicago 3, July 2017 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
2. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary 1 Ecological Momentary Assessment 2 EMA Data Set 3 The Model 4 Model Results 5 Summary 2 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
3. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Ecological Momentary Assessment Ecological Momentary Assessment (EMA) - Real-time data capture Addiction, depression, anxiety, and mood studies Long series of outcomes collected with intermittent missingness Most EMA studies ignore the missing data 3 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
4. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Statement of the Problem Shared parameter models - one approach if missingness is non-random Latent class pattern-mixture models used with intermittent missing data (Lin 04, Roy 03, Beunckens 08) Solution: Latent Trait Shared Parameter Mixed-Model for EMA to handle missing data 4 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
5. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Latent Trait Theory Also known as Item Response Theory IQ tests, Law School Admissions tests Each subject has latent trait or “ability” - intelligence Latent trait determined by number of correct questions answered, question difficulty, and discrimination parameter 5 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
6. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Item Response Theory Models Logistic Model written as: P(Rij = 1|θi ) = 1 1 + exp[−aj (θi − bj )] (1) aj : slope parameter for item j aj = a in One-Parameter Model (Rasch) bj : difficulty parameter for item j Rij = 1 subject i responds to prompt j θi Latent trait or “ability” of each subject assume θi ∼ N(0,1) Higher θi → higher “ability” 6 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
7. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary EMA Data collection Hedeker, Mermelstein, and Demirtas (08) 452 subjects in high school (9th or 10th grade) Positive affect (PA) and negative affect (NA) measured over 7-day period with 30 to 40 responses per subject Covariates include: Gender, Smoker, Negative Mood Regulation (NMR), Grade Point Average (GPA) Alone indicator separated into between-subject (AloneBS) and within-subjects (AloneWS) components 7 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
8. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Time-Bins Form 5 time-bins per day: Time-bin Description 3am - 8:59am Early Morning 9am - 2:59pm Mid-Day 3pm - 5:59pm Afternoon 6pm - 8:59pm Evening 9pm - 2:59am Late Evening Data collection over 1 week: mi = 5 × 7 = 35 8 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
9. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Response Indicator Setup All subjects have a unique response vector Rij ,where: j = 1, . . . , 35 time-intervals =(7 days x 5 periods) Rij = 1 participant responded Rij = 0 participant did not respond Rij = . no prompt generated 9 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
10. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Example data - rows (days) are stacked Response vector Rij =           . 1 . . 0 1 1 . . 0 1 0 . . 0 1 1 . . 0 0 . 1 1 1 . . . . 0 . . . 0 1           10 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
11. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Latent-Trait Shared Parameter Mixed-Model (LTSPMM) Will combine information about the response process and missingness process Why? Latent class approach usually has predefined idea about group composition Roy (Biometrics 08) notes that statistical tests for number of classes may also be difficult Link outcome model and missingness model by the latent trait θi 11 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
12. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Estimated LTSPMM - Longitudinal Model yij = xij β + γθi + συξi + eij i = 1, 2, . . . , N subjects, j = 1, 2, . . . , ni times yij : Negative Affect or Positive Affect, for subject i at time j xij : Subject covariates, β : vector of regression coefficients γ: regression coefficient for latent trait θi θi : latent trait for subject i ∼ N(0, 1) συ: random intercept standard deviation ξi : random intercept coefficient ∼ N(0, 1) eij : error terms ∼ N(0, σ2 e ) 12 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
13. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Estimated LTSPMM - Response Process logit(Rij ) = cj + aj θi One- or Two-Parameter Latent Trait Model j = 1, 2, . . . , mi time-bins cj = −aj bj : item-intercept parameter aj : discrimination parameter Rij = 1, 0, “.” Rij = 1 ⇒ subject i answered prompt in time-bin j Rij = 0 ⇒ subject i did not answer prompt in time-bin j Rij = “.” ⇒ no prompt in time-bin j 13 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
14. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Estimation in SAS SAS NLMIXED used to estimate models in a joint fashion Marginal Maximum Likelihood solved using Adaptive Gaussian Quadrature 4 models estimated (PA or NA, One- or Two-Parameter LTSPMM) Main interest: how are mood outcomes (PA or NA) influenced by model covariates? Will the LTSPMMs tell a different story than MAR and LC pattern-mixture model? 14 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
15. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Estimates (Standard Errors) Positive Affect MAR LC LT(1P) LT(2P) Intercept 6.449∗∗∗ 6.563∗∗∗ 6.501∗∗∗ 6.495∗∗∗ (0.342) (0.342) (0.341) (0.341) Smoker -0.189 -0.188 -0.182 -0.182 (0.106) (0.105) (0.105) (0.105) Male 0.218∗ 0.255∗ 0.252∗ 0.252∗ (0.110) (0.110) (0.111) (0.110) NMR 0.625∗∗∗ 0.618∗∗∗ 0.636∗∗∗ 0.637∗∗∗ (0.080) (0.079) (0.080) (0.080) GPA -0.133 -0.141∗ -0.158∗ -0.158∗ (0.072) (0.072) (0.073) (0.073) ∗∗∗ p<0.001,∗∗ p<0.01,∗ p<0.05 15 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
16. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Estimates (Standard Errors) Positive Affect MAR LC LT(1P) LT(2P) Alone (WS) -0.514∗∗∗ -0.514∗∗∗ -0.517∗∗∗ -0.514∗∗∗ (0.028) (0.028) (0.028) (0.028) Alone (BS) -1.397∗∗∗ -1.439∗∗∗ -1.399∗∗∗ -1.402∗∗∗ (0.271) (0.269) (0.269) (0.269) Latent Class 2 -0.026 (0.158) Latent Class 3 -0.456∗∗ (0.160) γ 0.162∗ 0.151∗ (0.069) (0.062) -2LogL 51742 51734 64963 64908 ∗∗∗ p<0.001,∗∗ p<0.01,∗ p<0.05 16 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
17. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Model Results Coefficient estimates for gender drastically different across the four models (males have higher average mood) One-parameter and two-parameter model: Positive Affect is influenced by the latent “ability” to respond PA → ˆ γ is positive and significant! If an individual is more responsive, their PA has a tendency to increase (feel better) Similar results also found for NA models 17 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
18. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Results Summary LTSPMM offers improvement over latent class pattern-mixture model Joint model linking longitudinal model with response model Two-parameter model had significantly better fit (-2LogL) than one-parameter model LTSPMMs had less biased estimates of gender coefficient than LC and MAR when: 1 Data simulated assuming LTSPMM was true model 2 Correlation exists between θ and model covariate (gender) 18 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
19. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Item Difficulties 1 2 3 4 5 −1.5 −1.0 −0.5 0.0 0.5 Item Difficulty Parameters Positive Affect,One−Parameter LTSPMM time−bin Difficulties Monday Tuesday Wednesday Thursday Friday Saturday Sunday 1 2 3 4 5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 Item Difficulty Parameters Positive Affect,Two−Parameter LTSPMM time−bin Difficulties Monday Tuesday Wednesday Thursday Friday Saturday Sunday 19 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
20. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Item Discriminations 1 2 3 4 5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Item Discrimination Parameters Positive Affect,Two−Parameter LTSPMM time−bin Discriminations Monday Tuesday Wednesday Thursday Friday Saturday Sunday 20 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
21. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary Response Patterns i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i13 i14 i15 i16 i17 i18 i19 i20 i21 i22 i23 i24 i25 i26 i27 i28 i29 i30 i31 i32 i33 i34 i35 θi Highest to Lowest Response Patterns and Latent Traits i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i13 i14 i15 i16 i17 i18 i19 i20 i21 i22 i23 i24 i25 i26 i27 i28 i29 i30 i31 i32 i33 i34 i35 Latent Class Response Patterns and Latent Classes LC 1 2 3 21 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models
22. Outline Ecological Momentary Assessment EMA Data Set The Model Model Results Summary The project described was supported by Award Number P01CA098262 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health. 22 John F. Cursio, PhD jcursio@uchicago.edu University of Chicago Latent Trait Shared Parameter Mixed-Models