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Statistical Adjustment and the Case of Marathon Records and Climate Change

November 9, 2017

There is often much confusion about what is meant by “statistical adjustment” when estimating and interpreting models that include more than one predictor variable. This issue commonly arises in the traditional multiple regression model, but is ubiquitous across nearly any class of multivariate models ranging from regression to factor analysis to complex structural equation models. Statistical adjustment goes by many names including an effect that is “controlled for”, is “unique to”, or is “above-and-beyond” the effects of one or more other predictors. Regardless of term, statistical adjustment attempts to equate factors in a model that were not controlled as part of the experimental design. An interesting recent example was described in a New York Times article about the relation between climate change and world record marathon times. Nearly five million finish times where drawn from 900 marathons spanning a 20 year period, and a nonlinear relation was found between temperature and finish time. The fastest times were recorded when temperatures were in the 40’s, and finish times systematically slowed with increasing temperature. This raises an interesting question about whether world records should be adjusted for race-time temperature. For example, the current world record holder would be replaced by the third place finisher on the record list when factoring in temperature. Similar arguments have been made in baseball about adjusting home run counts for elevation because the air resistance is markedly less in Denver than in Boston. Although an interesting argument among friends, the notion of statistical adjustment becomes much more serious in many applied research settings, particularly when studying issues such as end-of-grade achievement, substance use, psychopathology, or any of a myriad of outcomes in the behavioral and health sciences. Failure to account for potential confounding factors can lead to biased interpretations of causal effects that in turn threatens both the internal and external validity of the study. Dan discusses and demonstrates the idea of statistical control in greater detail in our Office Hours video series on multiple regression.

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Summer Workshop Schedule for 2018

October 10, 2017

We are pleased to announce our workshop schedule for this summer:

  • May 9-11: Network Analysis
  • May 21-25: Multilevel Modeling
  • June 4-8: Latent Class/Cluster Analysis and Mixture Modeling
  • June 18-22: Structural Equation Modeling
  • June 25-29: Longitudinal Structural Equation Modeling
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    This year, we will be holding all workshops at the Chapel Hill-Carrboro Hampton Inn & Suites, where we have also reserved room blocks for the convenience of our participants.  To learn more about what makes our workshops unique, please see our Training page.

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    CBA Office Hours on Linear Regression

    August 3, 2017
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    It is critical for researchers in the behavioral, health, and social sciences to have a full understanding of the linear regression model. Not only is this model important in its own right, but it serves as the foundation for more advanced statistical models, such as the multilevel model, factor analysis, structural equation modeling, generalized linear models, and many other techniques. For those seeking a first exposure to linear regression or simply looking for a refresher, we’ve launched a new series of CBA Office Hours videos that starts with the basics of the simple one-predictor model and proceeds to more advanced topics. So far, we’ve posted four episodes:

    We intend to add more videos as time goes on, focusing on such topics as interpretation in the multiple regression model, the difference between hierarchical versus simultaneous regression, how to incorporate categorical predictors, and how to test, probe, and plot interactions. To view all of the videos in this series in sequence, simply click the embedded video or go to our YouTube playlist on Linear Regression. You can also follow us on social media to be updated as new videos are added on this and other topics.

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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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