Abstract
The purpose of this article is to demonstrate ways to model nonlinear growth using three testing occasions. We demonstrate our growth models in the context of curriculum-based measurement using the fall, winter, and spring passage reading fluency benchmark assessments. We present a brief technical overview that includes the limitations of a growth model with three time points, and how nonlinear growth can be modeled and the associated limitations. We present results for a piecewise growth mixture modeling approach to model nonlinear growth for 1 to 3 classes, as well as to further explain individual differences and to capture heterogeneity of growth patterns. We discuss our interpretation of these results, as well as the implications of different methods for modeling nonlinear growth with three occasions.
|
Alonzo, J., Lai, C. F., Anderson, D., Park, B. J., Tindal, G. (2012). An examination of test-retest, alternate form reliability, and generalizability theory study of the easyCBM passage reading fluency assessments: Grade 4 (Technical Report No. 1219). University of Oregon, Eugene. Google Scholar | |
|
Alonzo, J., Tindal, G. (2007). The development of word and passage reading fluency measures in a progress monitoring assessment system (Technical Report No. 40). University of Oregon, Eugene. Google Scholar | |
|
Alonzo, J., Tindal, G., Ulmer, K., Glasgow, A. (2006). easyCBM online progress monitoring assessment system. Eugene, OR: Center for Educational Assessment Accountability. Available at http://easycbm.com Google Scholar | |
|
Al Otaiba, S., Petscher, Y., Pappamihiel, N. E., Williams, R. S., Dyrlund, A. K., Connor, C. (2009). Modeling oral reading fluency development in Latino students: A longitudinal study across second and third grade. Journal of Educational Psychology, 101, 315–329. doi: 10.1037/a0014698 Google Scholar | Crossref | Medline | ISI | |
|
Ardoin, S., Christ, T. (2008). Evaluating curriculum-based measurement slope estimates using data from triannual universal screenings. School Psychology Review, 37, 109–125. Google Scholar | ISI | |
|
Ardoin, S. P., Christ, T. J. (2009). Curriculum-based measurement of oral reading: Standard errors associated with progress monitoring outcomes from DIBELS, AIMSweb, and an experimental passage set. School Psychology Review, 38, 266–283. Google Scholar | ISI | |
|
Baker, D. L., Park, Y., Baker, S. K. (2012). The reading performance of English learners in grades 1–3: The role of initial status and growth on reading fluency in Spanish and English. Reading and Writing, 25, 251–281. doi: 10.1007/s11145-010-9261-z Google Scholar | Crossref | ISI | |
|
Baker, S. K., Smolkowski, K., Katz, R., Fien, H., Seeley, J. R., Kame’enui, E. J., Beck, C. T. (2008). Reading fluency as a predictor of reading proficiency in low-performing, high-poverty schools. School Psychology Review, 37, 18–37. Google Scholar | ISI | |
|
Bollen, K. A., Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley. Google Scholar | |
|
Carlo, G., Crockett, L. J., Randall, B. A., Roesch, S. C. (2007). A latent growth curve analysis of prosocial behavior among rural adolescents. Journal of Research on Adolescence, 17, 301–323. Google Scholar | Crossref | ISI | |
|
Christ, T. J. (2006). Short-term estimates of growth using curriculum-based measurement of oral reading fluency: Estimating standard error of the slope to construct confidence intervals. School Psychology Review, 35, 128–133. Google Scholar | ISI | |
|
Christ, T. J., Silberglitt, B., Yeo, S., Cormier, D. (2010). Curriculum-based measurement of oral reading: An evaluation of growth rates and seasonal effects among students served in general and special education. School Psychology Review, 39, 447–462. Google Scholar | ISI | |
|
Crowe, E. C., Connor, C. M., Petscher, Y. (2009). Examining the core: Relations among reading curricula, poverty, and first through third grade reading achievement. Journal of School Psychology, 47, 187–214. Google Scholar | Crossref | Medline | ISI | |
|
Deno, S., Fuchs, L., Marston, D., Shin, J. (2001). Using curriculum-based measurement to establish growth standards for students with learning disabilities. School Psychology Review, 30, 507–524. Google Scholar | ISI | |
|
Deno, S., Marston, D., Tindal, G. (1985). Direct and frequent curriculum-based measurement: An alternative for educational decision making. Special Services in the Schools, 2, 5–27. Google Scholar | Crossref | |
|
Fuchs, L. S. (2004). The past, present, and future of curriculum-based measurement research. School Psychology Review, 33, 188–192. Google Scholar | ISI | |
|
Fuchs, L. S., Fuchs, D., Hosp, M. K., Jenkins, J. R. (2001). Oral reading fluency as an indicator of reading competence: A theoretical, empirical, and historical analysis. Scientific Studies of Reading, 5, 239–256. Google Scholar | Crossref | |
