Growth Model Considerations in Early
Literacy Research
Yaacov PetscherFlorida Center for Reading
Research
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
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?
Univariate Longitudinal Factor Analysis
Multivariate Longitudinal Factor Analysis
Univariate Simplex Modeling
Cross-Lagged Latent Regression
Latent Growth
Parallel Process Latent Growth
Latent Growth SEM
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?
Latent Change Scores
Bivariate Latent Change Scores
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?
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
Analyses
• Univariate LCS– Evaluate patterns
• Multivariate LCS– Evaluate contributors to LCS
• Multilevel LCS– Evaluate differences in estimated
effects by classes and students
LNFCFI = .95TLI = .95RMSEA = .11SRMR = .08
PSFCFI = .94TLI = .95RMSEA = .09SRMR = .09
NWFCFI = .90TLI = .90RMSEA = .12SRMR = .09
ORF CFI = .94TLI = .94RMSEA = .12SRMR = .06
Just…no…
Model χ² df RMSEA CFI TLI BICContrained MLCS 784652 523 0.14 0.68 0.69 18221136Freed MLCS 468059 462 0.11 0.91 0.90 17905348
LNF ΔLNF1 ΔLNF2 ΔLNF3 ΔLNF4LNF1 0.80LNF2 -0.16LNF3 0.12LNF4 -0.04PSF1 0.10PSF2 0.03PSF3 -0.01NWF1 0.36NWF2 0.08NWF3 0.10
g0 18.01g1 0.50
∆ 𝐿𝑁𝐹=𝛼 𝑙𝑛𝑓 +𝛽𝑙𝑛𝑓 𝐿𝑁𝐹 [𝑡 −1 ]+𝛾𝑙𝑛𝑓 ,𝑝𝑠𝑓 𝑃𝑆𝐹 [𝑡 −1 ]+¿𝛾 𝑙𝑛𝑓 ,𝑛𝑤𝑓 𝑁𝑊 𝐹 [𝑡− 1]
.50 – (.16*LNF[t-1]) + (.10*PSF[t-1]) + (.36*NWF[t-1])
Range Differences
NWFΔNWF1 ΔNWF2 ΔNWF3 ΔNWF4 ΔNWF5 ΔNWF6 ΔNWF7 ΔNWF8 ΔNWF9
NWF1 0.65NWF2 0.93NWF3 0.7NWF4 0.58NWF5 0.4NWF6 0.11NWF7 0.3NWF8 0.22NWF9 0.2PSF1 0.15PSF2 -0.3PSF3 -0.05PSF4 0.24PSF5 -0.44PSF6 0.04 0.04LNF1 0.35LNF2 -0.4LNF3 0.01LNF4 -0.36LNF5 0.52ORF1 0.18ORF2 -0.21ORF3 0.21ORF4 -0.06ORF5 0.12ORF6 0.11
NWFΔNWF1 ΔNWF2 ΔNWF3 ΔNWF4 ΔNWF5 ΔNWF6 ΔNWF7 ΔNWF8 ΔNWF9
NWF1 0.65NWF2 0.93NWF3 0.7NWF4 0.58NWF5 0.4NWF6 0.11NWF7 0.3NWF8 0.22NWF9 0.2PSF1 0.15PSF2 -0.3PSF3 -0.05PSF4 0.24PSF5 -0.44PSF6 0.04 0.04LNF1 0.35LNF2 -0.4LNF3 0.01LNF4 -0.36LNF5 0.52ORF1 0.18ORF2 -0.21ORF3 0.21ORF4 -0.06ORF5 0.12ORF6 0.11
How to use the scores
• Create vector plots• Determinant importance– Comparing graphs– Relative importance– Screening applications
Multilevel LCS
• Model Comparisons– Parallel Process– Constant Change• Fixed Proportional at Levels
– Dual Change-Constrained Lag
Model X2 df AIC BIC RMSEA
Parallel Process Growth 23146 54 2401799 2401939 0.105
Constant - Fixed BW 18664 56 2397313 2397443 0.093
Constant Change - Fixed Between 18466 54 2397119 2397260 0.094
Constant Change - Fixed Within 17572 54 2396226 2396366 0.092
Dual Change 17403 52 2396061 2396212 0.092
Δχ² (2) = 169, p < .001
Conclusions
• LCS can help inform change and causation
• May be useful for informing multivariate screening
• Better target interventions• They are a pain to run
