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- All Subjects: Psychology--Statistical methods.
- Creators: Enders, Craig K.
Description
Including a covariate can increase power to detect an effect between two variables. Although previous research has studied power in mediation models, the extent to which the inclusion of a mediator will increase the power to detect a relation between two variables has not been investigated. The first study identified situations where empirical and analytical power of two tests of significance for a single mediator model was greater than power of a bivariate significance test. Results from the first study indicated that including a mediator increased statistical power in small samples with large effects and in large samples with small effects. Next, a study was conducted to assess when power was greater for a significance test for a two mediator model as compared with power of a bivariate significance test. Results indicated that including two mediators increased power in small samples when both specific mediated effects were large and in large samples when both specific mediated effects were small. Implications of the results and directions for future research are then discussed.
ContributorsO'Rourke, Holly Patricia (Author) / Mackinnon, David P (Thesis advisor) / Enders, Craig K. (Committee member) / Millsap, Roger (Committee member) / Arizona State University (Publisher)
Created2013
Description
Random Forests is a statistical learning method which has been proposed for propensity score estimation models that involve complex interactions, nonlinear relationships, or both of the covariates. In this dissertation I conducted a simulation study to examine the effects of three Random Forests model specifications in propensity score analysis. The results suggested that, depending on the nature of data, optimal specification of (1) decision rules to select the covariate and its split value in a Classification Tree, (2) the number of covariates randomly sampled for selection, and (3) methods of estimating Random Forests propensity scores could potentially produce an unbiased average treatment effect estimate after propensity scores weighting by the odds adjustment. Compared to the logistic regression estimation model using the true propensity score model, Random Forests had an additional advantage in producing unbiased estimated standard error and correct statistical inference of the average treatment effect. The relationship between the balance on the covariates' means and the bias of average treatment effect estimate was examined both within and between conditions of the simulation. Within conditions, across repeated samples there was no noticeable correlation between the covariates' mean differences and the magnitude of bias of average treatment effect estimate for the covariates that were imbalanced before adjustment. Between conditions, small mean differences of covariates after propensity score adjustment were not sensitive enough to identify the optimal Random Forests model specification for propensity score analysis.
ContributorsCham, Hei Ning (Author) / Tein, Jenn-Yun (Thesis advisor) / Enders, Stephen G (Thesis advisor) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2013
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
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
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
For this thesis a Monte Carlo simulation was conducted to investigate the robustness of three latent interaction modeling approaches (constrained product indicator, generalized appended product indicator (GAPI), and latent moderated structural equations (LMS)) under high degrees of nonnormality of the exogenous indicators, which have not been investigated in previous literature. Results showed that the constrained product indicator and LMS approaches yielded biased estimates of the interaction effect when the exogenous indicators were highly nonnormal. When the violation of nonnormality was not severe (symmetric with excess kurtosis < 1), the LMS approach with ML estimation yielded the most precise latent interaction effect estimates. The LMS approach with ML estimation also had the highest statistical power among the three approaches, given that the actual Type-I error rates of the Wald and likelihood ratio test of interaction effect were acceptable. In highly nonnormal conditions, only the GAPI approach with ML estimation yielded unbiased latent interaction effect estimates, with an acceptable actual Type-I error rate of both the Wald test and likelihood ratio test of interaction effect. No support for the use of the Satorra-Bentler or Yuan-Bentler ML corrections was found across all three methods.
ContributorsCham, Hei Ning (Author) / West, Stephen G. (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2010