|
Graney, S., Missall, K., Martinez, R., Bergstrom, M. (2009). A preliminary investigation of within-year growth patterns in reading and mathematics curriculum-based measures. Journal of School Psychology, 47, 121–142. doi: 10.1016/j.jsp.2008.12.001 Google Scholar | Crossref | Medline | ISI | |
|
Heck, R. H., Takahashi, R. (2006). Examining the impact of proposition 48 on graduation rates in division 1A football and program recruiting behavior: Testing a policy change model. Educational Policy, 20, 587–614. Google Scholar | SAGE Journals | ISI | |
|
Jung, T., Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2/1, 302–317. Google Scholar | Crossref | |
|
Kim, Y. S., Petscher, Y., Schatschneider, C., Foorman, B. (2010). Does growth rate in oral reading fluency matter in predicting reading comprehension achievement?. Journal of Educational Psychology, 102, 652–667. doi: 10.1037/a0019643 Google Scholar | Crossref | ISI | |
|
Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York, NY: Gilford. Google Scholar | |
|
Li, F., Duncan, T. E., Mcauley, E., Harmer, P., Smolkowski, K. (2000). A didactic example of latent curve analysis applicable to the study of aging. Journal of Aging and Health, 12, 388–425. Google Scholar | SAGE Journals | ISI | |
|
Logan, J. A. R., Petscher, Y. (2010). School profiles of at-risk student concentration: Differential growth in oral reading fluency. Journal of School Psychology, 48, 163–186. doi: 10.1016/j.jsp.2009.12.002 Google Scholar | Crossref | Medline | ISI | |
|
Muthén, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81–117. Google Scholar | Crossref | |
|
Muthén, B. O., Brown, C. H., Masyn, K., Jo, B., Khoo, S.-T., Yang, C.-C, . . . Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459–475. Google Scholar | Crossref | Medline | ISI | |
|
Muthén, L. K., Muthén, B. O. (1998–2010). Mplus User’s Guide (6th ed.). Los Angeles, CA: Author. Google Scholar | |
|
Nese, J. F. T., Biancarosa, G., Anderson, D., Lai, C. F., Alonzo, J., Tindal, G. (2012). Within-year oral reading fluency with CBM: A comparison of models. Reading and Writing, 25, 887–915. doi: 10.1007/s11145-011-9304-0 Google Scholar | Crossref | ISI | |
|
Puranik, C. S., Petscher, Y., Al Otaiba, S., Catts, H. W., Lonigan, C. J. (2008). Development of oral reading fluency in children with speech or language impairments: A growth curve analysis. Journal of Learning Disabilities, 41, 545–560. doi: 10.1177/0022219408317858 Google Scholar | SAGE Journals | ISI | |
|
Raudenbush, S. W., Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: SAGE. Google Scholar | |
|
Shapiro, E. S., Keller, M. A., Lutz, J. G., Santoro, L. E., Hintze, J. M. (2006). Curriculum-based measures and performance on state assessment and standardized tests: Reading and math performance in Pennsylvania. Journal of Psychoeducational Assessment, 24, 19–35. Google Scholar | SAGE Journals | ISI | |
|
Silberglitt, B., Hintze, J. M. (2007). How much growth can we expect? A conditional analysis of R-CBM growth rates by level of performance. Exceptional Children, 74, 71–84. Google Scholar | SAGE Journals | ISI | |
|
Speece, D. L., Case, L. P., Molloy, D. E. (2003). Responsiveness to general education instruction as the first gate to learning disabilities identification. Learning Disabilities Research & Practice, 18, 147–156. Google Scholar | Crossref | |
|
Stoolmiller, M. (1994). Antisocial behavior, delinquent peer association, and unsupervised wandering for boys: Growth and change form childhood to early adolescence. Multivariate Behavior Research, 29, 263–288. Google Scholar | Crossref | Medline | ISI | |
|
Tindal, G., Fuchs, L., Fuchs, D., Shinn, M., Deno, S., Germann, G. (1985). Empirical validation of criterion-referenced tests. Educational Researcher, 78, 203–209. Google Scholar | |
|
Wang, C., Algozzine, B., Ma, W., Porfeli, E. (2011). Oral reading rates of second-grade students. Journal of Educational Psychology, 103, 442–454. doi: 10.1037/a0023029 Google Scholar | Crossref | ISI | |
|
Wayman, M. M., Wallace, T., Wiley, H. I., Tichá, R., Espin, C. A. (2007). Literature synthesis on curriculum-based measurement in reading. The Journal of Special Education, 41, 85–120. Google Scholar | SAGE Journals | ISI | |
|
Wood, D. E. (2006). Modeling the relationship between oral reading fluency and performance on a statewide reading test. Educational Assessment, 11, 85–104. Google Scholar | Crossref | |
|
Yeo, S., Fearrington, J., Christ, T. J. (2011). An investigation of gender, income, and special education status bias on curriculum- based measurement slope in reading. School Psychology Quarterly, 26, 119–130. doi: 10.1037/a0023021 Google Scholar | Crossref | ISI |

