Abstract
Resurgence as Choice in Context (RaC2) is a quantitative model for evaluating the reemergence of a previously extinguished response when alternative reinforcement is worsened. Rooted in the matching law, RaC2 proposes that allocation between target and alternative responding is based on changes in the relative value of each response option over time, accounting for periods with and without alternative reinforcement. Given that practitioners and applied researchers may have limited experience with constructing quantitative models, we provide a step-by-step task analysis for building RaC2 using Microsoft Excel 2013. We also provide a few basic learning activities to help readers better understand RaC2 itself, the variables that affect the model’s predictions, and the clinical implications of those predictions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
All data described in this study are included in this published article and its supplementary information files.
Notes
For more recent versions of Microsoft Excel (i.e., after 2016), the formulas and text will remain the same. However, there may be some differences in the steps required to complete certain tasks, such as formatting cells or inserting a graph. For additional guidance on how to access features on newer versions of Excel, please see https://support.microsoft.com.
For illustrative purposes, we opt to use VI schedules here for ease of predicting the total number of reinforcers per hour. Of course, this can also be done with other types of schedules (e.g., fixed-ratio, fixed-time) as well for both RaC and RaC2.
In real-world application, these parameters can be freely estimated via the Generalized Reduced Gradient (GRG) Nonlinear Solving Method (Lasdon et al., 1978) in the Solver Add-In for Microsoft Excel. For an overview of how to install and use the Solver Add-In to estimate free parameters in quantitative behavioral models, see Reed et al. (2012).
This template is for educational purposes only. Readers may need to modify the scale of the y-axis to facilitate visual inspection of the data series depending on specific parameter values and experimental arrangements used within this model.
References
Athens, E. S., & Vollmer, T. R. (2010). An investigation of differential reinforcement of alternative behavior without extinction. Journal of Applied Behavior Analysis, 43(4), 569–589. https://doi.org/10.1901/jaba.2010.43-569
Baum, W. M., & Rachlin, H. C. (1969). Choice as time allocation. Journal of the Experimental Analysis of Behavior, 12(6), 861–874. https://doi.org/10.1901/jeab.1969.12-861
Briggs, A. M., Fisher, W. W., Greer, B. D., & Kimball, R. T. (2018). Prevalence of resurgence of destructive behavior when thinning reinforcement schedules during functional communication training. Journal of Applied Behavior Analysis, 51(3), 620–633. https://doi.org/10.1002/jaba.472
Brown, K. R., Greer, B. D., Craig, A. R., Sullivan, W. E., Fisher, W. W., & Roane, H. S. (2020). Resurgence following differential reinforcement of alternative behavior implemented with and without extinction. Journal of the Experimental Analysis of Behavior, 113(2), 449–467. https://doi.org/10.1002/jeab.588
Browning, K. (2019). Generating multiple-group simulations of the resurgence as choice model in R [Source Code]. Retrieved April 2023, from https://www.researchgate.net/publication/331073836_Generating_Multiple-Group_Simulations_of_the_Resurgence_as_Choice_Model_in_R
Cançado, C. R., Abreu-Rodrigues, J., & Aló, R. M. (2015). Reinforcement rate and resurgence: A parametric analysis. Revista Mexicana de Análisis de la Conducta, 41(2), 84–115. https://doi.org/10.5514/rmac.v41.i2.63739
Cook, J. E., & Lattal, K. A. (2019). Repeated, within-session resurgence. Journal of the Experimental Analysis of Behavior, 111(1), 28–47. https://doi.org/10.1002/jeab.496
Craig, A. R. (2017). Fitting the behavioral-momentum based model of extinction to obtained multiple-schedule extinction data using R [Source Code]. https://doi.org/10.13140/RG.2.2.27991.37288
