Essays
-
Longitudinal Data Analysis - Little, Todd D.
In this essay we review some of the emerging trends in modeling repeated measures data. Three general forms of longitudinal models are discussed: panel model designs, growth curve models, and intensive within‐person assessments. Each section discusses design elements that should be considered when using each of these types of longitudinal models, and introduces some emerging trends. In the section on panel designs, continuous time models and planned missing data models are introduced; these ideas will revolutionize the modeling and collection of panel data. In the section on growth curve models, the necessity of separately evaluating mean and covariance model fit is discussed. This section also introduces methods being used to carefully consider the time of measurements in temporal designs. Finally, the budding analysis of intensive within individual observations is considered, including recent work from mathematics that limits the generalizability of interindividual studies to individual outcomes. -
Models of Nonlinear Growth - Coulombe, Patrick
Models for nonlinear growth are not new, but have not been widely applied in the social and behavioral sciences. In this essay, we describe the fundamental issues relevant to choosing and using a nonlinear growth model. We discuss how researchers can go about choosing a model and then focus on the application of two specific nonlinear models: the fractional polynomial model and the piecewise model. We highlight recent work in reparameterization that allows researchers to choose models with parameters tailored specifically to research questions. We also review recent work on the topic of growth rates in nonlinear models that will allow researchers to obtain richer information from the application of nonlinear models. We conclude by pointing out some of the unresolved issues in the use of nonlinear growth models. -
Quantile Regression Methods - Fitzenberger, Bernd
Quantile regression is emerging as a popular statistical approach, which complements the estimation of conditional mean models. While the latter only focuses on one aspect of the conditional distribution of the dependent variable, the mean, quantile regression provides more detailed insights by modeling conditional quantiles. Quantile regression can therefore detect whether the partial effect of a regressor on the conditional quantiles is the same for all quantiles or differs across quantiles. Quantile regression can provide evidence for a statistical relationship between two variables even if the mean regression model does not. -
Regression Discontinuity Design - Meredith, Marc
Social scientists search for interventions in the real world that approximate the conditions of an experiment. One form of such natural experiments that is increasingly used in social science research is regression discontinuity (RD). RD designs are possible when there are thresholds that cause large changes in the assignment of treatments on the basis of small differences in a variable. For example, a high school junior in the state of Pennsylvania who scored 214 out of 240 on the 2012 PSAT test received the treatment of being a National Merit Semi‐Finalist, whereas a comparable student who scored 213 did not. The intuition behind a RD design is that we often can learn something about the effects of a treatment by comparing observations that barely receive a treatment (e.g., individuals with scores of 214 and just above on the PSAT) to observations that barely miss receiving a treatment (e.g., individuals who score 213 and just below on the PSAT). We discuss the assumptions under which the effects of treatment that are assigned based on a discontinuous threshold can be estimated using a RD design. We then illustrate how graphical analysis can be used to illustrate whether these assumptions are likely to hold. We conclude by discussing two examples of cutting‐edge research that employs RD designs and discussing areas of future research. -
Statistical Power Analysis - Aberson, Christopher L.
Statistical power refers to the probability of rejecting a false null hypothesis (i.e., finding what the researcher wants to find). Power analysis allows researchers to determine adequate sample size for designing studies with an optimal probability for rejecting false null hypotheses. When conducted correctly, power analysis helps researchers make informed decisions about sample size selection. Statistical power analysis most commonly involves specifying statistic test criteria (type I error rate), desired level of power, and the effect size expected in the population. This article outlines the basic concepts relevant to statistical power, factors that influence power, how to establish the different parameters for power analysis, and determination and interpretation of the effect size estimates for power. I also address innovative work such as the continued development of software resources for power analysis and protocols for designing for precision of confidence intervals (aka, accuracy in parameter estimation). Finally, I outline understudied areas such as power analysis for designs with multiple predictors, reporting and interpreting power analyses in published work, designing for meaningfully sized effects, and power to detect multiple effects in the same study. -
Structural Equation Modeling and Latent Variable Approaches - Liu, Alex
Structural equation modeling and latent variable approach (SEM) is experiencing rapid development with wide application as a result of using big data and modern computing technologies. This essay first gives an introduction of SEM, and then summarizes the foundational research in developing better fit indices and in developing more efficient computing algorithms. Also, we review two most important cutting‐edge researches in using SEM for causal analysis and in managing workflows of SEM. For the future SEM research, we have discussed issues of big data, new applications, equivalent models, and hybrid modeling. -
Text Analysis - Roberts, Carl W.
Even once words have been counted, or their themes and semantics quantitatively rendered as networks or grammars, it remains unclear what they reveal. Are the texts windows into historical facts that the analyst cannot experience in person, or are they windows into their authors' perspectives? A choice is needed here, because authors' perspectives may alter their renderings of “the facts” and, conversely, changes in an author's surroundings may prompt changes in her or his perspective. Next, is the researcher a novice who strives for fidelity to authors' perspectives, or is the researcher an expert whose perspective affords insights unknown to the authors? With contemporary growth in both world population and communication technologies, increasing contacts among peoples with disparate perspectives afford the social sciences an opportunity both to improve our understanding of these perspectives (or cultures) and to discontinue mining words for evidence consistent with theoretical perspectives of our own choosing. Modality analysis is a promising method for performing historical‐comparative analyses of political cultures based on the volumes of texts only recently available to us.