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- All Subjects: Multilevel Modeling
- Genre: Masters Thesis
- Creators: Enders, Craig K.
Description
Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain.
ContributorsMazza, Gina L (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Currently, there is a clear gap in the missing data literature for three-level models.
To date, the literature has only focused on the theoretical and algorithmic work
required to implement three-level imputation using the joint model (JM) method of
imputation, leaving relatively no work done on fully conditional specication (FCS)
method. Moreover, the literature lacks any methodological evaluation of three-level
imputation. Thus, this thesis serves two purposes: (1) to develop an algorithm in
order to implement FCS in the context of a three-level model and (2) to evaluate
both imputation methods. The simulation investigated a random intercept model
under both 20% and 40% missing data rates. The ndings of this thesis suggest
that the estimates for both JM and FCS were largely unbiased, gave good coverage,
and produced similar results. The sole exception for both methods was the slope for
the level-3 variable, which was modestly biased. The bias exhibited by the methods
could be due to the small number of clusters used. This nding suggests that future
research ought to investigate and establish clear recommendations for the number of
clusters required by these imputation methods. To conclude, this thesis serves as a
preliminary start in tackling a much larger issue and gap in the current missing data
literature.
To date, the literature has only focused on the theoretical and algorithmic work
required to implement three-level imputation using the joint model (JM) method of
imputation, leaving relatively no work done on fully conditional specication (FCS)
method. Moreover, the literature lacks any methodological evaluation of three-level
imputation. Thus, this thesis serves two purposes: (1) to develop an algorithm in
order to implement FCS in the context of a three-level model and (2) to evaluate
both imputation methods. The simulation investigated a random intercept model
under both 20% and 40% missing data rates. The ndings of this thesis suggest
that the estimates for both JM and FCS were largely unbiased, gave good coverage,
and produced similar results. The sole exception for both methods was the slope for
the level-3 variable, which was modestly biased. The bias exhibited by the methods
could be due to the small number of clusters used. This nding suggests that future
research ought to investigate and establish clear recommendations for the number of
clusters required by these imputation methods. To conclude, this thesis serves as a
preliminary start in tackling a much larger issue and gap in the current missing data
literature.
ContributorsKeller, Brian Tinnell (Author) / Enders, Craig K. (Thesis advisor) / Grimm, Kevin J. (Committee member) / Levy, Roy (Committee member) / Arizona State University (Publisher)
Created2015