Now showing 1 - 5 of 311
- ItemCharacterizing the Adventitious Model Error as a Random Effect in Item-Response-Theory Models(2023) Xu, Shuangshuang; Liu, Yang; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)When drawing conclusions from statistical inferences, researchers are usually concerned about two types of errors: sampling error and model error. The sampling error is caused by the discrepancy between the observed sample and the population from which the sample is drawn from (i.e., operational population). The model error refers to the discrepancy between the fitted model and the data-generating mechanism. Most item response theory (IRT) models assume that models are correctly specified in the population of interest; as a result, only sampling errors are characterized, not model errors. The model error can be treated either as fixed or random. The proposed framework in this study treats the model error as a random effect (i.e., an adventitious error) and provides an alternative explanation for the model errors in IRT models that originate from unknown sources. A random, ideally small amount of discrepancy between the operational population and the fitted model is characterized using a Dirichlet-Multinomial framework. A concentration/dispersion parameter is used in the Dirichlet-Multinomial framework to measure the amount of adventitious error between the operational population probability and the fitted model. In general, the study aims to: 1) build a Dirichlet-Multinomial framework for IRT models, 2) establish asymptotic results for estimating model parameters when the operational population probability is assumed known or unknown, 3) conduct numerical studies to investigate parameter recovery and the relationship between the concentration/dispersion parameter in the proposed framework and the Root Mean Square Error of Approximation (RMSEA), 4) correct bias in parameter estimates of the Dirichlet-Multinomial framework using asymptotic approximation methods, and 5) quantify the amount of model error in the framework and decide whether the model should be retained or rejected.
- ItemINVESTIGATING MODEL SELECTION AND PARAMETER RECOVERY OF THE LATENT VARIABLE AUTOREGRESIVE LATENT TRAJECTORY (LV-ALT) MODEL FOR REPEATED MEASURES DATA: A MONTE CARLO SIMULATION STUDY(2023) Houser, Ari; Harring, Jeffrey R; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Over the past several decades, several highly generalized models have been developed which can reduce, through parameter constraints, to a variety of classical models. One such framework, the Autoregressive Latent Trajectory (ALT) model, is a combination of two classical approaches to longitudinal modeling: the autoregressive or simplex family, in which trait scores at one occasion are regressed on scores at a previous occasion, and latent trajectory or growth curve models, in which individual trajectories are specified by a set of latent factors (typically a slope and an intercept) whose values vary across the population.The Latent Variable-Autoregressive Latent Trajectory (LV-ALT) model has been recently proposed as an extension of the ALT model in which the traits of interest are latent constructs measured by one or more indicator variables. The LV-ALT is presented as a framework by which one may compare the fit of a chosen model to alternative possibilities or use to empirically guide the selection of a model in the absence of theory, prior research, or standard practice. To date, however, there has not been any robust analysis of the efficacy or usefulness of the LV-ALT model for this purpose. This study uses a Monte Carlo simulation study to evaluate the efficacy of the basic formulation of the LV-ALT model (univariate latent growth process, single indicator variable) to identify the true model, model family, and key characteristics of the model under manipulated conditions of true model parameters, sample size, measurement reliability, and missing data. The performance of the LV-ALT model for model selection is mixed. Under most manipulated conditions, the best-fitting of nine candidate models was different than the generating model, and the cost of model misspecification for parameter recovery included significant increases in bias and loss of precision in parameter estimation. As a general rule, the LV-ALT should not be relied upon to empirically select a specific model, or to choose between several theoretical plausible models in the autoregressive or latent growth families. Larger sample size, greater measurement reliability, larger parameter magnitude, and a constant autoregressive parameter are associated with greater likelihood of correct model selection.
- ItemESTIMATING THE Q-DIFFUSION MODEL PARAMETERS BY APPROXIMATE BAYESIAN COMPUTATION(2023) Tian, Chen; Liu, Yang; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The Q-diffusion model is a cognitive process model that considers decision making as an unobservable information accumulation process. Both item and person parameters decide the trace line of the cognitive process, which further decides observed response and response time. Because the likelihood function for the Q-diffusion model is intractable, standard parameter estimation techniques such as the maximum likelihood estimation is difficult to apply. This project applies Approximate Bayesian Computation (ABC) to estimate parameters of the Q-diffusion model. Different from standard Markov chain Monte Carlo samplers that require pointwise evaluation of the likelihood function, ABC builds upon a program for data generation and a metric on the data space to gauge the similarity between imputed and observed data. This project aims to compare the performance of two criteria for gauging the similarity or distance. The limited-information criterion measures the distance in suitable summary statistics (i.e., variances, covariances, and means) between imputed and observed data. The enhanced limited information criterion additionally considers the dependencies among persons’ responses and response times. Bias, rooted mean squared error, and coverage of credible intervals were reported. Results show that when using posterior median as the point estimate, by jointly considering a person’s responses and response time, the enhanced criterion yielded less biased estimation on population scale of person power and slightly better item parameters. This SMC-ABC algorithm informs researchers about key data features that should be captured when determining the stopping rule for the algorithm.
- ItemReframing Children's Judgments of Consensus Reliability as a Process of Information Aggregation(2023) Levush, Karen Carmel; Butler, Lucas P; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Consensus is a compelling cue to the truth value of a given claim, but certain consensus patterns provide stronger evidence than others. This dissertation examines the developmental trajectory of children’s reasoning about the epistemic value of diverse perspectives for consensus’ reliability. One-hundred forty-four children between the ages of 7 and 9, as well as 48 adults, were introduced to a novel planet and alien groups that live there. Tasked with learning the “right things” about why various natural phenomena occur on this planet, participants were asked which one of two consensus groups, each of whom collectively thought something different, was the “better” group to ask. Participants rated their relative preference for one consensus group over another using a 6-point scale and were asked to explain their reasoning. These findings provide initial evidence that qualitative changes in children’s ability to consider how dependencies can lead to redundant information parallel the developmental shift in children’s appreciation for interpretive diversity in middle childhood.
- ItemMother-child and father-child "serve and return" interactions at 9 months: Associations with children's language skills at 18, 24, and 30 months(2023) Chen, Yu; Cabrera, Natasha J; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Infants learn language through the back-and-forth interactions with their parents where they “serve” by vocalizing, gesturing, or looking and parents “return” in a temporally and semantically contingent way. My dissertation focuses on these “serve and return” (SR) interactions between 9-month-old infants and their mothers and fathers (n = 296 parents and 148 infants) from ethnically and socioeconomically diverse backgrounds by examining the variability in SR interactions explained by maternal and paternal psychological distress, the association between SR interactions and children’s language skills at 18, 24, and 30 months, and the moderation effect of maternal and paternal SR interactions on language outcomes. Psychological distress was indicated by parent-reported depressive symptoms, parenting stress, and role overload, and SR interactions were transcribed and coded from video-taped parent-child toy play activities during home visits. I report three major findings. First, neither maternal nor paternal psychological distress was significantly associated with and SR interactions at 9 months, controlling for demographic factors. Second, fathers who responded to their child’s serves more promptly and mothers who provided more semantically relevant responses had children with higher receptive and expressive language skills, respectively, at 18 and 30 months. Third, fathers’ semantically relevant responses were negatively associated with children’s receptive language skills at 24 months; however, this main effect was moderated by mothers’ semantically relevant responses. Understanding how mothers and fathers engage in temporally and semantically contingent social interactions with their children during the first year, especially among families from diverse backgrounds, would enable programs and policies to more effectively promote early language development and reduce gaps in school readiness.