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@PHDTHESIS{Kiefer:795766,
author = {Kiefer, Christoph},
othercontributors = {Mayer, Axel and Steyer, Rolf},
title = {{A}verage and conditional treatment effects on count
outcomes : a moment-based approach},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
reportid = {RWTH-2020-08541},
pages = {1 Online-Ressource (iii, 148 Seiten) : Illustrationen,
Diagramme},
year = {2020},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, Rheinisch-Westfälische Technische
Hochschule Aachen, 2020},
abstract = {In this thesis, we develop a statistical framework to
investigate average and conditional effects of a treatment
or intervention on a count outcome. For example, in the
field of drug and substance use prevention, the effects of
interventions on the outcome variable daily/weekly count of
alcoholic drinks or cigarettes consumed can been examined.
In clinical psychology, treatment effects on count outcomes
such as instances of binge eating among patients with eating
disorders or counts of classroom violations in children with
ADHD can been examined. Further examples are treatment
effects on counts of correctly answered items in a cognitive
test, days of absenteeism, or counts of traffic violations.
The framework is termed moment-based approach and is based
on regression models with a logarithmic link function. The
moment-based approach overcomes three major shortcomings of
earlier approaches estimating treatment effects on count
outcomes: First, effect definitions are based on the
stochastic theory of causal effects (Steyer, Mayer, Fiege,
2014). This theory provides unambiguous definitions of
atomic or individual causal effects as differences between
conditional expectations under treatment and under control
(i.e., a reference group). Further, causality conditions
under which estimated average and conditional treatment
effects may be interpreted as aggregates of atomic or
individual causal effects are explicated. In contrast, in
regression models with a logarithmic link function it is
common to inspect treatment effects defined as ratios of
conditional expectations under treatment and under control.
We caution that these ratio effects have a different causal
interpretation than difference effects. For example, the
simple ratio of group averages in a randomized experiment
does not represent an average of individual ratio effects --
unlike the simple difference of group averages, which is
also an average of individual difference effects. Second,
traditional approaches examining treatment effects on count
outcomes, treat the size of treatment groups and values of
observed covariates as fixed-by-design, that is,
predetermined by the experimenter. If in fact group sizes
and covariates are not predetermined -- as is the case in
most psychological and social science studies --, this
assumption can lead to underestimated standard errors and,
thus, inflated Type 1 error rates and decreased power for
average and conditional treatment effect estimates. The
moment-based approach offers an alternative by treating both
group sizes and covariates as random or stochastic
variables, which can substantially improve statistical
inferences. Third, the moment-based approach allows to
account for measurement error in covariates. While earlier
approaches were based on generalized linear models with a
logarithmic link function (e.g., Poisson regression models),
we use a structural equation modeling framework. In a
negative binomial multigroup structural equation model, it
is possible to simultaneously estimate measurement models
for latent variables (i.e., decomposing true scores and
measurement error in fallible indicators) and a negative
binomial regression model with these latent variables as
regressors. While ignoring measurement error in the
generalized linear models might lead to biased estimation of
both the regression coefficients and the corresponding
effect estimates, these issues are circumvented in the
moment-based approach. In this thesis, the moment-based
approach is developed and extended in a step-by-step manner.
First, we motivate the need for a new approach by presenting
and discussing the three aforementioned shortcomings of
earlier approaches (i.e., interpretation of exponentiated
regression coefficients and marginal effects) in detail.
Second, we introduce the key idea of the moment-based
approach in a simple case considering only a single, but
stochastic covariate using a generalized linear model. In a
Monte Carlo simulation study, we compare the performance of
a traditional (marginal effects) approach with the
performance of the moment-based approach. Third, we extend
the statistical framework to the negative binomial
multigroup structural equation model and include multiple,
possibly latent covariates as well as stochastic group sizes
in our effect computations. Fourth, we relax the assumption
of multivariate normally distributed covariates from
previous steps and derive a generalized moment-based
approach accounting for various kinds of normally and
non-normally distributed covariates. As a result, we achieve
a suitable approach for a broader range of applied data
analyses. Finally, we discuss guidelines how and when the
moment-based approach should be applied and have an outlook
on possible further developments.},
cin = {721630},
ddc = {150},
cid = {$I:(DE-82)721630_20161130$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2020-08541},
url = {https://publications.rwth-aachen.de/record/795766},
}
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