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News and Updates


Modeling Nonlinear Growth Trajectories

June 20, 2017

In this installment to our series of Office Hour videos on growth curve modeling, Patrick describes how to model nonlinear trajectories. Although the most basic form of growth model specifies a linear trajectory in which the model-implied change in the outcome is constant per unit-change in time, many constructs under study in the social and behavioral sciences follow nonlinear trajectories over time such that that the amount of change in the outcome depends on precisely when in time this change occurs. For example, there may be larger amounts of observed change between time 1 and 2, less change between time 5 and 6, and no change at all between time 9 and 10. Indeed, there may even be a point in time at which the direction of change reverses entirely. A common misunderstanding is that growth models can only incorporate functions that capture linear change over time, and this is actually not the case. In this episode of Office Hours Patrick explores three different approaches that allow for the estimation of nonlinear change within a growth model; all three methods are available in the structural equation approach to growth curve modeling, and two of three are available within the multilevel approach.

Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling, 15, 513-533.

Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling, 16, 676-701.

To see all episodes in this series, see our Growth Modeling playlist on YouTube.

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Using Nested Data to Enhance Causal Inference

May 30, 2017

There has been an ongoing controversy about whether a mother’s use of antidepressants during pregnancy results in elevated rates of autism in their children. Although much research has focused on this question, it has been limited by the omission of potential confounding variables and the study of just one child per mother. A recent study published in the Journal of the American Medical Association and widely distributed in a CBS News report presents research findings that considers both extensive potential confounders and multiple siblings born to the same mother. First, the study used 500 covariates to estimate propensity scores to compare child autism for mother’s who did and did not use antidepressants during pregnancy. Results indicated that, after balancing on all 500 confounders, there were no differences in autism between the two groups. Although insightful, this method used advanced statistical controls to examine just one child per family. To enhance causal inference, the study then considered mothers with at least two children, one of whom was exposed to antidepressants in utero and one who was not. The use of multiple births nested within mother allowed for an explicit test of within-mother effects of antidepressant exposure while controlling for a host of mother-specific characteristics (e.g., genetic risk) to better isolate the effects of antidepressant exposure while holding mother constant. Again, no differences in autism rates were found. The results of the nested data models may be much more convincing because control of between-mother effects was achieved through the hierarchical design of the study rather than by invoking statistical controls applied to just one child per mother. This is an excellent example of using nested data structures and advanced statistical models to make stronger inferences about group differences.

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Regression to the Mean in Everyday Life

May 12, 2017

Regression to the mean is an often misunderstood phenomena that routinely arises in both empirical research and in every day life. First described by Sir Francis Galton, regression to the mean is a process by which a measured observation that obtains an extreme value on one assessment will tend to obtain a less extreme value on a subsequent assessment, and vice versa. Galton found that, on average, taller fathers tended to have shorter sons, and shorter fathers tended to have taller sons. This same phenomenon has been observed in financial markets, standardized testing, child development, treatment outcome studies, and even professional sports. A recent article in the New York Times described this very process when exploring whether your favorite football team will get better or worse next season. Although an entertaining example, regression to the mean is critically important to fully understand in any longitudinal research study; Donald Campbell and David Kenny explore these issues in detail in their 1999 book A Primer on Regression Artifacts. Whether studying treatment interventions, high risk groups, high stakes testing, health outcomes, or any other topic of significance, regression to the mean must be understood, embraced, and mitigated. As Sir Francis Galton concluded in 1889, “Some people hate the very name of statistics but I find them full of beauty and interest. Whenever they are not brutalised, but handled by higher methods, and warily interpreted, their power of dealing with complicated phenomena is extraordinary.” His words still ring true more than a century later.

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Introduction to latent class / profile analysis

April 17, 2017

Although latent class analysis (LCA) and latent profile analysis (LPA) were developed decades ago, these models have gained increasing recent prominence as tools for understanding heterogeneity within multivariate data. Dan introduces these models through a hypothetical example where the goal is to identify voter blocks within the Republican Party by surveying which issues voters regard as most important. He begins by contrasting LCA/LPA models to the more familiar factor analysis model: whereas factor analysis assumes that individuals differ by degrees on continuous latent dimensions (e.g., fiscal conservatism, social conservatism), LCA/LPA models instead posit that individuals fall into latent categories (e.g., fiscal conservatives, social conservatives). Dan then describes the implementation and interpretation of LCA/LPA models and the potential inclusion of predictors and outcomes of class membership. He also briefly notes several advanced extensions of LCA/LPA, including latent transition analysis, growth mixture modeling, and factor mixture models.

Early references on LCA and LPA include:

  • Gibson, W. A. (1959). Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24, 229–252.
  • Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin.


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Growth modeling within a structural equation modeling framework

March 31, 2017

In a prior episode of Office Hours, Patrick explored “Growth modeling in a multilevel modeling framework.” In the current episode he discusses how growth models can also be estimated within the structural equation modeling (SEM) framework. He begins with a brief review of the confirmatory factor analysis model and describes this as the foundation of the latent curve model (LCM) estimated within the SEM. He explains the motivation for using the observed repeated measures as multiple indicators defining one or more underlying latent growth factors. He then describes using this formulation to estimate an LCM that he then extends to include time-invariant and time-varying covariates. He concludes with a brief description of multivariate LCMs that allow for the simultaneous estimation of growth processes in two or more constructs at once.

To see all episodes in this series, see our Growth Modeling playlist.

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