who was most likely to receive special education services both during Kindergarten and through
8th grade (Table III.3). Analyses included a large number of individual and school predictors
known to be associated with special education placement or disability identification. The
contributions of each level were assessed through four successive models, with individual
predictors hypothesized to be more impactful than school predictors. In Model 4, the contextual
effect of schooling interacted with individual characteristics was tested as an extension to the
frog pond effect. It was expected that individual academic performance, behavior, and
race/ethnicity would be differentially influenced by schooling compositions.
Model 1: Individual-level predictors only. The first model utilized only individual- level predictors (modeled at level 2) to assess the probability of receiving services during the
first year of school and over time. The intercept corresponds to spring of Kindergarten, the first
time point at which special education status was recorded. Results indicate that male
Kindergartners were 4 times more likely to have an IEP in Kindergarten than females;
Kindergartners whose parents reported a disability were 5 times more likely to have an IEP; and
Kindergartners who performed better academically were slightly less likely (2%) to have an IEP
(OR = .98). Next, the intercept for time was modeled at level 1, and indicates that students were
9.67 times more likely to be placed with each passing grade. Students whose mothers were more
educated were more likely to have an IEP over time (OR = 1.09), and students with better
academic achievement were 1% less likely to have an IEP over time (OR = .99). Model fit
information indicates that 34% of the variance in IEP status occurred between schools and 77%
occurred between individuals within each school.
Model 2: School-level predictors only. Next, the influence of school-level predictors (modeled at level 3) was included in analyses without modeling individual-level predictors. This
step was important to model given that much previous research investigating special education
service receipt used only school-level variables, as well as to evaluate how including both
individual and school predictors in Model 3 would change estimates obtained from only school
predictors in Model 2. Students who attended a school with more students with disabilities per
classroom were 23% more likely to have an IEP in Kindergarten. At the slope, the overall effect
of time did not attain statistical significance in this model and most predictors did not influence
change in likelihood of experiencing special education over time. However, attending a larger
school decreased the odds of having an IEP over time by 12%. Model fit information indicates
that with only school-level predictors included, this model fit the data significantly worse than
when only individual-level predictors were modeled (∆AIC=2,139 and ∆BIC=2,075). 36% of the
variability in IEP status occurred between schools, while 85% of the variability in IEP status was
due to between-person differences within schools.
Model 3: Individual and school predictors. In the third model, both individual and school predictors were analyzed together (though no interactions were included). Results were
similar to those obtained from Model 1 and Model 2 in that males, students with a disability, and
lower-achieving students were most likely to have an IEP in Kindergarten. In addition, this
model revealed evidence for a frog pond effect in urban schools and in schools with more
students with disabilities, as students attending non-urban schools and schools with a higher
number of students with disabilities in each classroom were again more likely to have an IEP in
Kindergarten.
The factors predicting change in likelihood of having an IEP over time were also similar
to Model 1, but the inclusion of both individual- and school-level variables revealed that students
likely to receive an IEP over time (OR = .85). Though students attending a larger school were
less likely to have an IEP over time in Model 2, including individual-level predictors rendered all
school-level predictors non-significant at the slope. Model fit information indicated that this
model fit the data better than either Model 1 (∆AIC = -423 and ∆BIC = -223) or Model 2 (∆AIC
= -2,563 and ∆BIC = -2,298). Though the variance coefficients were largely similar to Model 1,
this model explained 34% of the variance in the school-level intercept and 35% of the variance in
the individual-level intercept over Model 2. The ICC's were most similar to Model 1, with 33%
and 78% of the variability in IEP status occurring between and within schools, respectively.
Model 4: Full model with cross-level interactions. In the fourth and final model, an extension to frog pond effect was assessed by interacting individual-level achievement,
race/ethnicity, and behavior with their corresponding school-level counterparts. To improve
model parsimony and reduce degrees of freedom, several non-significant terms in Model 3 were
dropped in Model 4 (e.g., the Level 1 by Level 3 interactions, or change in school-level variables
over time). Further analyses not reported here indicated that the exclusion of these terms did not
influence the estimates of other variables.
Including cross-level interaction terms did not change the significant individual-level
estimates reported at either the intercept or slope in Model 3. However, at the school level,
attending an urban school ceased to be a statistically significant predictor of special education
status, while attending a school with a higher proportion of students performing above academic
proficiency on statewide testing did attain statistical significance at the p < .05 level (OR = .98).
Attending schools with a higher classroom numbers of students with disabilities continued to be
a strong predictor of individual special education status (OR = 1.30). However, there was no
that be student race/ethnicities interacting with schoolwide proportions of non-White students or
students receiving free lunch; individual academic performance interacting with schoolwide
proportions of proficient students; or individual behaviors interacting with schoolwide
aggregates of student behaviors. Moreover, this model appeared to fit similarly to Model 3
(though, slightly worse: ∆AIC = -64 and ∆BIC = -40), again indicating little evidence for differential individual likelihoods of placement as a function of schoolwide characteristics.
Analysis 2: Among Special Education Students, What Predicts Earlier or Later Service