Methods: Data (n = 206 youth: ages 5-17 years) from an evaluation of a Midwest TRC facility (Boel-Studt, 2017) were analyzed using quantile regression (QR). QR is an alternative to ordinary least squares (OLS) regression that estimates the relation between predictor(s) and the dependent variable at designated points (quantiles) along the conditional distribution of the dependent variable (Petscher, 2016). The dependent variables included LOS (weeks) and change in functioning pre and post-treatment scores from the Child and Adolescent Functional Assessment Scale (CAFAS; Hodges, 1997). Crisis intervention included combined incidents of restraint and seclusion. Specifically, we estimated the relations between CR interventions during treatment across 10 quantiles of LOS and CAFAS change scores. QR results were compared to OLS to evaluate differences in estimates and implications of the results given the choice of using a conditional means model (OLS) or a conditional tau model (QR).
Results: OLS regressions demonstrated that CR was a statistically significant predictor of LOS [F(1, 204)=19.13, p<.001, total R2=0.08] and change in functioning [F(1, 204)=14.32, p<.001, total R2=0.06]. However, QR demonstrated that CR was not a statistically significant predictor of LOS in treatment at the .05, .90, and .95 quantiles, with each quantile interpreted as a percentile of the dependent variable, such that for youth with a LOS in the 5th percentile, CR was not a significant predictor of LOS. Additionally, CR was not a statistically significant predictor for clients with minimal change in functioning (<.35 quantile) or extreme improvement in functioning (.95 quantile). Contrary to OLS, QR revealed there was no relation between CR and change in functioning for youth who fell within the 95th percentile or below the 35th percentile of functional improvement. Although CR influenced outcomes of some youth, the QR revealed cut-off points where CR did not influence LOS or functional outcomes of youth scoring at designated points (quantiles) along the dependent variable distributions.
Conclusions: The findings support that QR modeled important nuances in relations between treatment factors and outcomes that were masked using OLS methods. QR results provided critical information for treatment considerations, specifically, that CR interventions are an important treatment factor to consider for some youth in TRC. Identifying alternatives to traditional CR should be considered as this may reduce LOS; further supporting improved outcomes of youth in TRC.