@misc{WilbertBoernertRinglebLueke2022,
  author    = {Wilbert, J{\"u}rgen and B{\"o}rnert-Ringleb, Moritz and L{\"u}ke, Timo},
  title     = {Statistical Power of Piecewise Regression Analyses of Single-Case Experimental Studies Addressing Behavior Problems},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  number    = {814},
  issn      = {1866-8364},
  doi       = {10.25932/publishup-58115},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-581150},
  pages     = {13},
  year      = {2022},
  abstract  = {In intervention research, single-case experimental designs are an important way to gain insights into the causes of individual changes that yield high internal validity. They are commonly applied to examine the effectiveness of classroom-based interventions to reduce problem behavior in schools. At the same time, there is no consensus on good design characteristics of single-case experimental designs when dealing with behavioral problems in schools. Moreover, specific challenges arise concerning appropriate approaches to analyzing behavioral data. Our study addresses the interplay between the test power of piecewise regression analysis and important design specifications of single-case research designs. Here, we focus on the influence of the following specifications of single-case research designs: number of measurement times, the initial frequency of the behavior, intervention effect, and data trend. We conducted a Monte-Carlo study. First, simulated datasets were created with specific design conditions based on reviews of published single-case intervention studies. Following, data were analyzed using piecewise Poisson-regression models, and the influence of specific design specifications on the test power was investigated. Our results indicate that piecewise regressions have a high potential of adequately identifying the effects of interventions for single-case studies. At the same time, test power is strongly related to the specific design specifications of the single-case study: Few measurement times, especially in phase A, and low initial frequencies of the behavior make it impossible to detect even large intervention effects. Research designs with a high number of measurement times show robust power. The insights gained are highly relevant for researchers in the field, as decisions during the early stage of conceptualizing and planning single-case experimental design studies may impact the chance to identify an existing intervention effect during the research process correctly.},
  language  = {en}
}
@article{WilbertBoernertRinglebLueke2022,
  author    = {Wilbert, J{\"u}rgen and B{\"o}rnert-Ringleb, Moritz and L{\"u}ke, Timo},
  title     = {Statistical Power of Piecewise Regression Analyses of Single-Case Experimental Studies Addressing Behavior Problems},
  series = {Frontiers in Education},
  volume    = {7},
  journal   = {Frontiers in Education},
  publisher = {Frontiers Media},
  address   = {Lausanne, Schweiz},
  issn      = {2504-284X},
  doi       = {10.3389/feduc.2022.917944},
  pages     = {1 -- 13},
  year      = {2022},
  abstract  = {In intervention research, single-case experimental designs are an important way to gain insights into the causes of individual changes that yield high internal validity. They are commonly applied to examine the effectiveness of classroom-based interventions to reduce problem behavior in schools. At the same time, there is no consensus on good design characteristics of single-case experimental designs when dealing with behavioral problems in schools. Moreover, specific challenges arise concerning appropriate approaches to analyzing behavioral data. Our study addresses the interplay between the test power of piecewise regression analysis and important design specifications of single-case research designs. Here, we focus on the influence of the following specifications of single-case research designs: number of measurement times, the initial frequency of the behavior, intervention effect, and data trend. We conducted a Monte-Carlo study. First, simulated datasets were created with specific design conditions based on reviews of published single-case intervention studies. Following, data were analyzed using piecewise Poisson-regression models, and the influence of specific design specifications on the test power was investigated. Our results indicate that piecewise regressions have a high potential of adequately identifying the effects of interventions for single-case studies. At the same time, test power is strongly related to the specific design specifications of the single-case study: Few measurement times, especially in phase A, and low initial frequencies of the behavior make it impossible to detect even large intervention effects. Research designs with a high number of measurement times show robust power. The insights gained are highly relevant for researchers in the field, as decisions during the early stage of conceptualizing and planning single-case experimental design studies may impact the chance to identify an existing intervention effect during the research process correctly.},
  language  = {en}
}
@techreport{Tuebbicke2020,
  type      = {Working Paper},
  author    = {T{\"u}bbicke, Stefan},
  title     = {Entropy Balancing for Continuous Treatments},
  series = {CEPA Discussion Papers},
  journal   = {CEPA Discussion Papers},
  number    = {21},
  issn      = {2628-653X},
  doi       = {10.25932/publishup-47895},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-478950},
  pages     = {32},
  year      = {2020},
  abstract  = {Interest in evaluating the effects of continuous treatments has been on the rise recently. To facilitate the estimation of causal effects in this setting, the present paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainm{\"u}ller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem, allowing for much more computationally efficient implementation compared to other available methods. EBCT weights reliably eradicate Pearson correlations between covariates and the continuous treatment variable. This is the case even when other methods based on the generalized propensity score tend to yield insufficient balance due to strong selection into different treatment intensities. Moreover, the optimization procedure is more successful in avoiding extreme weights attached to a single unit. Extensive Monte-Carlo simulations show that treatment effect estimates using EBCT display similar or lower bias and uniformly lower root mean squared error. These properties make EBCT an attractive method for the evaluation of continuous treatments. Software implementation is available for Stata and R.},
  language  = {en}
}