Estimating Relative Stability in Developmental Research: A Critique of Modern Approaches and a Novel Method

Abstract

Objective

Developmental/life-course (DLC) criminologists often study the age-graded trajectories of traits and behaviors known to correlate with antisocial outcomes. Much of this work has attempted to discern whether traits like impulse control are relatively stable across different portions of the life course. A range of statistical techniques have been employed by researchers attempting to parameterize relative stability. Yet, despite these attempts, much of the evidence remains mixed.

Methods

We draw on data from the Pathways to Desistance study to examine whether the methods typically used to analyze longitudinal development provide a parameter estimate for relative stability.

Results

The results of our demonstration reveal that none of the methods typically employed by DLC researchers provide a parameter estimate for relative stability. In order to address this oversight, we develop a novel method—P(Δ)—that can be used to estimate the amount of relative (in)stability that is observed in a longitudinal dataset.

Conclusions

Although P(Δ) provides a direct estimate of the degree to which relative (in)stability is observed in one’s dataset, there are several important points that must be considered by future DLC researchers in order to further develop P(Δ) into a statistic that can be used for inferential analysis. We consider these points in the discussion.

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Notes

  1. 1.

    We owe a special thanks to Carol Schubert who provided the alpha values upon request.

  2. 2.

    Substantive findings for the MMC were unchanged when age dummies were included and when control variables for race and sex were included in the analysis. Also, substantive findings were unchanged when the alternative coding for the wave variable (i.e., the timing between waves in months) was utilized; these estimates suggested respondents increased in impulse control by approximately 0.048 points every 12 months. Considering the Pathways study spanned a 7-year period, this effect translates into roughly 0.339 points gained, on average, over the course of the project.

  3. 3.

    A series of alternative models were estimated where the error covariance matrix was specified with different structures (e.g., unstructured, an autoregressive structure, and the Toeplitz structure). Parameter estimates were substantively unchanged when these models were estimated.

  4. 4.

    It is worth noting that one can perform an approximate analysis of Jeffreys’s Bayes factor scale—a useful method for identifying the best-fitting model via the BIC statistic—by exponentiating the difference between the BIC values for two models (see Nagin 2005: 69). We would like to thank an anonymous reviewer for pointing this out.

  5. 5.

    This number was calculated with the binomial coefficient (i.e., the formula for combinations) because ordering does not matter (i.e., we do not want to count AB as unique from BA):

    \(\frac{n!}{r!(n - r)!} = \frac{854!}{2!(854 - 2)!} = \frac{(854*853)}{2} = 364,231\)

  6. 6.

    A secondary consideration is whether the trials (i.e., two randomly drawn cases) should be weighted to account for the starting position of case 1 relative to case 2. In other words, should P(Δ) give more weight to cases that reliably change rankings when they started further apart at baseline?

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Acknowledgments

The Pathways to Desistance project was supported by funds from the following: Office of Juvenile Justice and Delinquency Prevention (2007-MU-FX-0002), National Institute of Justice (2008-IJ-CX-0023), John D. and Catherine T. MacArthur Foundation, William T. Grant Foundation, Robert Wood Johnson Foundation, William Penn Foundation, Center for Disease Control, National Institute on Drug Abuse (R01DA019697), Pennsylvania Commission on Crime and Delinquency, and the Arizona Governor’s Justice Commission. We are grateful for their support. The content of this paper, however, is solely the responsibility of the authors and does not necessarily represent the official views of these agencies. No support was received from any of these agencies for the present study.

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Correspondence to J. C. Barnes.

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The authors would like to thank Arjan Blokland for his helpful comments on the original manuscript. The final product was much improved based on his suggestions as well as those provided by the anonymous reviewers.

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Barnes, J.C., El Sayed, S.A., TenEyck, M. et al. Estimating Relative Stability in Developmental Research: A Critique of Modern Approaches and a Novel Method. J Quant Criminol 33, 319–346 (2017). https://doi.org/10.1007/s10940-016-9298-5

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Keywords

  • Relative stability
  • Impulse control
  • Longitudinal models