A case study on cumulative logit models with low frequency and mixed effects

Master of ScienceDepartment of StatisticsPerla E. Reyes CuellarData with ordinal responses may be encountered in many research fields, such as social, medical, agriculture or financial sciences. In this paper, we present a case study on cumulative logit models with low frequency and mixed effects and discuss some strengths and limitations of the current methodology. Two plant pathologists requested our statistical advice to fit a cumulative logit mixed model seeking for the effect of six commercial products on the control of a seed and seedling disease in soybeans in vitro. In their attempt to estimate the model parameters using a generalized linear mixed model approach with PROC GLIMMIX, the model failed to converge. Three alternative approaches to solve the problem were examined: 1) stratifying the data searching for the random effect; 2) assuming the random effect would be small and reducing the model to a fixed model; and 3) combining the original categories of the response variable to a lower number of categories. In addition, we conducted a power analysis to evaluate the required sample size to detect treatment differences. The results of all the proposed solutions were similar. Collapsing categories for a cumulative/proportional odds model has little effect on estimation. The sample size used in the case study is enough to detect a large shift of frequencies between categories, but not for moderated changes. Moreover, we do not have enough information to estimate a random effect. Even when it is present, the results regarding the fixed factors: pathogen, evaluation day, and treatment effects are the same as the obtained by the fixed model alternatives. All six products had a significant effect in slowing the effect of the pathogen, but the effects vary between pathogen species and assessment timing or date

Causal inference under the K-nearest neighbors interference model

Doctor of PhilosophyDepartment of StatisticsMichael J HigginsIn causal inference, an experiment exhibits treatment interference when the treatment status of one unit affects the response of other units. While traditional causal inference methods often assume no interference between units, there has been a recent abundance of work on the design and analysis of experiments under treatment interference--- for example, those conducted on social networks. Failure to account for interference may lead to biased estimates of treatment effects and wrong conclusions. In this dissertation, we propose the K-nearest neighbors interference model (KNNIM)---a model of treatment interference where the response of a unit depends only on its treatment status and the statuses of units within its K-neighborhood. Current methods for detecting interference include carefully designed randomized experiments and conditional randomization tests on a set of focal units. We give guidance on how to choose focal units under KNNIM. We then conduct a simulation study to evaluate the efficacy of existing methods for detecting arbitrary network interference under KNNIM with this choice of focal units. We show that this choice of focal units leads to powerful tests of treatment interference which outperform experimental methods. Then, we extend the potential outcomes approach and the K-neighborhood interference framework to define causal estimands for direct and K-nearest neighbors indirect effects where interference is allowed within K-neighborhoods of individuals. Under completely randomized and Bernoulli-randomized designs, we provide a closed-form solution to compute the marginal and joint probabilities of units being exposed to treatment exposures of interest. We then propose Horvitz-Thompson unbiased estimators for the defined estimands under K-neighborhood interference assumption. We derive properties of the proposed estimators and provide conservative variance estimators. We then demonstrate how an assumption of no interaction between direct and indirect effects can improve estimates. To demonstrate the proposed causal methods, we perform a simulation study and apply our proposed methods on an anti-conflict study from a randomized experiment among middle school students in New Jersey. Finally, we develop additional estimators of the defined estimands under an assumption of no interaction between the indirect effects. This may enhance the estimation of standard errors by increasing the number of units under this assumption. Properties of the developed estimators are derived as well as conservative variance estimators of the defined estimands

Estimation of Causal Effects Under K-Nearest Neighbors Interference

Considerable recent work has focused on methods for analyzing experiments which exhibit treatment interference -- that is, when the treatment status of one unit may affect the response of another unit. Such settings are common in experiments on social networks. We consider a model of treatment interference -- the K-nearest neighbors interference model (KNNIM) -- for which the response of one unit depends not only on the treatment status given to that unit, but also the treatment status of its $K$ ``closest'' neighbors. We derive causal estimands under KNNIM in a way that allows us to identify how each of the $K$-nearest neighbors contributes to the indirect effect of treatment. We propose unbiased estimators for these estimands and derive conservative variance estimates for these unbiased estimators. We then consider extensions of these estimators under an assumption of no weak interaction between direct and indirect effects. We perform a simulation study to determine the efficacy of these estimators under different treatment interference scenarios. We apply our methodology to an experiment designed to assess the impact of a conflict-reducing program in middle schools in New Jersey, and we give evidence that the effect of treatment propagates primarily through a unit's closest connection

Detecting Treatment Interference under the K-Nearest-Neighbors Interference Model

We propose a model of treatment interference where the response of a unit depends only on its treatment status and the statuses of units within its K-neighborhood. Current methods for detecting interference include carefully designed randomized experiments and conditional randomization tests on a set of focal units. We give guidance on how to choose focal units under this model of interference. We then conduct a simulation study to evaluate the efficacy of existing methods for detecting network interference. We show that this choice of focal units leads to powerful tests of treatment interference which outperform current experimental methods