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Description
The present study examined the association of pain intensity and goal progress in a community sample of 132 adults with chronic pain who participated in a 21 day diary study. Multilevel modeling was employed to investigate the effect of morning pain intensity on evening goal progress as mediated by pain's interference with afternoon goal pursuit. Moderation effects of pain acceptance and pain catastrophizing on the associations between pain and interference with both work and lifestyle goal pursuit were also tested. The results showed that the relationship between morning pain and pain's interference with work goal pursuit in the afternoon was significantly moderated by a pain acceptance. In addition, it was found that the mediated effect differed across levels of pain acceptance; that is: (1) there was a significant mediation effect when pain acceptance was at its mean and one standard deviation below the mean; but (2) there was no mediation effect when pain acceptance was one standard deviation above the mean. It appears that high pain acceptance significantly attenuates the power of nociception in disrupting one's work goal pursuit. However, in the lifestyle goal model, none of the moderators were significant nor was there a significant association between pain interference with goal pursuit and goal progress. Only morning pain intensity significantly predicted afternoon interference with lifestyle goal pursuit. Further interpretation of the present findings and potential explanations of those inconsistencies are elaborated on discussion. Limitations and the clinical implication of the current study were considered, along with suggestions for future studies.
ContributorsMun, Chung Jung (Author) / Karoly, Paul (Thesis advisor) / Okun, Morris A. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2014
Description
Missing data are common in psychology research and can lead to bias and reduced power if not properly handled. Multiple imputation is a state-of-the-art missing data method recommended by methodologists. Multiple imputation methods can generally be divided into two broad categories: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution (e.g., multivariate normal). FCS, on the other hand, imputes variables one at a time, drawing missing values from a series of univariate distributions. In the single-level context, these two approaches have been shown to be equivalent with multivariate normal data. However, less is known about the similarities and differences of these two approaches with multilevel data, and the methodological literature provides no insight into the situations under which the approaches would produce identical results. This document examined five multilevel multiple imputation approaches (three JM methods and two FCS methods) that have been proposed in the literature. An analytic section shows that only two of the methods (one JM method and one FCS method) used imputation models equivalent to a two-level joint population model that contained random intercepts and different associations across levels. The other three methods employed imputation models that differed from the population model primarily in their ability to preserve distinct level-1 and level-2 covariances. I verified the analytic work with computer simulations, and the simulation results also showed that imputation models that failed to preserve level-specific covariances produced biased estimates. The studies also highlighted conditions that exacerbated the amount of bias produced (e.g., bias was greater for conditions with small cluster sizes). The analytic work and simulations lead to a number of practical recommendations for researchers.
ContributorsMistler, Stephen (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona (Committee member) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.
ContributorsBlackwell, Kimberly Carol (Author) / Millsap, Roger E (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2011
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
In the past, it has been assumed that measurement and predictive invariance are consistent so that if one form of invariance holds the other form should also hold. However, some studies have proven that both forms of invariance only hold under certain conditions such as factorial invariance and invariance in the common factor variances. The present research examined Type I errors and the statistical power of a method that detects violations to the factorial invariant model in the presence of group differences in regression intercepts, under different sample sizes and different number of predictors (one or two). Data were simulated under two models: in model A only differences in the factor means were allowed, while model B violated invariance. A factorial invariant model was fitted to the data. Type I errors were defined as the proportion of samples in which the hypothesis of invariance was incorrectly rejected, and statistical power was defined as the proportion of samples in which the hypothesis of factorial invariance was correctly rejected. In the case of one predictor, the results show that the chi-square statistic has low power to detect violations to the model. Unexpected and systematic results were obtained regarding the negative unique variance in the predictor. It is proposed that negative unique variance in the predictor can be used as indication of measurement bias instead of the chi-square fit statistic with sample sizes of 500 or more. The results of the two predictor case show larger power. In both cases Type I errors were as expected. The implications of the results and some suggestions for increasing the power of the method are provided.
ContributorsAguilar, Margarita Olivera (Author) / Millsap, Roger E. (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2010
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