Browsing by Subject "Multilevel models"
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Item Accounting for multiple membership data in adolescent social networks : an analysis of simulated data(2016-05) Peek, Jaclyn Kara; Beretvas, Susan Natasha; Powers, Daniel A.Multilevel modeling allows for the modeling of nested structures such as students nested within middle schools and middle schools nested within high schools. These kinds of hierarchies are common in social science research. Pure hierarchies may exist, where one variable is completely nested within another. Multiple membership (MM) structures occur when some lower level units are members of more than one higher level clustering unit (e.g., a student attends more than one high school). An extension to the conventional multilevel model, the multiple membership random effects model (MMREM) can be used to handle MM data. I compare a random effects model with and without multiple membership effects to demonstrate the possible benefit of accounting for the MM structure. We replicate an existing study on student academic outcomes (Tranmer et al., 2013) which assumes a multiple membership data structure, and add a comparison to a non-MM (i.e. single membership) model in order to assess the improvement in model fit. The original study investigated the effect of school, area, and social network membership in friendship dyads and triads on academic achievement in adolescents, with age, gender, and ethnicity as covariates. Our models retain the MM structure found in the original social network data. The original data is confidential and unavailable for use – therefore, a major component of this report is the simulation of this dataset in R. Results indicate that multiple membership does not necessarily lead to better goodness-of-fit as measured by DIC. Accounting for MM data structure initially produced a worse-fitting model. Artificially inflating the fixed and random effects that generated the simulated academic performance outcome led to the opposite effect. We conclude that the scale of random effects is important in determining the DIC measure of fit, and propose a full simulation study to more conclusively test our original hypothesis.Item Alternative estimation approaches for some common Item Response Theory models(2010-08) Sabouri, Pooneh, 1980-; Powers, Daniel A.; Beretvas, Susan N.In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion by introducing a multilevel level framework for these two Item Response Theory Models. We explain Bock and Aitkin's (1981) work to estimate item parameters for these two models. Finally we illustrate these models with a LSAT exam data and two statistical softwares; R project and Stata.Item Approaches to modeling self-rated health in longitudinal studies : best practices and recommendations for multilevel models(2012-05) Sasson, Isaac; Powers, Daniel A.; Umberson, Debra J.Self-rated health (SRH) is an outcome commonly studied by demographers, epidemiologists, and sociologists of health, typically measured using an ordinal scale. SRH is analyzed in cross-sectional and longitudinal studies for both descriptive and inferential purposes, and has been shown to have significant validity with regard to predicting mortality. Despite the wide spread use of this measure, only limited attention is explicitly given to its unique attributes in the case of longitudinal studies. While self-rated health is assumed to represent a latent continuous and dynamic process, SRH is actually measured discretely and asymmetrically. Thus, the validity of methods ignoring the scale of measurement remains questionable. We compare three approaches to modeling SRH with repeated measures over time: linear multilevel models (MLM or LGM), including corrections for non-normality; and marginal and conditional ordered-logit models for longitudinal data. The models are compared using simulated data and illustrated with results from the Health and Retirement Study. We find that marginal and conditional models result in very different interpretations, but that conditional linear and non-linear models result in similar substantive conclusions, albeit with some loss of power in the linear case. In conclusion, we suggest guidelines for modeling self-rated health and similar ordinal outcomes in longitudinal studies.Item Bayesian estimation of a longitudinal mediation model with three-level clustered data(2015-12) Israni, Anita; Beretvas, Susan Natasha; Hersh, Matthew; Pituch, Keenan; Roberts, Gregory; Whittaker, TiffanyLongitudinal modeling allows researchers to capture changes in variables that take time to exert their effects. Furthermore, incorporating mediation into a longitudinal model allows for researchers to test causal inferences about, for example, how an independent variable might affect growth in an outcome variable through growth in a mediating variable. In scenarios in which multiple variables are measured over time, the parallel process model can be used to model the inter-relationships among the measures’ trajectories where both processes are modeled to have their own separate but related growth parameters. The hierarchical linear modeling (HLM) framework can be used to model a parallel process model and allows for easy extensions to handle multiple levels and non-hierarchical data, such as cross-classified or multiple membership data structures, in clustered data. This study assessed a three-level parallel process model couched in the context of longitudinal mediation where treatment was assigned at the cluster level, matching a longitudinal cluster randomized trial design. The treatment’s effect on growth in an outcome is modeled as mediated by the growth in a mediating variable at the cluster and individual level, resulting in a cross-level and cluster-level mediated effect. A simulation and real data analysis study were conducted using a fully Bayesian analysis. In the simulation study, the following four factors were manipulated to assess the recovery of the parameters of interest: mediated effect size, random effects variance component values, number of measurement occasions, and number of clusters. Overall, relative parameter bias and statistical power improved for higher values for each of the four factors. The cross-level mediated effects were less biased and had greater statistical power than the cluster-level mediated effects. For the mediated effects that were truly zero, coverage rates based on the highest posterior density intervals showed mostly acceptable rates for the cross-level mediated effect and when path b was zero paired with a non-zero path a for the cluster-level effect. For conditions with a true value of zero for the cluster-level mediated effect with a path a of zero, the cluster-level coverage rates provided over-coverage. Results are discussed along with clarification of study limitations and suggestions for future research. Recommendations for applied researchers are also noted.Item Introduction to power and sample size in multilevel models(2012-05) Venkatesan, Harini; Beretvas, Susan NatashaIn this report we give a brief introduction to the multilevel models, provide a brief summary of the need for using the multilevel model, discuss the assumptions underlying use of multilevel models, and present by means of example the necessary steps involved in model building. This introduction is followed by a discussion of power and sample size determination in multilevel designs. Some formulae are discussed to provide insight into the design aspects that are most influential in terms of power and calculation of standard errors. Finally we conclude by discussing and reviewing the simulation study performed by Maas and Hox (2005) about the influence of different sample sizes at individual as well as group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors.Item An overview of multilevel regression(2010-12) Kaplan, Andrea Jean; Smith, Martha K., 1944-; Luecke, John EdwinDue to the inherently hierarchical nature of many natural phenomena, data collected rests in nested entities. As an example, students are nested in schools, school are nested in districts, districts are nested in counties, and counties are nested within states. Multilevel models provide a statistical framework for investigating and drawing conclusions regarding the influence of factors at differing hierarchical levels of analysis. The work in this paper serves as an introduction to multilevel models and their comparison to Ordinary Least Squares (OLS) regression. We overview three basic model structures: variable intercept model, variable slope model, and hierarchical linear model and illustrate each model with an example of student data. Then, we contrast the three multilevel models with the OLS model and present a method for producing confidence intervals for the regression coefficients.