Growth Model Considerations in Early Literacy Research Yaacov Petscher Florida 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

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

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

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

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

Just…no… Modelχ²dfRMSEACFITLIBIC Contrained MLCS Freed MLCS

LNF ΔLNF1ΔLNF2ΔLNF3ΔLNF4 LNF10.80 LNF LNF30.12 LNF PSF10.10 PSF20.03 PSF NWF10.36 NWF20.08 NWF g g10.50

Range Differences

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 PSF PSF40.24 PSF PSF60.04 LNF10.35 LNF2-0.4 LNF30.01 LNF LNF50.52 ORF10.18 ORF ORF30.21 ORF ORF50.12 ORF60.11

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 PSF PSF40.24 PSF PSF60.04 LNF10.35 LNF2-0.4 LNF30.01 LNF LNF50.52 ORF10.18 ORF ORF30.21 ORF ORF50.12 ORF60.11

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 ModelX2dfAICBICRMSEA Parallel Process Growth Constant - Fixed BW Constant Change - Fixed Between Constant Change - Fixed Within Dual Change 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