Multilevel modeling is a common approach to modeling longitudinal change in behavioral sciences. While many researchers use linear functional forms to model change across time, researchers sometimes anticipate nonlinear change. In such cases, researchers often fit polynomial functional forms, such as quadratic or cubic forms. Polynomial functional forms are suitable in many situations, but there are other functional forms that could potentially better match the researcher’s theory about the nature of the longitudinal change. “Truly” nonlinear models, such as exponential and logistic models, have been used to model biological phenomena and may also be useful for psychological research. Such models, however, are non-nested, meaning that likelihood ratio tests cannot be used to select among models if one or more truly nonlinear models are in the candidate model set. Information criteria offer a flexible framework for model selection that can accommodate truly nonlinear models, but there currently is no research directly exploring the ability of information criteria to select truly nonlinear multilevel models. In this dissertation, two Monte Carlo simulation studies were conducted to examine the performance of two frequently used information criteria: AIC and BIC. The goal of the first study was to examine their ability to select unconditional models with correctly specified nonlinear functional forms. Higher L1 and L2 sample sizes, a higher ICC, and greater distinction between nonlinear functional forms generally improved correct model selection rates, but BIC appeared to be better than AIC when identifying more distinct nonlinear functional forms and AIC appeared to be better when the forms were less distinct. The goal of the second study was to examine the ability of AIC and BIC to select a model with a “more correct” predictor set when the underlying functional form was truly nonlinear. In many cases, information criteria were able to identify models determined to be more correct, but no clear pattern emerged between AIC and BIC. Finally, the utility of truly nonlinear functional forms was demonstrated in two behavioral health applications, both of which contained substantively interesting nonlinear trends that would have been missed if analysis had been limited to the linear functional form.

Comparing theories represented by statistical models is central to psychological research. Historically, comparisons between so called “non-nested” models have been error prone in the absence of a null hypothesis test. Recent research by Levy and Hancock and Merkle, You, and Preacher has extended Vuong’s Likelihood Ratio Test of non-nested models to Structural Equation Models (SEMs). A notable omission of recent work is the extension of Vuong’s test to the case of multilevel regression- a common approach for modeling longitudinal or grouped data. This dissertation leverages the similarities between SEMs and multilevel models to extend Vuong’s test to the multilevel framework. The logic of Vuong’s test as it relates to multilevel regression was explored and a SAS macro developed to facilitate the comparison between two models known to be non-nested a priori. The ability of Vuong’s test to select the true or “best” model was compared to that of information criteria in three simulation studies reflecting scenarios in which non-nestedness is commonly encountered in multilevel regression: non-nested covariate sets, level 1 residual covariance structures, and functional forms. Selection rates of the incorrect models were also examined. Vuong’s test showed almost no incorrect model selection across all scenarios, although its power to select the correct model was generally modest. Model comparisons among information criteria tended to be more sensitive than Vuong’s test but also selected the incorrect model more often. Finally, Vuong’s test was applied to three real data sets comparing competing models in the same scenarios as the simulation studies. Implications and recommendations for use are discussed.

Partially nested data structures occur when some units (typically individuals) are nested within groups while others are not nested. An adjustment to the standard multilevel model for 2-level data structures to accommodate partially nested data was proposed by Bauer, Sterba, and Hallfors, where individuals at Level 1 are either nested within treatment groups or are independent at Level 2. The model was heteroscedastic, estimating separate Level 1 residuals for control and treatment arms. The focus of the current body of work was on extending this 2-level model in two ways. The extension in the first simulation study involved incorporating a higher level of nesting, such as schools. The extension in the second study involved incorporating a lower level of nesting, inclusive of repeated measures. This heteroscedastic longitudinal partially nested model included separate estimates of individual-level variance in intercepts, variance in slopes for the time effect, and the covariance between them. Given the strengths of such a model, a third study examined various methods for formally testing the hypothesis that individuals within treatment groups become similar as a function of time. Finally, findings from all three simulation studies were demonstrated using data from an intervention targeting slow readers. While performance of the model incorporating a higher level of nesting was not overly problematic, the longitudinal model did not perform well. As parameter estimates were biased in the longitudinal model, performance of tests proposed in the third study could not be properly evaluated. Implications for partially nested model extensions are discussed.

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Despite the critical role of withdrawal, craving, and positive affect (PA) and negative affect (NA) in smoking relapse, relatively little is known about the temporal and predictive relationship between these constructs within the first day of abstinence. This pilot study aims to characterize dynamic changes in withdrawal, craving, and affect over the course of early abstinence using ecological momentary assessment. Beginning immediately after smoking, moderate and heavy smoking participants (n = 15 per group) responded to hourly surveys assessing craving, withdrawal, NA, and PA. Univariate and multivariate multilevel random coefficient modeling was used to describe the progression of craving, withdrawal/NA, and PA and to test correlations between these constructs at the subject level over the course of early abstinence. Heavy smokers reported greater craving from 1-4 hr of abstinence and greater withdrawal/NA after 3 or more hours as compared with moderate smokers. Level of withdrawal/NA was strongly positively associated with craving, and PA was negatively correlated with craving; however, the temporal dynamics of these correlations differed substantially. The association between withdrawal/NA and craving decreased over early abstinence, whereas the reverse was observed for PA. These findings can inform experimental studies of nicotine abstinence as well as their clinical applications to smoking cessation efforts. In particular, these results help to elucidate the role of PA in nicotine abstinence by demonstrating its independent association with nicotine craving over and above withdrawal/NA. If supported by future studies, these findings can refine experimental methods and clinical approaches for smoking cessation.