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Growth Models with Time-Varying Covariates

June 20, 2017
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In a prior episode of Office Hours, Patrick discussed predicting growth by time-invariant covariates (TICs), predictors for which the numerical values are constant over time. In this episode, Patrick describes the inclusion of time-varying covariates (TVCs), predictors with numerical values that can differ across time. Examples of TVCs are numerous and include time-specific measures of depression, anxiety, substance use, marital status, onset of diagnosis, or dropout from treatment, among many others. When TICs are included in a growth model, the time-invariant predictors are used to directly predict the growth factors (e.g., intercept, slope). In contrast, when TVCs are included in a growth model, the effects of the time-varying predictors bypass the growth factors and directly influence the repeated measures. There are many ways that TVC influences can be included in the model, and models can be further extended to include both TICs and TVCs simultaneously. Patrick works through a hypothetical example and concludes with a summary of strengths and limitations of these models.

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

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Growth Models with Time-Invariant Covariates

June 20, 2017
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Once an optimal model of linear or nonlinear change has been established, it is often of interest to try to predict individual differences in change over time. In this installment of our Office Hours series on growth modeling, Patrick discusses how to incorporate time-invariant covariates (TICS) into a growth model.

TICs are predictors that do not change as a function of time, for instance, biological sex, country of origin, birth order, or any person-level characteristic assessed only at the initial time point. TICs are used as predictors of the latent growth factors in the SEM or entered as Level 2 predictors of intercepts and slopes in the MLM; in both approaches, tests are obtained regarding the extent to which information on the TIC in part contributes to the growth process under study. Although the interpretation of predictors of the intercept factor are straightforward, predictors of the slope factor are more complex given the interaction between the predictor and time. These slope effects must be probed further to more fully understand the nature of the effect. Patrick discusses these issues in greater details and makes recommendations for using these in practice.

Bauer, D.J., & Curran, P.J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.

Curran, P. J., Bauer, D. J., & Willoughby, M. T. (2004). Testing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437-448.

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

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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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