Falls are a public health concern for older adults with or without cognitive impairment, including clinical Mild Cognitive Impairment (MCI) and Alzheimer’s Disease (AD) dementia. Executive function (EF) is linked to falls and is notably impaired in individuals with MCI and AD dementia. However, it is unclear which EF assessments are associated with falls in older adults with intact cognition, MCI, and AD dementia. Apolipoprotein E4 (ApoE4) increases the risk of MCI and AD dementia, with limited information suggesting decreased EF and gait impairment in ApoE4 carriers. The purpose of this study was to 1) investigate the relationships between EF assessments and falls (fall history and future fall) by cognitive status (intact cognition, MCI, AD dementia) and 2) determine if ApoE4 moderates the relationship between EF and falls across cognitive status. EF assessments included Digit Span (DS), Trail Making Test (ΔTMT), Stroop Interference Test, Controlled Oral Word Association assessments of phonemic and semantic fluency (COWAC), and Clock Drawing Test. Binary logistic regression was used with secondary data to analyze the EF and falls relationship. Results showed a significant association of the ΔTMT with fall history but may not be appropriate for use with people with AD dementia due to a floor effect. Significant interaction effects were shown between AD dementia and DS, ΔTMT, and EF as a latent variable, where individuals with a fall history had better EF performance. The interaction effects are influenced by the lower percentage of reported falls in people with severe AD dementia. In the second aim, a confounding effect exposed a potential four-way interaction where higher EF in ApoE4 non-carriers with AD dementia experienced a future fall without a fall history. Overall, more research is needed to determine which EF assessments are best suited for fall risk assessment and whether ApoE4 plays a role in the relationship between EF and falls. Since the low percentage of reported falls in people with severe AD dementia exposed a differing trend between EF and falls, more research is needed to develop valid and reliable tools for collecting fall data in individuals with severe AD dementia.

Collider effects pose a major problem in psychological research. Colliders are third variables that bias the relationship between an independent and dependent variable when (1) the composition of a research sample is restricted by the scores on a collider variable or (2) researchers adjust for a collider variable in their statistical analyses. Both cases interfere with the accuracy and generalizability of statistical results. Despite their importance, collider effects remain relatively unknown in the social sciences. This research introduces both the conceptual and the mathematical foundation for collider effects and demonstrates how to calculate a collider effect and test it for statistical significance. Simulation studies examined the efficiency and accuracy of the collider estimation methods and tested the viability of Thorndike’s Case III equation as a potential solution to correcting for collider bias in cases of biased sample selection.

This research explores tests for statistical suppression. Suppression is a statistical phenomenon whereby the magnitude of an effect becomes larger when another variable is added to the regression equation. From a causal perspective, suppression occurs when there is inconsistent mediation or negative confounding. Several different estimators for suppression are evaluated conceptually and in a statistical simulation study where we impose suppression and non-suppression conditions. For each estimator without an existing standard error formula, one was derived in order to conduct significance tests and build confidence intervals. Overall, two of the estimators were biased and had poor coverage, one worked well but had inflated type-I error rates when the population model was complete mediation. As a result of analyzing these three tests, a fourth was considered in the late stages of the project and showed promising results that address concerns of the other tests. When the tests were applied to real data, they gave similar results and were consistent.

Statistical inference from mediation analysis applies to populations, however, researchers and clinicians may be interested in making inference to individual clients or small, localized groups of people. Person-oriented approaches focus on the differences between people, or latent groups of people, to ask how individuals differ across variables, and can help researchers avoid ecological fallacies when making inferences about individuals. Traditional variable-oriented mediation assumes the population undergoes a homogenous reaction to the mediating process. However, mediation is also described as an intra-individual process where each person passes from a predictor, through a mediator, to an outcome (Collins, Graham, & Flaherty, 1998). Configural frequency mediation is a person-oriented analysis of contingency tables that has not been well-studied or implemented since its introduction in the literature (von Eye, Mair, & Mun, 2010; von Eye, Mun, & Mair, 2009). The purpose of this study is to describe CFM and investigate its statistical properties while comparing it to traditional and casual inference mediation methods. The results of this study show that joint significance mediation tests results in better Type I error rates but limit the person-oriented interpretations of CFM. Although the estimator for logistic regression and causal mediation are different, they both perform well in terms of Type I error and power, although the causal estimator had higher bias than expected, which is discussed in the limitations section.

Research and theory in social psychology and related fields indicates that people simultaneously hold many cultural identities. And it is well evidenced across relevant fields (e.g., sociology, marketing, economics) that salient identities are instrumental in a variety of cognitive and behavioral processes, including decision-making. It is not, however, well understood how the relative salience of various cultural identities factors into the process of making identity-relevant choices, particularly ones that require an actor to choose between conflicting sets of cultural values or beliefs. It is also unclear whether the source of that salience (e.g., chronic or situational) is meaningful in this regard. The current research makes novel predictions concerning the roles of cultural identity centrality and cultural identity situational salience in three distinct aspects of the decision-making process: Direction of decision, speed of decision, and emotion related to decision. In doing so, the research highlights two under-researched forms of culture (i.e., political and religious) and uses as the focal dependent variable a decision-making scenario that forces participants to choose between the values of their religious and political cultures and, to some degree, behave in an identity-inconsistent manner. Results indicate main effects of Christian identity centrality and democrat identity centrality on preference for traditional versus gender-neutral (i.e., non-traditional/progressive) restrooms after statistically controlling for covariates. Additionally, results show a significant main effect of democrat identity centrality and a significant interaction effect of Christian and democrat identity centrality on positive emotion linked to the decision. Post hoc analyses further reveal a significant quadratic relationship between Christian identity centrality and emotion related to the decision. There was no effect of situational strength of democrat identity salience on the decision. Neither centrality or situational strength had any effect on the speed with which participants made their decisions. This research theoretically and empirically advances the study of cultural psychology and carries important implications for identity research and judgment and decision-making across a variety of fields, including management, behavioral economics, and marketing.

