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A Model for Time-Varying Cumulative Classroom / Teacher Effects on Students ’ Growth

Multilevel growth curve analysis has been commonly used tomodel students’ learning trajectories while at the same time addressing the dependency in educational data. The data structure becomes more complicated with student mobility as most of the students move to a different classroom with a different teacher every year. To account for classroom/teacher effects, Raudenbush (1993) proposed a cross-classified random effects model (CCREM) where repeated measures were cross-classified by students and teachers, and teacher effects across time were treated as exchangeable. Whereas that accute-effects CCREM (Figure 1a) assumes that previous classroom membership does not affect outcome at a later time, Raudenbush and Bryk (2002) also discussed a cumulative effects CCREM (Figure 1b) that assume constant teacher effects for all subsequent measurements. However, as raised in Cafri, Hedeker, and Aarons (2015) and McCaffrey, Lockwood, Koretz, and Hamilton (2004), such an assumption of constant teacher effects is questionable, as it is generally expected that teacher effects are weaker for a later time. A model that correctly captures the cumulative teacher effects is of interest for three reasons. First, the cumulative effect estimates themselves should be of substantive interest as they quantify the influences of teaching at a particular grade level across time. Second, as incorrect modeling of the variance-covariance structure was shown to bias random component and fixed effect standard error estimates in multilevel modeling in general (Berkhof & Kampen, 2004) and in CCREM specifically (Cafri et al., 2015; Luo & Kwok, 2009; Meyers & Beretvas, 2006), growth parameters and parameters of interest may be biased with the cumulative teacher effects assumed either zero or constant across time. Third, as cumulative