1. Growth Model Considerations in Early Literacy Research Yaacov Petscher Florida Center for Reading Research

2. What do we want to model? How students are changing over time Individual differences in change How change in one skill relates to change in another Causes of individual change Causes of individual differences in individual change

3. Progress Monitoring What does growth in syntax ability look like in K? Do students differ in their growth patterns in syntax? What is the relationship between growth in syntax and growth in listening comprehension? What causes growth in syntax? What causes individual differences in syntax growth?

4. Univariate Longitudinal Factor Analysis

5. Multivariate Longitudinal Factor Analysis

6. Univariate Simplex Modeling

7. Cross-Lagged Latent Regression

8. Latent Growth

9. Parallel Process Latent Growth

10. Latent Growth SEM

11. So what? Each model exists for a specific purpose Differences contribute to individual practical problems – Minimum N – # of Occasions – # of Variables Can we combine the growth and causal models to extract similar types of information?

12. Latent Change Scores

13. Bivariate Latent Change Scores

16. Research Questions What are the growth trajectories of students’ early literacy skills? Can these be better informed by dynamic developmental relations? Are there differences in dynamic developmental relations between-students vs. between- classes?

17. Data and Measures Sample size = 77,675 students; 4,774 classes DIBELS Assessments – ISF: Kindergarten – LNF: K-1 – PSF: K-1 – NWF: K-2 – ORF: 1-3 Something reliability/validity

18. Analyses Univariate LCS – Evaluate patterns Multivariate LCS – Evaluate contributors to LCS Multilevel LCS – Evaluate differences in estimated effects by classes and students

20. LNF CFI =.95 TLI =.95 RMSEA =.11 SRMR =.08

21. PSF CFI =.94 TLI =.95 RMSEA =.09 SRMR =.09

22. NWF CFI =.90 TLI =.90 RMSEA =.12 SRMR =.09

23. ORF CFI =.94 TLI =.94 RMSEA =.12 SRMR =.06

25. Just…no… Modelχ²dfRMSEACFITLIBIC Contrained MLCS7846525230.140.680.6918221136 Freed MLCS4680594620.110.910.9017905348

26. LNF ΔLNF1ΔLNF2ΔLNF3ΔLNF4 LNF10.80 LNF2-0.16 LNF30.12 LNF4-0.04 PSF10.10 PSF20.03 PSF3-0.01 NWF10.36 NWF20.08 NWF3 0.10 g018.01 g10.50

27. Range Differences

28. NWF ΔNWF1ΔNWF2ΔNWF3ΔNWF4ΔNWF5ΔNWF6ΔNWF7ΔNWF8ΔNWF9 NWF10.65 NWF20.93 NWF30.7 NWF40.58 NWF50.4 NWF60.11 NWF70.3 NWF80.22 NWF90.2 PSF10.15 PSF2-0.3 PSF3-0.05 PSF40.24 PSF5-0.44 PSF60.04 LNF10.35 LNF2-0.4 LNF30.01 LNF4-0.36 LNF50.52 ORF10.18 ORF2-0.21 ORF30.21 ORF4-0.06 ORF50.12 ORF60.11

29. NWF ΔNWF1ΔNWF2ΔNWF3ΔNWF4ΔNWF5ΔNWF6ΔNWF7ΔNWF8ΔNWF9 NWF10.65 NWF20.93 NWF30.7 NWF40.58 NWF50.4 NWF60.11 NWF70.3 NWF80.22 NWF90.2 PSF10.15 PSF2-0.3 PSF3-0.05 PSF40.24 PSF5-0.44 PSF60.04 LNF10.35 LNF2-0.4 LNF30.01 LNF4-0.36 LNF50.52 ORF10.18 ORF2-0.21 ORF30.21 ORF4-0.06 ORF50.12 ORF60.11

30. How to use the scores Create vector plots Determinant importance – Comparing graphs – Relative importance – Screening applications

31. Multilevel LCS Model Comparisons – Parallel Process – Constant Change Fixed Proportional at Levels – Dual Change-Constrained Lag ModelX2dfAICBICRMSEA Parallel Process Growth2314654240179924019390.105 Constant - Fixed BW1866456239731323974430.093 Constant Change - Fixed Between1846654239711923972600.094 Constant Change - Fixed Within1757254239622623963660.092 Dual Change1740352239606123962120.092 Δχ² (2) = 169, p <.001

33. Conclusions LCS can help inform change and causation May be useful for informing multivariate screening Better target interventions They are a pain to run