Matching Items (3)
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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
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Description
This dissertation examines a planned missing data design in the context of mediational analysis. The study considered a scenario in which the high cost of an expensive mediator limited sample size, but in which less expensive mediators could be gathered on a larger sample size. Simulated multivariate normal data were generated from a latent variable mediation model with three observed indicator variables, M1, M2, and M3. Planned missingness was implemented on M1 under the missing completely at random mechanism. Five analysis methods were employed: latent variable mediation model with all three mediators as indicators of a latent construct (Method 1), auxiliary variable model with M1 as the mediator and M2 and M3 as auxiliary variables (Method 2), auxiliary variable model with M1 as the mediator and M2 as a single auxiliary variable (Method 3), maximum likelihood estimation including all available data but incorporating only mediator M1 (Method 4), and listwise deletion (Method 5).
The main outcome of interest was empirical power to detect the mediated effect. The main effects of mediation effect size, sample size, and missing data rate performed as expected with power increasing for increasing mediation effect sizes, increasing sample sizes, and decreasing missing data rates. Consistent with expectations, power was the greatest for analysis methods that included all three mediators, and power decreased with analysis methods that included less information. Across all design cells relative to the complete data condition, Method 1 with 20% missingness on M1 produced only 2.06% loss in power for the mediated effect; with 50% missingness, 6.02% loss; and 80% missingess, only 11.86% loss. Method 2 exhibited 20.72% power loss at 80% missingness, even though the total amount of data utilized was the same as Method 1. Methods 3 – 5 exhibited greater power loss. Compared to an average power loss of 11.55% across all levels of missingness for Method 1, average power losses for Methods 3, 4, and 5 were 23.87%, 29.35%, and 32.40%, respectively. In conclusion, planned missingness in a multiple mediator design may permit higher quality characterization of the mediator construct at feasible cost.
The main outcome of interest was empirical power to detect the mediated effect. The main effects of mediation effect size, sample size, and missing data rate performed as expected with power increasing for increasing mediation effect sizes, increasing sample sizes, and decreasing missing data rates. Consistent with expectations, power was the greatest for analysis methods that included all three mediators, and power decreased with analysis methods that included less information. Across all design cells relative to the complete data condition, Method 1 with 20% missingness on M1 produced only 2.06% loss in power for the mediated effect; with 50% missingness, 6.02% loss; and 80% missingess, only 11.86% loss. Method 2 exhibited 20.72% power loss at 80% missingness, even though the total amount of data utilized was the same as Method 1. Methods 3 – 5 exhibited greater power loss. Compared to an average power loss of 11.55% across all levels of missingness for Method 1, average power losses for Methods 3, 4, and 5 were 23.87%, 29.35%, and 32.40%, respectively. In conclusion, planned missingness in a multiple mediator design may permit higher quality characterization of the mediator construct at feasible cost.
ContributorsBaraldi, Amanda N (Author) / Enders, Craig K. (Thesis advisor) / Mackinnon, David P (Thesis advisor) / Aiken, Leona S. (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2015
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Description
Time metric is an important consideration for all longitudinal models because it can influence the interpretation of estimates, parameter estimate accuracy, and model convergence in longitudinal models with latent variables. Currently, the literature on latent difference score (LDS) models does not discuss the importance of time metric. Furthermore, there is little research using simulations to investigate LDS models. This study examined the influence of time metric on model estimation, interpretation, parameter estimate accuracy, and convergence in LDS models using empirical simulations. Results indicated that for a time structure with a true time metric where participants had different starting points and unequally spaced intervals, LDS models fit with a restructured and less informative time metric resulted in biased parameter estimates. However, models examined using the true time metric were less likely to converge than models using the restructured time metric, likely due to missing data. Where participants had different starting points but equally spaced intervals, LDS models fit with a restructured time metric resulted in biased estimates of intercept means, but all other parameter estimates were unbiased, and models examined using the true time metric had less convergence than the restructured time metric as well due to missing data. The findings of this study support prior research on time metric in longitudinal models, and further research should examine these findings under alternative conditions. The importance of these findings for substantive researchers is discussed.
ContributorsO'Rourke, Holly P (Author) / Grimm, Kevin J. (Thesis advisor) / Mackinnon, David P (Thesis advisor) / Chassin, Laurie (Committee member) / Aiken, Leona S. (Committee member) / Arizona State University (Publisher)
Created2016