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Nowadays, Gaussian Process (GP) has been recognized as an indispensable statistical tool in computer experiments. Due to its computational complexity and storage demand, its application in real-world problems, especially in "big data" settings, is quite limited. Among many strategies to tailor GP to such settings, Gramacy and Apley (2015) proposed local approximate GP (laGP), which constructs approximate predictive equations by constructing small local designs around the predictive location under certain criterion. In this dissertation, several methodological extensions based upon laGP are proposed. One methodological contribution is the multilevel global/local modeling, which deploys global hyper-parameter estimates to perform local prediction. The second contribution comes from extending the laGP notion of "locale" to a set of predictive locations, along paths in the input space. These two contributions have been applied in the satellite drag emulation, which is illustrated in Chapter 3. Furthermore, the multilevel GP modeling strategy has also been applied to synthesize field data and computer model outputs of solar irradiance across the continental United States, combined with inverse-variance weighting, which is detailed in Chapter 4. Last but not least, in Chapter 5, laGP's performance has been tested on emulating daytime land surface temperatures estimated via satellites, in the settings of irregular grid locations. / Doctor of Philosophy / In many real-life settings, we want to understand a physical relationship/phenomenon. Due to limited resources and/or ethical reasons, it is impossible to perform physical experiments to collect data, and therefore, we have to rely upon computer experiments, whose evaluation usually requires expensive simulation, involving complex mathematical equations. To reduce computational efforts, we are looking for a relatively cheap alternative, which is called an emulator, to serve as a surrogate model. Gaussian process (GP) is such an emulator, and has been very popular due to fabulous out-of-sample predictive performance and appropriate uncertainty quantification. However, due to computational complexity, full GP modeling is not suitable for “big data” settings. Gramacy and Apley (2015) proposed local approximate GP (laGP), the core idea of which is to use a subset of the data for inference and further prediction at unobserved inputs. This dissertation provides several extensions of laGP, which are applied to several real-life “big data” settings. The first application, detailed in Chapter 3, is to emulate satellite drag from large simulation experiments. A smart way is figured out to capture global input information in a comprehensive way by using a small subset of the data, and local prediction is performed subsequently. This method is called “multilevel GP modeling”, which is also deployed to synthesize field measurements and computational outputs of solar irradiance across the continental United States, illustrated in Chapter 4, and to emulate daytime land surface temperatures estimated by satellites, discussed in Chapter 5.