Craig, A. R., & Shahan, T. A. (2016). Behavioral momentum theory fails to account for the effects of reinforcement rate on resurgence. Journal of the Experimental Analysis of Behavior, 105(3), 375–392. https://doi.org/10.1002/jeab.207
Craig, A. R., Browning, K. O., Nall, R. W., Marshall, C. M., & Shahan, T. A. (2017). Resurgence and alternative-reinforcer magnitude. Journal of the Experimental Analysis of Behavior, 107(2), 218–233. https://doi.org/10.1002/jeab.245
Critchfield, T. S., & Reed, D. D. (2009). What are we doing when we translate from quantitative models? The Behavior Analyst, 32(2), 339–362. https://doi.org/10.1007/BF03392197
da Silva, S. P., Maxwell, M. E., & Lattal, K. A. (2008). Concurrent resurgence and behavioral history. Journal of the Experimental Analysis of Behavior, 90(3), 313–331. https://doi.org/10.1901/jeab.2008.90-313
Davison, M. C., & Tustin, R. D. (1978). The relation between the generalized matching law and signal-detection theory. Journal of the Experimental Analysis of Behavior, 29(2), 331–336. https://doi.org/10.1901/jeab.1978.29-331
Devenport, L. D., & Devenport, J. A. (1994). Time-dependent averaging of foraging information in least chipmunks and golden-mantled ground squirrels. Animal Behaviour, 47(4), 787–802. https://doi.org/10.1006/anbe.1994.1111
Doughty, A. H., da Silva, S. P., & Lattal, K. A. (2007). Differential resurgence and response elimination. Behavioural Processes, 75(2), 115–128. https://doi.org/10.1016/j.beproc.2007.02.025
Dowdy, A., Hantula, D. A., Travers, J. C., & Tincani, M. (2021). Meta-analytic methods to detect publication bias in behavior science research. Perspectives on Behavior Science, 45(1), 37–52. https://doi.org/10.1007/s40614-021-00303-0
Falligant, J. M., Chin, M. D., & Kurtz, P. F. (2022a). Renewal and resurgence of severe problem behavior in an intensive outpatient setting: Prevalence, magnitude, and implications for practice. Behavioral Interventions, 37(3), 909–924. https://doi.org/10.1002/bin.1878
Falligant, J. M., Hagopian, L. P., Kranak, M. P., & Kurtz, P. F. (2022b). Quantifying increases in problem behavior following downshifts in reinforcement: A retrospective analysis and replication. Journal of the Experimental Analysis of Behavior, 118(1), 148–155. https://doi.org/10.1002/jeab.769
Fisher, W. W., Greer, B. D., Fuhrman, A. M., Saini, V., & Simmons, C. A. (2018). Minimizing resurgence of destructive behavior using behavioral momentum theory. Journal of Applied Behavior Analysis, 51(4), 831–853. https://doi.org/10.1002/jaba.499
Fisher, W. W., Saini, V., Greer, B. D., Sullivan, W. E., Roane, H. S., Fuhrman, A. M., Craig, A. R., & Kimball, R. T. (2019). Baseline reinforcement rate and resurgence of destructive behavior. Journal of the Experimental Analysis of Behavior, 111(1), 75–93. https://doi.org/10.1002/jeab.488
Fisher, W. W., Fuhrman, A. M., Greer, B. D., Mitteer, D. R., & Piazza, C. C. (2020). Mitigating resurgence of destructive behavior using the discriminative stimuli of a multiple schedule. Journal of the Experimental Analysis of Behavior, 113(1), 263–277. https://doi.org/10.1002/jeab.552
Frank-Crawford, M. A., Borrero, J. C., Newcomb, E. T., Doan, T., Fisher, A., & Rooker, G. W. (2021). Accumulated and distributed response–reinforcer arrangements during the treatment of escape-maintained problem behavior. Journal of Applied Behavior Analysis, 54(4), 1566–1585. https://doi.org/10.1002/jaba.870
Fuhrman, A. M., Fisher, W. W., & Greer, B. D. (2016). A preliminary investigation on improving functional communication training by mitigating resurgence of destructive behavior. Journal of Applied Behavior Analysis, 49(4), 884–899. https://doi.org/10.1002/jaba.338
Fuhrman, A. M., Lambert, J. M., & Greer, B. D. (2022). A brief review of expanded-operant treatments for mitigating resurgence. The Psychological Record, 72(2), 319–323. https://doi.org/10.1007/s40732-021-00456-z
Greer, B. D., & Shahan, T. A. (2019). Resurgence as choice: Implications for promoting durable behavior change. Journal of Applied Behavior Analysis, 52(3), 816–846. https://doi.org/10.1002/jaba.573
Greer, B. D., Fisher, W. W., Saini, V., Owen, T. M., & Jones, J. K. (2016). Functional communication training during reinforcement schedule thinning: An analysis of 25 applications. Journal of Applied Behavior Analysis, 49(1), 105–121. https://doi.org/10.1002/jaba.265
Greer, B. D., Fisher, W. W., Retzlaff, B. J., & Fuhrman, A. M. (2020). A preliminary evaluation of treatment duration on the resurgence of destructive behavior. Journal of the Experimental Analysis of Behavior, 113(1), 251–262. https://doi.org/10.1002/jeab.567
Hagopian, L. P., Fisher, W. W., Sullivan, M. T., Acquisto, J., & LeBlanc, L. A. (1998). Effectiveness of functional communication training with and without extinction and punishment: A summary of 21 inpatient cases. Journal of Applied Behavior Analysis, 31(2), 211–235. https://doi.org/10.1901/jaba.1998.31-211
Hagopian, L. P., Toole, L. M., Long, E. S., Bowman, L. G., & Lieving, G. A. (2004). A comparison of dense-to-lean and fixed lean schedules of alternative reinforcement and extinction. Journal of Applied Behavior Analysis, 37(3), 323–338. https://doi.org/10.1901/jaba.2004.37-323
Hagopian, L. P., Boelter, E. W., & Jarmolowicz, D. P. (2011). Reinforcement schedule thinning following functional communication training: Review and recommendations. Behavior Analysis in Practice, 4(1), 4–16. https://doi.org/10.1007/BF03391770
Herrnstein, R. J. (1970). On the law of effect. Journal of Experimental Analysis of Behavior, 13(2), 243–266. https://doi.org/10.1901/jeab.1970.13-243
Jacobs, K. W., Morford, Z. H., King, J. E., & Hayes, L. J. (2017). Predicting the effects of interventions: A tutorial on the disequilibrium model. Behavior Analysis in Practice, 10(1), 195–208. https://doi.org/10.1007/s40617-017-0176-x
Killeen, P. R. (1981). Incentive theory. In Nebraska Symposium on Motivation (Vol. 29, pp. 169–216). University of Nebraska Press.
Killeen, P. R. (1994). Mathematical principles of reinforcement. Behavioral and Brain Sciences, 17(1), 105–135. https://doi.org/10.1017/S0140525X00033628
Kimball, R. T., Greer, B. D., Fuhrman, A. M., & Lambert, J. M. (2023). Relapse and its mitigation: Toward behavioral inoculation. Journal of Applied Behavior Analysis, 1–20. Advance online publication. https://doi.org/10.1002/jaba.971
Kranak, M. P., & Falligant, J. M. (2021). Further investigation of resurgence following schedule thinning: Extension to an inpatient setting. Behavioral Interventions, 36(4), 1003–1012. https://doi.org/10.1002/bin.1831
Kurtz, P. F., Boelter, E. W., Jarmolowicz, D. P., Chin, M. D., & Hagopian, L. P. (2011). An analysis of functional communication training as an empirically supported treatment for problem behavior displayed by individuals with intellectual disabilities. Research in Developmental Disabilities, 32(6), 2935–2942. https://doi.org/10.1016/j.ridd.2011.05.009
Lasdon, L. S., Waren, A. D., Jain, A., & Ratner, M. (1978). Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Transactions on Mathematical Software (TOMS), 4(1), 34–50. https://doi.org/10.1145/355769.355773
Lattal, K. A., & Wacker, D. (2015). Some dimensions of recurrent operant behavior. Revista Mexicana de Análisis de la Conducta, 41(2), 1–13. https://doi.org/10.5514/rmac.v41.i2.63716
Lattal, K. A., Cançado, C. R., Cook, J. E., Kincaid, S. L., Nighbor, T. D., & Oliver, A. C. (2017). On defining resurgence. Behavioural Processes, 141(1), 85–91. https://doi.org/10.1016/j.beproc.2017.04.018
Leitenberg, H., Rawson, R. A., & Mulick, J. A. (1975). Extinction and reinforcement of alternative behavior. Journal of Comparative and Physiological Psychology, 88(2), 640–652. https://doi.org/10.1037/h0076418
Lieving, G. A., & Lattal, K. A. (2003). Recency, repeatability, and reinforcer retrenchment: An experimental analysis of resurgence. Journal of the Experimental Analysis of Behavior, 80(2), 217–233. https://doi.org/10.1901/jeab.2003.80-217
Marsteller, T. M., & St Peter, C. C. (2012). Resurgence during treatment challenges. Revista Mexicana de Análisis de la Conducta, 38(1), 7–23. Retrieved April 2023, from https://www.redalyc.org/pdf/593/59335804002.pdf
Mazur, J. E. (1996). Procrastination by pigeons: Preference for larger, more delayed work requirements. Journal of the Experimental Analysis of Behavior, 65(1), 159–171. https://doi.org/10.1901/jeab.1996.65-159
McDowell, J. J. (2005). On the classic and modern theories of matching. Journal of the Experimental Analysis of Behavior, 84(1), 111–127. https://doi.org/10.1901/jeab.2005.59-04
Mitteer, D. R., Greer, B. D., Randall, K. R., & Haney, S. D. (2022). On the scope and characteristics of relapse when treating severe destructive behavior. Journal of Applied Behavior Analysis, 55(3), 688–703. https://doi.org/10.1002/jaba.912
Muething, C., Pavlov, A., Call, N., Ringdahl, J., & Gillespie, S. (2021). Prevalence of resurgence during thinning of multiple schedules of reinforcement following functional communication training. Journal of Applied Behavior Analysis, 54(2), 813–823. https://doi.org/10.1002/jaba.791
Nevin, J. A., & Grace, R. C. (2000). Behavioral momentum and the law of effect. The Behavioral and Brain Sciences, 23(1), 73–90. https://doi.org/10.1017/S0140525X00002405
Nevin, J. A., & Wacker, D. P. (2013). Response strength and persistence. In G. J. Madden, W. V. Dube, T. D. Hackenberg, G. P. Hanley, & K. A. Lattal (Eds.), APA handbook of behavior analysis, Vol. 2. Translating principles into practice (pp. 109–128). American Psychological Association. https://doi.org/10.1037/13938-005
Newcomb, E. T., Wright, J. A., & Camblin, J. G. (2019). Assessment and treatment of aggressive behavior maintained by access to physical attention. Behavior Analysis: Research & Practice, 19(3), 222–231. https://doi.org/10.1037/bar0000136
Nuta, R., Koudys, J., & O'Neill, P. (2021). Parent treatment integrity across multiple components of a behavioral intervention. Behavioral Interventions, 36(4), 796–816. https://doi.org/10.1002/bin.1817
Podlesnik, C. A., Ritchey, C. M., Kuroda, T., & Cowie, S. (2022). A quantitative analysis of the effects of alternative reinforcement rate and magnitude on resurgence. Behavioural Processes, 198, Article 104641. https://doi.org/10.1016/j.beproc.2022.104641
Reed, D. D., & Kaplan, B. A. (2011). The matching law: A tutorial for practitioners. Behavior Analysis in Practice, 4(2), 15–24. https://doi.org/10.1007/BF03391780
Reed, D. D., Kaplan, B. A., & Brewer, A. T. (2012). Tutorial on the use of Excel 2010 and Excel for Mac 2011 for conducting delay-discounting analyses. Journal of Applied Behavior Analysis, 45(2), 375–386. https://doi.org/10.1901/jaba.2012.45-375
Reed, D. D., Niileksela, C. R., & Kaplan, B. A. (2013). Behavioral economics: A tutorial for behavior analysts in practice. Behavior Analysis in Practice, 6(1), 34–54. https://doi.org/10.1007/BF03391790
Rooker, G. W., Jessel, J., Kurtz, P. F., & Hagopian, L. P. (2013). Functional communication training with and without alternative reinforcement and punishment: An analysis of 58 applications. Journal of Applied Behavior Analysis, 46(4), 708–722. https://doi.org/10.1002/jaba.76
Saini, V., Miller, S. A., & Fisher, W. W. (2016). Multiple schedules in practical application: Research trends and implications for future investigation. Journal of Applied Behavior Analysis, 49(2), 421–444. https://doi.org/10.1002/jaba.300
Saini, V., Fisher, W. W., & Pisman, M. D. (2017). Persistence during and resurgence following noncontingent reinforcement implemented with and without extinction. Journal of Applied Behavior Analysis, 50(2), 377–392. https://doi.org/10.1002/jaba.380
Schepers, S. T., & Bouton, M. E. (2015). Effects of reinforcer distribution during response elimination on resurgence of an instrumental behavior. Journal of Experimental Psychology: Animal Learning & Cognition, 41(2), 179–192. https://doi.org/10.1037/xan0000061
Shahan, T. A., & Craig, A. R. (2017). Resurgence as choice. Behavioural Processes, 141(1), 100–127. https://doi.org/10.1016/j.beproc.2016.10.006
Shahan, T. A., & Greer, B. D. (2021). Destructive behavior increases as a function of reductions in alternative reinforcement during schedule thinning: A retrospective quantitative analysis. Journal of the Experimental Analysis of Behavior, 116(2), 243–248. https://doi.org/10.1002/jeab.708
Shahan, T. A., Browning, K. O., & Nall, R. W. (2020a). Resurgence as choice in context: Treatment duration and on/off alternative reinforcement. Journal of the Experimental Analysis of Behavior, 113(1), 57–76. https://doi.org/10.1002/jeab.563
Shahan, T. A., Browning, K. O., Nist, A. N., & Sutton, G. M. (2020b). Resurgence and downshifts in alternative reinforcement rate. Journal of the Experimental Analysis of Behavior, 114(2), 163–178. https://doi.org/10.1002/jeab.625
Smith, S. W., & Greer, B. D. (2022). Phase duration and resurgence. Journal of the Experimental Analysis of Behavior, 117(1), 91–104. https://doi.org/10.1002/jeab.725
Smith, B. M., Smith, G. S., Shahan, T. A., Madden, G. J., & Twohig, M. P. (2017). Effects of differential rates of alternative reinforcement on resurgence of human behavior. Journal of the Experimental Analysis of Behavior, 107(1), 191–202. https://doi.org/10.1002/jeab.241
St Peter Pipkin, C. S. P., Vollmer, T. R., & Sloman, K. N. (2010). Effects of treatment integrity failures during differential reinforcement of alternative behavior: A translational model. Journal of Applied Behavior Analysis, 43(1), 47–70. https://doi.org/10.1901/jaba.2010.43-47
Sterling-Turner, H. E., & Watson, T. S. (2002). An analog investigation of the relationship between treatment acceptability and treatment integrity. Journal of Behavioral Education, 11(1), 39–50. https://doi.org/10.1023/A:1014333305011
Sweeney, M. M., & Shahan, T. A. (2013). Effects of high, low, and thinning rates of alternative reinforcement on response elimination and resurgence. Journal of the Experimental Analysis of Behavior, 100(1), 102–116. https://doi.org/10.1002/jeab.26
Trask, S., Keim, C. L., & Bouton, M. E. (2018). Factors that encourage generalization from extinction to test reduce resurgence of an extinguished operant response. Journal of the Experimental Analysis of Behavior, 110(1), 11–23. https://doi.org/10.1002/jeab.446
Volkert, V. M., Lerman, D. C., Call, N. A., & Trosclair-Lasserre, N. (2009). An evaluation of resurgence during treatment with functional communication training. Journal of Applied Behavior Analysis, 42(1), 145–160. https://doi.org/10.1901/jaba.2009.42-145
Vollmer, T. R., Peters, K. P., Kronfli, F. R., Lloveras, L. A., & Ibañez, V. F. (2020). On the definition of differential reinforcement of alternative behavior. Journal of Applied Behavior Analysis, 53(3), 1299–1303. https://doi.org/10.1002/jaba.701
Winterbauer, N. E., & Bouton, M. E. (2012). Effects of thinning the rate at which the alternative behavior is reinforced on resurgence of an extinguished instrumental response. Journal of Experimental Psychology: Animal Behavior Processes, 38(3), 279–291. https://doi.org/10.1037/a0028853
Acknowledgments
The authors acknowledge Jasmeen Kaur, Nathalie Fernandez, Brittney Workman, and Hailee Hall for their helpful feedback on prior drafts of this article. The authors also thank the anonymous reviewers with their invaluable feedback on the learning activities and template.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of Interest
On behalf of all authors, there are no conflicts of interest to report.
Informed Consent
This study did not involve research with humans or animals, and informed consent was not applicable.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Laureano, B., Falligant, J.M. Modeling Behavioral Persistence with Resurgence as Choice in Context (RaC2): A Tutorial. Behav Analysis Practice 16, 640–651 (2023). https://doi.org/10.1007/s40617-023-00796-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40617-023-00796-y