Background: Data on children's ability to answer assessment questions correctly paints an incomplete portrait of what they know and can do mathematically; yet, it remains a common basis for program evaluation. Indeed, pre-post-assessment correctness is necessary but insufficient evidence for making inferences about learning and program effectiveness; assessment should also evaluate the strategies developed to solve problems. There is evidence to suggest that using Learning Trajectories (LTs; Clements & Sarama, 2021) as the basis for instruction increases "correctness" in kindergarten populations. However, the impact of LTs on "strategy sophistication" has not been examined. We describe a statistical technique that models strategy sophistication and apply it to investigate the efficacy of LTs in early length-measurement (LM). Objective: The present study analyzes the "strategies" deployed by children in research project (Sarama et al., 2021) to answer two question: RQ1: Do children in the LT condition use more sophisticated strategies relative to their peers in two counterfactual conditions? RQ2: How do we model strategy sophistication in the presence of informative missing data? Setting: This study leverages data shared with us from "Evaluating the Efficacy of the Learning Trajectories in Early Mathematics," funded by the Institute of Education Sciences. This randomized control trial took place in an urban school district in a Mountain West state. Population: The sample was composed of 186 kindergarten students (104 girls) from 16 classrooms across six schools (four public; n = 149). Table 2 presents demographic information for the public schools. Intervention: The intervention was composed of three experimental conditions: the LT group, the reverse-order (REV) group, and control group (BAU). Only the LT and REV group received ten one-on-one instructional sessions. In the LT condition each instructor had access to a set of instructional activities that aligned with each level of the developmental progression and selected activities based on the child's present level of thinking. As children demonstrated higher levels of thinking, they were encouraged to use more sophisticated strategies (e.g., Level 3, iterating with a single unit instead of Level 2, using multiple units; Table 1). The REV group received 10 length activities selected from each level of the developmental progression in reverse order (Table 1 and LearningTrajetories.org). Thus, students were exposed to similar activities as the LT condition, but began with the most sophisticated level: Level 5. REV instructors provided feedback about the correctness of children's solutions, but did not modify activities to accommodate less sophisticated levels of thinking. Research Design: All students for whom we acquired parental consent were administered a preassessment prior to random assignment. The pre- and post-assessment was composed of 26 items adapted from extant instruments (Battista, 2012; Clements et al., 2008/2021) and scored for correctness and strategy sophistication. We tested two child-level covariates: child sex (0 = girl) and school type (public/private; 0 = public) are coded as binary. Data Collection and Analysis: A team of coders watched pre- and post-assessment videos and assigned their behavior into one of up to 10 research-based strategy sophistication codes (Clements et al., 2008/2021) These codes were collapsed into a 4-level ordinal outcome variable (where 0 = "Unlikely to Solve", 1 = "Low", 2 = "Medium", and 3 = "High"). Behaviors identified as "Other", "Strategy not observed", or "NA" could not be assigned into the 4-level ordinal outcome. We deem these behaviors "nondetectable" and/or "non-codable" and were assigned into the hurdle component of the statistical model (Fig. 1). Hurdle Model: In a naïve modeling approach, "non-detectable" and "non-codable" strategies would be treated as missing data and removed prior to analysis. However, this would lead to undesirable outcomes: 1) reduced sample size and diminished power; 2) biased cause-and-effect inferences due to informative missingness; and 3) exclusion of items due to missing data. Our hurdle ordinal logit model allows us to account for informative missingness and model the two data-generating processes separately: 1) detection probability (); and 2) ordinal sophistication once a strategy has been detected (). Intuitively, our model is the usual cumulative logit (McCullagh, 1980) weighted by the probability of detecting a strategy. We assign the same set of covariates using the logit link to both parts of the model: pre-sophistication Rasch score, experimental condition, child sex, and school type, in addition to random intercepts by child (), item (), and classroom () (see Fig. 2). Estimation took place in a Bayesian paradigm using No-U-Turn Hamiltonian Monte Carlo (NUTS HMC, Hoffman & Gelman, 2014) implemented in Stan (Stan Development Team, 2020). Diagnostics revealed robust convergence with no model misspecification and Effective Sample Sizes of at least 1000 on all parameters. Results: Model 6 had the smallest Bayesian information criteria (WAIC and LOOIC) among the 8 models tested (Table 3) and was selected as the preferred model. Pre-sophistication and experimental condition had a statistically significant effect on the odds of strategy detection (Table 4). LT and REV students had 2.2 (1.6, 3.0) and 1.5 (1.1, 2.1) times greater odds of exhibiting a detectable strategy, respectively, relative to the BAU peers. Comparing the two one-to-one instructional approaches, students in the LT condition were more likely to use a detectable strategy relative to those in the REV condition (posterior probability = 99.3%). Given a strategy was detected, LT students had 2.4 (1.6, 4.1) times greater odds of using a more sophisticated strategy relative to BAU students (Table 5) and were also more likely to use a more sophisticated strategy relative to REV students (posterior probability = 97.9%). Private school students had 1.7 (1.2, 2.7) times greater odds of using a more sophisticated strategy once a strategy was detected, compared to public school students. Conclusions: Novel methods in the present study enable us to construct multidimensional arguments about the efficacy of early interventions. Results indicated a greater probability that kindergarten students in the LT condition used detectable, mathematically relevant problem-solving strategies relative to their peers in counterfactual conditions. Additionally, there was a 98% probability that LT students used more sophisticated strategies. This underscores the benefits of teaching early length-measurement following a learning trajectory.