The aging process is often coupled with major life changes such as retirement, death of friends and family members, and declines in physical and psychological functioning. Intuitively, any one or a conjunction of these events might be expected to lead to decreases in positive affect (PA) and increases in negative affect (NA). However, older adults tend to be emotionally positive and stable even late in life. Thus, it is possible that emotion-based strategies for coping with the challenges presented in later life can be used effectively by older adults, even amidst potential vulnerabilities in other domains. The design of effective interventions and technologies aimed at facilitating this coping process, will depend on understanding that emotions can influence health in different ways. Affect level and intraindividual variability (IIV) are independently related to distal factors such as personality and health-related outcomes such as immune functioning and mortality, among others. By nature, emotions are subject to daily fluctuations that cannot be captured by investigation of mean affect levels alone. Research on affect IIV has focused primarily on whether there are stability differences in younger and older adults. In general, older adults tend to be more stable, perhaps because the failure to regulate emotions is particularly detrimental for older adults’ physiological health. It is therefore important to understand how proximal factors in everyday life lead to intraindividual emotional changes. The primary goal of this study was to identify the factors occurring within older adults’ daily lives that predicted emotional deviations and to determine whether individuals differed in the types of factors that were emotionally-relevant. As such, it was imperative to employ a methodology that could differentiate the factors that evoked consistent emotional responses across all individuals from the factors whose impact on affect were person-dependent. Specifically, participants were given online surveys three times per day for 20 consecutive weekdays that included assessments of their current positive and negative emotional states and questions (at least once per day) about their stress, pain, sleep quality, life space, physical activity, and social activity. Multilevel modeling (MLM) was used to determine if there was significant affect IIV for these older adults and how much IIV could be explained by these proximal predictors. This analysis approach was used because it is well-suited for nested data (in this case, observations nested within-persons) and does not assume independence of observations (which is a concern when individuals receive repeated assessments). Additionally, MLM analyzes the complete dataset rather than complete cases (individuals), which allowed for comparison of fixed effects regression models and random effects regression models. Random effects models, which are the hallmark of MLM, enabled the analysis of potential individual differences in the within-person relationships between the predictors and affect. As expected, there was significant affect IIV in these older adults for both PA and NA. The predictors of PA and NA were analyzed first in isolation (referred to as “isolated models”) and then when controlling for the other proximal variables (referred to as “full models”). The random effects isolated models were generally better fitting than the fixed effects isolated models, indicating that the models that did not constrain individual predictor-affect slopes to be the same across persons (random) were more accurate representations of the observed data than models that constrained individuals’ slopes to be the same (fixed). Full fixed slopes and full random slopes models were built in stepwise fashion based on the results of the isolated models. Again, the random effects full models better fit the observed data than the fixed effects models for both PA and NA, providing strong evidence in favor of the hypothesis that a larger percentage of affect IIV would be explained when allowing individual differences in the within-person predictor-affect relationships. The full random models accounted for 32% of the PA IIV, and 45% of the NA IIV. These were both better fitting than their respective null models, indicating that overall, the proximal predictors accounted for significant proportions of the within-person PA and NA variance. Certain factors accounted for larger percentages of the IIV than others and in general, there were differences between the PA and NA model in terms of which factors led to emotional fluctuations. Subjective health accounted for the largest percentage of PA IIV and stress accounted for the largest percentage of NA IIV. Additionally, subjective health, life space, stress, and pain were significant unique predictors of PA, NA, or both. However, there were specific unique effects across both PA and NA, namely, the slope variances for stress and pain. Follow-up analyses were unable to account for these slope variances using person-level predictors. In essence, an individual’s emotional reactivity to pain and stress did not depend on his or her overall mean level of those factors, or of the other daily predictors. This provided further evidence that PA and NA should be treated as separable variables (e.g., it is possible for a daily event to decrease older adult’s positivity without necessarily increasing their negativity) but also highlighted factors that have pervasive influences on emotion regardless of valence, which is harmonious with models of affect that propose a dynamic relationship between PA and NA. The results from this study have theoretical and practical implications. Theories on emotional stability often focus on if and why older adults are more stable than younger adults. Findings of the present study both support and expand upon these theories by identifying within an older adult population, which proximal factors were likely to cause emotional deviations after partialling out the effects of other daily variables, including factors that were previously unstudied in this domain. The analysis methodology implemented in the present research allowed for direct investigation of whether certain individuals were more prone to the influences of these factors than others. These results are discussed in the context of coping and resiliency theories that posit individual differences in emotional responses to stimuli based on these capabilities. From a practical perspective, these results highlight that the design of interventions and technologies intended to provide older adults with effective skills and resources to maintain or improve their emotional well-being should be tailored to individuals’ affective profiles.

Sluggish cognitive tempo (SCT) is a construct that includes symptoms of slowness, mental confusion, excessive daydreaming, low motivation, and drowsiness/sleepiness. SCT is often co-morbid with attention-deficit/hyperactivity disorder (ADHD), and SCT symptoms are associated with significant academic and interpersonal impairment above and beyond the influence of ADHD symptoms. Despite the overlap between ADHD and SCT and associated impairments, no studies have evaluated how evidence-based psychosocial interventions for adolescents with ADHD impact symptoms of SCT. This study examined whether SCT symptoms improved in a sample of 274 young adolescents with ADHD who received either an organizational skills or a homework completion intervention. SCT intervention response was evaluated broadly in all participants, and specifically, for participants in the clinical range for SCT symptom severity at baseline. Change in ADHD symptoms of inattention, executive functioning, and motivation was examined as potential predictors of improvement in SCT. Multilevel modeling analyses indicated that SCT symptoms decreased at the same rate for adolescents in both the organizational skills and homework completion interventions when compared to the waitlist group (d = .410). For adolescents with parent-reported clinical levels of SCT, the decrease in symptoms was more pronounced (d = .517), with the interventions decreasing the total score of SCT by 2.91 (one symptom). Additionally, in the high SCT group, behavior regulation executive functioning, metacognitive executive functioning, and inattention predicted change. Clinical implications and future directions are discussed, including development of interventions for adolescents with high levels of SCT.

The Student Risk Screening Scale—Internalizing/Externalizing (SRSS-IE) was developed to screen elementary-aged students for Emotional and Behavioral Disorders (EBD). Its use has been extended to middle schools with little evidence that it measures the same constructs as in elementary schools. Scores of a middle school population from the SRSS-IE are analyzed with Multilevel Confirmatory Factor Analysis (MCFA) to examine its factor structure, factorial invariance between females and males, and its reliability. Several MCFA models are specified, and compared, with two retained for further analysis. The first model is a single-level model with chi-square and standard errors adjusted for the clustered nature of the data. The second model is a two-level model. Both support the hypothesized structure found in elementary populations of two factors (Externalizing and Internalizing). All items load on only one factor except Peer Rejection, which loads on both. Reliability is estimated for both models using several methods, which result in reliability coefficients ranging between .89-.98. Both models also show evidence of Configural, Metric, and Scalar invariance between females and males. While more research is needed to provide other kinds of evidence of validity in middle school populations, results from this study indicate that the SRSS-IE is an effective screening tool for EBD.

Conventional statistical methods assuming data sampled under simple random sampling are inadequate for use on complex survey data with a multilevel structure and non-independent observations. In structural equation modeling (SEM) framework, a researcher can either use the ad-hoc robust sandwich standard error estimators to correct the standard error estimates (Design-based approach) or perform multilevel analysis to model the multilevel data structure (Model-based approach) to analyze dependent data. In a cross-sectional setting, the first study aims to examine the differences between the design-based single-level confirmatory factor analysis (CFA) and the model-based multilevel CFA for model fit test statistics/fit indices, and estimates of the fixed and random effects with corresponding statistical inference when analyzing multilevel data. Several design factors were considered, including: cluster number, cluster size, intra-class correlation, and the structure equality of the between-/within-level models. The performance of a maximum modeling strategy with the saturated higher-level and true lower-level model was also examined. Simulation study showed that the design-based approach provided adequate results only under equal between/within structures. However, in the unequal between/within structure scenarios, the design-based approach produced biased fixed and random effect estimates. Maximum modeling generated consistent and unbiased within-level model parameter estimates across three different scenarios. Multilevel latent growth curve modeling (MLGCM) is a versatile tool to analyze the repeated measure sampled from a multi-stage sampling. However, researchers often adopt latent growth curve models (LGCM) without considering the multilevel structure. This second study examined the influences of different model specifications on the model fit test statistics/fit indices, between/within-level regression coefficient and random effect estimates and mean structures. Simulation suggested that design-based MLGCM incorporating the higher-level covariates produces consistent parameter estimates and statistical inferences comparable to those from the model-based MLGCM and maintain adequate statistical power even with small cluster number.

Numerous ways to meta-analyze single-case data have been proposed in the literature, however, consensus on the most appropriate method has not been reached. One method that has been proposed involves multilevel modeling. This study used Monte Carlo methods to examine the appropriateness of Van den Noortgate and Onghena's (2008) raw data multilevel modeling approach to the meta-analysis of single-case data. Specifically, the study examined the fixed effects (i.e., the overall average baseline level and the overall average treatment effect) and the variance components (e.g., the between person within study variance in the average baseline level, the between study variance in the overall average baseline level, the between person within study variance in the average treatment effect) in a three level multilevel model (repeated observations nested within individuals nested within studies). More specifically, bias of point estimates, confidence interval coverage rates, and interval widths were examined as a function of specific design and data factors. Factors investigated included (a) number of primary studies per meta-analysis, (b) modal number of participants per primary study, (c) modal series length per primary study, (d) level of autocorrelation, and (3) variances of the error terms. The results of this study suggest that the degree to which the findings of this study are supportive of using Van den Noortgate and Onghena's (2008) raw data multilevel modeling approach to meta-analyzing single-case data depends on the particular effect of interest. Estimates of the fixed effects tended to be unbiased and produced confidence intervals that tended to overcover but came close to the nominal level as level-3 sample size increased. Conversely, estimates of the variance components tended to be biased and the confidence intervals for those estimates were inaccurate.

The purpose was to investigate the relationship between Canadian and Saskatchewan PISA 2009 reading performance and organizational learning (OL) conditions as perceived by students and principals when selected student and school characteristics were taken into consideration. Gender, Aboriginal status, and socioeconomic status were the student characteristics that were considered. School size, urban versus rural school community, proportion of students self-identified as Aboriginal, and school average socioeconomic status were school characteristics taken into consideration. A nationally represented sample of 978 schools and 23,207 15-year-old students across the ten Canadian provinces participated in the PISA 2009. Within this sample, 1,997 students and 99 schools were from Saskatchewan. Principal components analyses were conducted to produce components for the calculation of two composite (OL) indices: a Student OL Index based on the Canada and OECD PISA student questionnaires and a School OL Index based on OECD PISA school questionnaire. Subsequently, two hierarchal linear modelling analyses were employed to examine the association of student-level OL index and school-level OL index with reading performance. Across Canadian and Saskatchewan schools, students’ perspective of OL conditions was positively associated with reading performance in the presence of the selected student and school characteristics. Except for one school-level OL component (i.e., principal’s perspective of school culture/environment) in the Canadian model, school-level OL conditions were not significantly associated to reading performance in the presence of student and school characteristics. With the adjustment of student and contextual characteristics incorporated in the modelling, the average reading performance was comparable across Canadian and Saskatchewan schools, 528 and 523 respectively. Variance decomposition of final models indicated that 55% of the Canadian school-level variance in reading achievement and 68% of the Saskatchewan school-level variance were explained by the selected student and school characteristics along with student perspective of OL conditions. The findings from this study supported the hypothesis that OL conditions are associated with student achievement. Additionally, it was noted that the effect of OL conditions was of similar magnitude to that of the socioeconomic status effect. Furthermore, the findings from this study further emphasized the importance of the student voice within the school OL framework.

Studies on relations between number of sessions and effect of psychotherapy have usually assumed a constant rate of change across different lengths of therapy, explained by a model called the dose-effect model. This assumption has been challenged by the good-enough level (GEL) model, which makes the prediction that the rate of change will vary as a function of total number of sessions. This study aimed to compare these models. We also assessed the relationship between reliable and clinically significant change (RCSI) and total dose of therapy. Participants were drawn from two datasets in the Swedish primary care (n = 640) and adult psychiatric care (n = 249). The participants made session-wise ratings on the Clinical Outcomes in Routine Evaluation-Outcome Measure (CORE-OM). Multilevel analyses indicated a better fit using the GEL-model, with some reservations concerning RCSI and patterns of change. The results may indicate a general lawful relationship that may have implications for future research, as well as psychotherapy practice and policy making.

Very low birth weight and extremely low birth weight neonates have tremendous risk of mortality. This is a grave concern; however, survival alone is not the goal of neonatal intensive care. Survival, along with a reduction or elimination of life long morbidity is the aim of neonatal intensive care. Human milk is known as the best nutrition for babies and a growing body of evidence supports that human milk is critical in helping these fragile neonates mitigate the overwhelming risks they face. Therefore, the purpose of this study was to examine the relationship between neonatal severity of illness and human milk, specifically mothers own milk (MOM), donor human milk (DHM), and total human milk (THM) intake in very low birth weight (VLBW) and extremely low birth weight (ELBW) infants over the first six weeks of life. Although there is a growing body of evidence that supports the use of human milk in this fragile neonatal population, information is lacking about the relationship between human milk and neonatal illness severity. The current study was a secondary data analysis from a National Institutes of Health (NIH) funded R21 study in a level three NICU in Florida. Multilevel modeling was used for data analysis to examine relationships between maternal dyad characteristics and severity of illness, operationalized by the Score for Neonatal Acute Physiology-II (SNAP-II), at 12 hours of life and at the end of each week of life for six weeks. Growth models (linear, quadratic, piecewise) were examined to determine the best model fit for the data, then predictor variables were added and model fit was tested. Birth weight was added to final models as a control as it is seen as a proxy for severity of illness in the literature. Model six demonstrated a significant inverse relationship between MOM(mL) (γMOM(mL)) = -.000079, p < .05) and SNAP-II scores (Deviance = 287.862, Δχ2(df) = 31.38(1), p < .001, AIC = 303.862, BIC = 336.930). Model 11 demonstrated a significant inverse relationship between THM(mL) (γTHM(mL) = -.000127, p < .001) and SNAP-II scores (Deviance = 279.280, Δχ2(df) = 30.859(1), p < .001, AIC = 295.280, BIC = 328.347). No relationships were noted between severity of illness and DHM(mL), MOM(%), DHM(%), or THM(%). Therefore the relationships noted between MOM(mL) and THM(mL) and neonatal severity of illness should be interpreted with caution.