A mathematical model of psychotherapy: An investigation using dynamic non-linear equations to model the therapeutic relationship

References

• Aharonovich , E. , Amrhein , P. , Bisaga , A. , Nunes , E. , & Hasin , D. 2008 Cognition, commitment language, and behavior change among cocaine-dependent patients . Psychology of Addictive Behaviors , 22 4 , 557 – 562 . doi: 10.1037/a0012971 .
   PubMed Web of Science ®Google Scholar
• Anderson , T. , Lunnen , K.M. and Ogles , B.M. 2010 . “ Putting models and techniques in context ” . In The heart and soul of change: delivering what works in therapy , 2nd ed , Edited by: Duncan , B.L. , Miller , S.D. , Wampold , B.E. and Hubble , M.A. 143 – 166 . Washington , DC : American Psychological Association .
   Google Scholar
• Barrett , M.S. , Chua , W.-J. , Crits-Christoph , P. , Gibbons , M.B. , & Thompson , D. 2008 Early withdrawal from mental health treatment: Implications for psychotherapy practice . Psychotherapy: Theory, Research, Practice, Training , 45 , 247 – 267 . doi: 10.1037/0033-3204.45.2.247 .
   PubMed Web of Science ®Google Scholar
• Bohart , A.C. and Tallman , K. 2010 . “ Clients: The neglected common factor ” . In The heart and soul of change: delivering what works in therapy , 2nd ed , Edited by: Duncan , B.L. , Miller , S.D. , Wampold , B.E. and Hubble , M.A. 83 – 112 . Washington , DC : American Psychological Association .
   Google Scholar
• Centorrino , F. , Hernan , M.A. , Drago-Ferrante , G. , Rendall , M. , Apicella , A. , Langar , G. and Baldessarini , R.J. 2001 . Factors associated with noncompliance with psychiatric outpatient visits . Psychiatric Services , 52 ( 3 ) : 378 – 380 .
   PubMed Web of Science ®Google Scholar
• Coan , J.A. and Gottman , J.M. 2007 . Sampling, experimental central and generalizability in the study of marital process models . Journal of Marriage and the Family , 69 : 73 – 80 .
   Web of Science ®Google Scholar
• Cook , J. , Tyson , R. , White , J. , Rushe , R. , Gottman , J. and Murray , J. 1995 . