Skip to main content

Advertisement

Log in

Psychometric Properties and Development of the Brief Adolescent Prosocial Perception Scales (BAPPS)

  • Original Paper
  • Published:
Journal of Child and Family Studies Aims and scope Submit manuscript

Abstract

Prosociality represents an important aspect of social functioning in adolescents and is related to the risk of psychological problems. The current paper describes the development and psychometric testing of two new short-form versions of prosocial perceptions named the Brief Adolescent Prosocial Perceptions Scale Self- (BAPPS-S) and Parent-report (BAPPS-P). Parent and child dyads (N = 3,976; 89 % White; aged 11–17 years) took part in a large cross-sectional survey. The BAPPS were completed alongside other measures of prosociality, social support and emotional and behavioural problems. Exploratory (n = 1,988) and confirmatory (n = 1,988) factor analysis supported a single factor solution that is related to, although separate from, conduct disorders. The scales showed good internal consistency and concurrent validity. Moreover, the BAPPS demonstrated incremental validity by accounting for significant variance in clinical outcome measures over and above that explained by existing measures of prosociality. The study demonstrated that the BAPPS have good initial psychometric properties. Potential clinical uses are discussed, including providing valuable information on young people’s strengths and resiliencies that can inform clinical formulation and intervention.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bailey, V. (1998). Conduct disorder in young children. In P. J. Graham (Ed.), Cognitive behaviour therapy for children and families (pp. 95–109). Cambridge: Cambridge University Press.

    Google Scholar 

  • Bandura, A., Pastorelli, C., Barbaranelli, C., & Caprara, G. V. (1999). Self-efficacy pathways to childhood depression. Journal of Personality and Social Psychology, 76, 258–269. doi:10.1037//0022-3514.76.2.258.

    Article  PubMed  Google Scholar 

  • Blechman, E. A., & Culhane, S. E. (1993). Aggressive, depressive, and prosocial coping with affective challenges in early adolescence. The Journal of Early Adolescence, 13, 361–382. doi:10.1177/0272431693013004002.

    Article  Google Scholar 

  • Byrne, B. M. (2001). Structural equation modelling with AMOS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Carlo, G., Padilla-Walker, L. M., & Day, R. D. (2011). A test of the economic strain model on adolescents’ prosocial behaviors. Journal of Research on Adolescence, 21, 842–848. doi:10.1111/j.1532-7795.2011.00742.x.

    Article  Google Scholar 

  • Chen, X., Li, D., Li, Z., Li, B., & Liu, M. (2000). Sociable and prosocial dimensions of social competence in Chinese children: Common and unique contributions to social, academic, and psychological adjustment. Developmental Psychology, 36, 302–314. doi:10.1037//0012-1649.36.3.302.

    Article  PubMed  Google Scholar 

  • Cohen, J. (1988). Statistical power analysis for the behavioural sciences. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Costello, A. B., & Osborne, J. W. (2005). Best practice in exploratory factor analysis: Recommendations for getting the most from your analysis. Practical Assessment Research & Practice, 10, 1–9. Retrieved from http://pareonline.net/getvn.asp?v=10&n=7.

  • Crick, N. R. (1996). The role of overt aggression, relational aggression, and prosocial behavior in the prediction of children’s future social adjustment. Child Development, 67, 2317. doi:10.2307/1131625.

    Article  PubMed  Google Scholar 

  • Culotta, C. M., & Goldstein, S. E. (2008). Adolescents’ aggressive and prosocial behavior: Associations with jealousy and social anxiety. The Journal of Genetic Psychology, 169, 21–33. doi:10.3200/GNTP.169.1.21-33.

    Article  PubMed  Google Scholar 

  • De Los Reyes, A., & Kazdin, A. E. (2005). Informant discrepancies in the assessment of childhood psychopathology: A critical review, theoretical framework, and recommendations for further study. Psychological Bulletin, 131, 483–509. doi:10.1037/0033-2909.131.4.483.

    Article  PubMed  Google Scholar 

  • Dicky, W. C., & Blumberg, S. J. (2004). Revising the factor structure of the strengths and difficulties questionnaire: United States, 2001. Journal of the American Academy of Child and Adolescent Psychiatry, 43, 1159–1167. doi:10.1097/01.chi.0000132808.36708.a9.

    Article  Google Scholar 

  • Eisenberg, N., & Fabes, R. A. (1998). Prosocial development. In N. Eisenberg (Ed.), Handbook of child psychology. Social, emotional and personality development (Vol. 3, pp. 701–778). New York: Wiley.

    Google Scholar 

  • Eisenberg, N., Fabes, R. A., Karbon, M., Murphy, B. C., Wosinski, M., Polazzi, L., et al. (1996). The relations of children’s dispositional prosocial behavior to emotionality, regulation, and social functioning. Child Development, 67, 974–992. doi:10.1111/j.1467-8624.1996.tb01777.x.

    Article  PubMed  Google Scholar 

  • Eisenberg, N., & Mussen, P. H. (1989). The roots of prosocial behavior in children. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Fabes, R. A., Carlo, G., Kupanoff, K., & Laible, D. (1999). Early adolescence and prosocial/moral behavior I: The role of individual processes. The Journal of Early Adolescence, 19, 5–16. doi:10.1177/0272431699019001001.

    Article  Google Scholar 

  • Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272–299. doi:10.1037/1082-989X.4.3.272.

    Article  Google Scholar 

  • Ford, T., Tingay, K., & Wolpert, M. (2006). CORC’s survey of routine outcome monitoring and national CAMHS dataset developments: A response to Johnston and Gower. Child and Adolescent Mental Health, 11, 50–52. doi:10.1111/j.1475-3588.2005.00390.x.

    Article  Google Scholar 

  • Gaderman, A. M., Guhn, M., & Zumbo, B. D. (2012). Estimating ordinal reliability for likert-type and ordinal item response data: A conceptual, empirical, and practical guide. Practical Assessment, Research & Evaluation, 17. Retrieved from http://pareonline.net/getvn.asp?v=17&n=3.

  • Goodman, R. (2001). Psychometric properties of the strengths and difficulties questionnaire. Journal of the American Academy of Child and Adolescent Psychiatry, 40, 1337–1345. doi:10.1097/00004583-200111000-00015.

    Article  PubMed  Google Scholar 

  • Goodman, R., Ford, T., Corbin, T., & Meltzer, H. (2004). Using the Strengths and Difficulties Questionnaire (SDQ) multi-informant algorithm to screen looked-after children for psychiatric disorders. European Child and Adolescent Psychiatry, 13(Suppl. 2), 25–31. doi:10.1007/s00787-004-2005-3.

    Google Scholar 

  • Goodman, R., Ford, T., Richards, H., Gatward, R., & Meltzer, H. (2000). The development and well-being assessment: Description and initial validation of an integrated assessment of child and adolescent psychopathology. Journal of Child Psychology and Psychiatry, 41, 645–55. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/10946756.

    Google Scholar 

  • Green, H., McGinnity, A., Meltzer, H., Ford, T., & Goodman, R. (2005). Mental health of children and young people in Great Britain. London: The Stationary Office.

    Google Scholar 

  • Greener, S. H. (2000). Peer assessment of children’s prosocial behaviour. Journal of Moral Education, 29, 47–60. doi:10.1080/030572400102925.

    Article  Google Scholar 

  • Greener, S. H., & Crick, N. R. (1999). Normative beliefs about prosocial behaviour in middle childhood: What does it mean to be nice? Social Development, 8, 349–363. doi:10.1111/1467-9507.00100.

    Article  Google Scholar 

  • Gresham, F. M., Cook, C. R., Crews, S. D., & Kern, L. (2004). Social skills training for children and youth with emotional and behavioral disorders: Validity considerations and future directions. Behavioral Disorders, 30, 32–46. Retrieved from www.ccbd.net/sites/default/files/BDv30n1 Gresham.pdf.

  • Gresham, F. M., & Elliot, S. N. (1990). Social skills rating system. Minneapolis, MN: NCS Pearson.

    Google Scholar 

  • Haroz, E. E., Murray, L. K., Bolton, P., Betancourt, T., & Bass, J. K. (2013). Adolescent resilience in Northern Uganda: The role of social support, prosocial behaviour in reducing mental health problems. Journal of Research on Adolescence, 23, 138–148. doi:10.1111/j.1532-7795.2012.00802.x.

    Article  Google Scholar 

  • Harter, S. (1999). The construction of the self: A developmental perspective. New York: Guilford Press.

    Google Scholar 

  • Hay, D. F. (1994). Prosocial development. Journal of Child Psychology and Psychiatry, 35, 29–71. doi:10.1111/j.1469-7610.1994.tb01132.x.

    Article  PubMed  Google Scholar 

  • Hay, D. F., & Pawlby, S. (2003). Prosocial development in relation to children’s and mothers’ psychological problems. Child Development, 74, 1314–1327. doi:10.1111/1467-8624.00609.

    Article  PubMed  Google Scholar 

  • Hay, D. F., Payne, A., & Chadwick, A. (2004). Peer relations in childhood. Journal of Child Psychology and Psychiatry, 45, 84–108. doi:10.1046/j.0021-9630.2003.00308.x.

    Article  PubMed  Google Scholar 

  • Haynes, S. N., & Lench, H. C. (2003). Incremental validity of new clinical assessment measures. Psychological Assessment, 15, 456–466. doi:10.1037/1040-3590.15.4.456.

    Article  PubMed  Google Scholar 

  • Holgado-Tello, F. P., Chacón, S., Barbero-Garcia, I., & Vila-Abad, E. (2010). Polychoric cersus person correlations in exploratory and confirmatory factor analysis of ordinal variables. Quality & Quantity, 44, 153–166. doi:10.1007/s11135-008-9190-y.

    Article  Google Scholar 

  • Howell, D. (2007). Statistical methods for psychology (6th ed.). Belmont, CA: Thomson/Wadsworth.

    Google Scholar 

  • Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modelling: A Multidisciplinary Journal, 6, 1–55. doi:10.1080/10705519909540118.

    Article  Google Scholar 

  • Johnson, J., Wood, A. M., Gooding, P., Taylor, P. J., & Tarrier, N. (2011). Resilience to suicidality: The buffering hypothesis. Clinical Psychology Review, 31, 563–591. doi:10.1016/j.cpr.2010.12.007.

    Article  PubMed  Google Scholar 

  • Joseph, S., & Wood, A. (2010). Assessment of positive functioning in clinical psychology: Theoretical and practical issues. Clinical Psychology Review, 30, 830–838. doi:10.1016/j.cpr.2010.01.002.

    Article  PubMed  Google Scholar 

  • Kim, Y.-H., & Chiu, C.-Y. (2011). Emotional costs of inaccurate self-assessments: Both self-effacement and self-enhancement can lead to dejection. Emotion, 11, 1096–1104. doi:10.1037/a0025478.

    Article  PubMed  Google Scholar 

  • Kim, H. K., & Leve, L. D. (2011). Substance use and delinquency among middle school girls in foster care: A three-year follow-up of a randomized controlled trial. Journal of Consulting and Clinical Psychology, 79, 740–750. doi:10.1037/a0025949.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ladd, G. W., Herald-Brown, S. L., & Andrews, R. K. (2009). The Child Behavior Scale (CBS) revisited: A longitudinal evaluation of CBS subscales with children, preadolescents, and adolescents. Psychological Assessment, 21, 325–339. doi:10.1037/a0016205.

    Article  PubMed  Google Scholar 

  • Ladd, G. W., & Profilet, S. M. (1996). The Child Behavior Scale: A teacher-report measure of young children’s aggressive, withdrawn, and prosocial behaviors. Developmental Psychology, 32, 1008–1024. doi:10.1037/0012-1649.32.6.1008.

    Article  Google Scholar 

  • Laye-Gindhu, A., & Schonert-Reichl, K. A. (2005). Nonsuicidal self-harm among community adolescents: Understanding the “whats” and “whys” of self-harm. Journal of Youth and Adolescence, 34, 447–457. doi:10.1007/s10964-005-7262-z.

    Article  Google Scholar 

  • Layous, K., Nelson, S. K., Oberle, E., Schonert-Reichl, K. A., & Lyubomirsky, S. (2012). Kindness counts: Prompting prosocial behavior in preadolescents boosts peer acceptance and well-being. PLoS One, 7, e51380. doi:10.1371/journal.pone.0051380.

    Article  PubMed  PubMed Central  Google Scholar 

  • Linley, P. A., Maltby, J., Wood, A. M., Osborne, G., & Hurling, R. (2009). Measuring happiness: The higher order factor structure of subjective and psychological well-being measures. Personality and Individual Differences, 47, 878–884. doi:10.1016/j.paid.2009.07.010.

    Article  Google Scholar 

  • Lyons, M. D., Huebner, E. S., Hills, K. J., & Shinkareva, S. V. (2012). The dual-factor model of mental health: Further study of the determinants of group differences. Canadian Journal of School Psychology, 27, 183–196. doi:10.1177/0829573512443669.

    Article  Google Scholar 

  • McCrystal, P., Percy, A., & Higgins, K. (2007). Exclusion and marginalisation in adolescence: The experience of school exclusion on drug use and antisocial behaviour. Journal of Youth Studies, 10, 35–54. doi:10.1080/13676260701196103.

    Article  Google Scholar 

  • McCullough, M. E., Emmons, R. A., & Tsang, J.-A. (2002). The grateful disposition: A conceptual and empirical topography. Journal of Personality and Social Psychology, 82, 112–127. doi:10.1037//0022-3514.82.1.112.

    Article  PubMed  Google Scholar 

  • Oberle, E., Schonert-Reichl, K. A., & Thomson, K. C. (2010). Understanding the link between social and emotional well-being and peer relations in early adolescence: Gender-specific predictors of peer acceptance. Journal of Youth and Adolescence, 39, 1330–1342. doi:10.1007/s10964-009-9486-9.

    Article  PubMed  Google Scholar 

  • O’Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test. Behavior Research Methods, Instrumentation, and Computers, 32, 396–402. doi:10.3758/BF03200807.

    Article  Google Scholar 

  • Office of National Statistics Social and Vital Statistics Division. (2004). Mental health of children and young people in Great Britain, 2004. Colchester, Essex: UK Data Archive.

    Google Scholar 

  • Olsson, C. A., Bond, L., Burns, J. M., Vella-Brodrick, D. A., & Sawyer, S. M. (2003). Adolescent resilience: A concept analysis. Journal of Adolescence, 26, 1–11. doi:10.1016/S0140-1971(02)00118-5.

    Article  PubMed  Google Scholar 

  • Padesky, C. A., & Mooney, K. A. (2012). Strengths-based cognitive behavioural therapy: A four-step model to build resilience. Clinical Psychology & Psychotherapy, 19, 283–290. doi:10.1002/cpp.1795.

    Article  Google Scholar 

  • Park, N. (2004). The role of subjective well-being in positive youth development. The Annals of the American Academy of Political and Social Science, 591, 25–39. doi:10.1177/0002716203260078.

    Article  Google Scholar 

  • Pastorelli, C., Barbaranelli, C., Cermak, I., Rozsa, S., & Caprara, G. V. (1997). Measuring emotional instability, prosocial behavior and aggression in pre-adolescents: A cross-national study. Personality and Individual Differences, 23, 691–703. doi:10.1016/S0191-8869(97)00056-1.

    Article  Google Scholar 

  • Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177. doi:10.1037//1082-989X.7.2.147.

    Article  PubMed  Google Scholar 

  • Scourfield, J., John, B., Martin, N., & McGuffin, P. (2004). The development of prosocial behaviour in children and adolescents: A twin study. Journal of Child Psychology and Psychiatry, 45, 927–935. doi:10.1111/j.1469-7610.2004.t01-1-00286.x.

    Article  PubMed  Google Scholar 

  • StataCorp. (2011). Stata structural equation modelling reference manual. College Station, TX: StataCorp LP.

    Google Scholar 

  • Steinhausen, H.-C., Bősiger, R., & Metzke, C. W. (2006). Stability, correlates, and outcomes of adolescent suicidal risk. Journal of Child Psychology and Psychiatry, 47, 713–722. doi:10.1111/j.1469-7610.2005.01569.x.

    Article  PubMed  Google Scholar 

  • Suldo, S., Thalji, A., & Ferron, J. (2011). Longitudinal academic outcomes predicted by early adolescents’ subjective well-being, psychopathology, and mental health status yielded from a dual factor model. The Journal of Positive Psychology, 6, 17–30. doi:10.1080/17439760.2010.536774.

    Article  Google Scholar 

  • Tam, V. C. (2008). Coping profiles among Chinese adolescents in Hong Kong: A person-centered approach. International Journal of Adolescent Medicine and Health, 20, 73–83. doi:10.1515/IJAMH.2008.20.1.73.

    Article  PubMed  Google Scholar 

  • Taylor, P. J., & Wood, A. M. (2012). Discrepancies in parental and self-appraisals of prosocial characteristics predict emotional problems in adolescents. British Journal of Clinical Psychology. doi:10.1111/bjc.12013.

  • Tedeschi, R. G., & Kilmer, R. P. (2005). Assessing strengths, resilience, and growth to guide clinical interventions. Professional Psychology: Research and Practice, 36, 230–237. doi:10.1037/0735-7028.36.3.230.

    Article  Google Scholar 

  • Tremblay, R. E., Loeber, R., Gagnon, C., Charlebois, P., Larivée, S., & LeBlanc, M. (1991). Disruptive boys with stable and unstable high fighting behaviour patterns during junior elementary school. Journal of Abnormal Child Psychology, 19, 285–300. doi:10.1007/BF00911232.

    Article  PubMed  Google Scholar 

  • Van Roy, B., Groholt, B., Heyerdahl, S., & Clench-Aas, J. (2010). Understanding discrepancies in parent–child reporting of emotional and behavioural problems: Effects of relational and socio-demographic factors. BMC Psychiatry, 10, 1–12. doi:10.1186/1471-244X-10-56.

    Article  Google Scholar 

  • Van Roy, B., Veenstra, M., & Clench-Aas, J. (2008). Construct validity of the five-factor strengths and difficulties questionnaire (SDQ) in pre-, early- and late-adolescence. The Journal of Child Psychology and Psychiatry, 49, 1304–1313. doi:10.1111/j.1469-7610.2008.01942.x.

    Article  Google Scholar 

  • Weir, K., & Duveen, G. (1981). Further development and validation of the prosocial behavior questionnaire for use by teachers. Journal of Child Psychology and Psychiatry, 22, 357–374. doi:10.1111/j.1469-7610.1981.tb00561.x.

    Article  PubMed  Google Scholar 

  • Wentzel, K. R., Filisetti, L., & Looney, L. (2007). Adolescent prosocial behavior: The role of self-processes and contextual cues. Child Development, 78, 895–910. doi:10.1111/j.1467-8624.2007.01039.x.

    Article  PubMed  Google Scholar 

  • Weston, R., & Gore, P. A. (2006). A brief guide to structural equation modelling. The Counseling Psychologist, 34, 719–751. doi:10.1177/0011000006286345.

    Article  Google Scholar 

  • Whiteside, S. P., McCarthy, D. M., & Miller, J. D. (2007). An examination of the factor structure of the social skills rating system parent elementary form. Assessment, 14, 246–254. doi:10.1177/1073191107302062.

    Article  PubMed  Google Scholar 

  • Wood, A. M., & Joseph, S. (2010). The absence of positive psychological (eudemonic) wellbeing as a risk factor for depression: A ten year cohort study. Journal of Affective Disorders, 122, 213–217. doi:10.1016/j.jad.2009.06.032.

    Article  PubMed  Google Scholar 

  • Wood, A. M., & Tarrier, N. (2010). Positive clinical psychology: A new vision and strategy for integrated research and practice. Clinical Psychology Review, 30, 819–829. doi:10.1016/j.cpr.2010.06.003.

    Article  PubMed  Google Scholar 

  • Worthington, R. L., & Whittaker, T. A. (2006). Scale development research: A content analysis and recommendations for best practices. The Counseling Psychologist, 34, 806–838. doi:10.1177/0011000006288127.

    Article  Google Scholar 

  • Zahn-Waxler, C., Shirtcliff, E. A., & Marceau, K. (2008). Disorders of childhood and adolescence: Gender and psychopathology. Annual Review of Clinical Psychology, 4, 275–303. doi:10.1146/annurev.clinpsy.3.022806.091358.

    Article  PubMed  Google Scholar 

  • Zimmer-Gembeck, M. J., Hunter, T. A., & Pronk, R. (2007). A model of behaviors, peer relations and depression: Perceived social acceptance as a mediator and the divergence of perceptions. Journal of Social and Clinical Psychology, 26, 273–302. doi:10.1521/jscp.2007.26.3.273.

    Article  Google Scholar 

  • Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442. doi:10.1037/0033-2909.99.3.43.

    Article  Google Scholar 

Download references

Acknowledgments

The data used in this paper were from the “mental health of children and young people in Great Britain, 2004” survey, commissioned by the department of health and the Scottish executive health department and undertaken by the Office of National Statistics. Data from this survey have been made available for research via the UK data archive (www.data-archive.ac.uk). These data have received crown copyright. The UK data archive, data commissioners, creators, depositors and copyright holders bear no responsibility for the analysis or interpretation of the data in the current study. Thanks go to Dr. Hannah Taylor, Dr. Zoe Tsivou and Dr. Wendy MacDonald for their assistance in this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter J. Taylor.

Appendices

Appendix 1: Initial BAPPS Item Set

BAPPS-S

BAPPS-P

Caring/kind hearted

Reliable and responsible

Nice personality

Well behaved

Generous

Keen to learn

Well behaved

Grateful/appreciative

Polite

Good at school work

Good at school work

Interested in many thingsa

Reliable and responsible

Polite

Raising money for charity/helping others

Caring/kind hearted

Good with friends

Gets on well with rest of family

Good fun/good sense of humour

Good fun/good sense of humour

Easy-going

Likes family activities

Out-going/sociable

Easy-going

Helpful at home

Affectionate

Good at musica

Does homework without needing to be reminded

Good at drama/actinga

Good with friends

Independent

Generous

Good at art/making thingsa

Independent

Good with computersa

Bounces back quickly after set-backsa

Good at sporta

Takes care of appearancea

Helps around the home

Creative activities: art, acting, music, making thingsa

Keeps his/her bedroom tidy

Livelya

Good at sporta

  1. aItems excluded by judges from analysis

Appendix 2: Definition of Prosociality

Prosociality can be generally understood as a positive orientation towards ones social context. Prosociality involves a number of facets, representing dispositions towards particular patterns of behaviour. These include the following:

  1. a.

    Behaviours involving helping, caring for, sharing with or supporting others.

  2. b.

    Affiliative behaviours demonstrating interpersonal warmth, social co-operation or inclusiveness. These may include adopting a pleasant, warm or friendly demeanour, or adopting a supportive style of interaction with others.

  3. c.

    In some ways, prosocial behaviour can be seen as the opposite of anti-social behaviour. Anti-social behaviour can involve acts that are not directed at a specific individual, but jar against societal norms and values, for example, the young person who is untidy and disorganized, or uninterested and disruptive at school. Therefore, a further facet of prosocial behaviour may involve a consistency with ‘prosocial expectations’. This involves the extent to which young people meet the expectations and norms that are set by their parents, caregivers or other authority figures (e.g., teachers).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taylor, P.J., Wood, A.M. Psychometric Properties and Development of the Brief Adolescent Prosocial Perception Scales (BAPPS). J Child Fam Stud 23, 1417–1429 (2014). https://doi.org/10.1007/s10826-013-9798-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10826-013-9798-y

Keywords

Navigation