Mediation analysis is used to investigate how an independent variable, X, is related to an outcome variable, Y, through a mediator variable, M (MacKinnon, 2008). If X represents a randomized intervention it is difficult to make a cause and effect inference regarding indirect effects without making no unmeasured confounding assumptions using the potential outcomes framework (Holland, 1988; MacKinnon, 2008; Robins & Greenland, 1992; VanderWeele, 2015), using longitudinal data to determine the temporal order of M and Y (MacKinnon, 2008), or both. The goals of this dissertation were to (1) define all indirect and direct effects in a three-wave longitudinal mediation model using the causal mediation formula (Pearl, 2012), (2) analytically compare traditional estimators (ANCOVA, difference score, and residualized change score) to the potential outcomes-defined indirect effects, and (3) use a Monte Carlo simulation to compare the performance of regression and potential outcomes-based methods for estimating longitudinal indirect effects and apply the methods to an empirical dataset. The results of the causal mediation formula revealed the potential outcomes definitions of indirect effects are equivalent to the product of coefficient estimators in a three-wave longitudinal mediation model with linear and additive relations. It was demonstrated with analytical comparisons that the ANCOVA, difference score, and residualized change score models’ estimates of two time-specific indirect effects differ as a function of the respective mediator-outcome relations at each time point. The traditional model that performed the best in terms of the evaluation criteria in the Monte Carlo study was the ANCOVA model and the potential outcomes model that performed the best in terms of the evaluation criteria was sequential G-estimation. Implications and future directions are discussed.

The goal of diagnostic assessment is to discriminate between groups. In many cases, a binary decision is made conditional on a cut score from a continuous scale. Psychometric methods can improve assessment by modeling a latent variable using item response theory (IRT), and IRT scores can subsequently be used to determine a cut score using receiver operating characteristic (ROC) curves. Psychometric methods provide reliable and interpretable scores, but the prediction of the diagnosis is not the primary product of the measurement process. In contrast, machine learning methods, such as regularization or binary recursive partitioning, can build a model from the assessment items to predict the probability of diagnosis. Machine learning predicts the diagnosis directly, but does not provide an inferential framework to explain why item responses are related to the diagnosis. It remains unclear whether psychometric and machine learning methods have comparable accuracy or if one method is preferable in some situations. In this study, Monte Carlo simulation methods were used to compare psychometric and machine learning methods on diagnostic classification accuracy. Results suggest that classification accuracy of psychometric models depends on the diagnostic-test correlation and prevalence of diagnosis. Also, machine learning methods that reduce prediction error have inflated specificity and very low sensitivity compared to the data-generating model, especially when prevalence is low. Finally, machine learning methods that use ROC curves to determine probability thresholds have comparable classification accuracy to the psychometric models as sample size, number of items, and number of item categories increase. Therefore, results suggest that machine learning models could provide a viable alternative for classification in diagnostic assessments. Strengths and limitations for each of the methods are discussed, and future directions are considered.

Understanding how adherence affects outcomes is crucial when developing and assigning interventions. However, interventions are often evaluated by conducting randomized experiments and estimating intent-to-treat effects, which ignore actual treatment received. Dose-response effects can supplement intent-to-treat effects when participants are offered the full dose but many only receive a partial dose due to nonadherence. Using these data, we can estimate the magnitude of the treatment effect at different levels of adherence, which serve as a proxy for different levels of treatment. In this dissertation, I conducted Monte Carlo simulations to evaluate when linear dose-response effects can be accurately and precisely estimated in randomized experiments comparing a no-treatment control condition to a treatment condition with partial adherence. Specifically, I evaluated the performance of confounder adjustment and instrumental variable methods when their assumptions were met (Study 1) and when their assumptions were violated (Study 2). In Study 1, the confounder adjustment and instrumental variable methods provided unbiased estimates of the dose-response effect across sample sizes (200, 500, 2,000) and adherence distributions (uniform, right skewed, left skewed). The adherence distribution affected power for the instrumental variable method. In Study 2, the confounder adjustment method provided unbiased or minimally biased estimates of the dose-response effect under no or weak (but not moderate or strong) unobserved confounding. The instrumental variable method provided extremely biased estimates of the dose-response effect under violations of the exclusion restriction (no direct effect of treatment assignment on the outcome), though less severe violations of the exclusion restriction should be investigated.

The comparison of between- versus within-person relations addresses a central issue in psychological research regarding whether group-level relations among variables generalize to individual group members. Between- and within-person effects may differ in magnitude as well as direction, and contextual multilevel models can accommodate this difference. Contextual multilevel models have been explicated mostly for cross-sectional data, but they can also be applied to longitudinal data where level-1 effects represent within-person relations and level-2 effects represent between-person relations. With longitudinal data, estimating the contextual effect allows direct evaluation of whether between-person and within-person effects differ. Furthermore, these models, unlike single-level models, permit individual differences by allowing within-person slopes to vary across individuals. This study examined the statistical performance of the contextual model with a random slope for longitudinal within-person fluctuation data.

A Monte Carlo simulation was used to generate data based on the contextual multilevel model, where sample size, effect size, and intraclass correlation (ICC) of the predictor variable were varied. The effects of simulation factors on parameter bias, parameter variability, and standard error accuracy were assessed. Parameter estimates were in general unbiased. Power to detect the slope variance and contextual effect was over 80% for most conditions, except some of the smaller sample size conditions. Type I error rates for the contextual effect were also high for some of the smaller sample size conditions. Conclusions and future directions are discussed.

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.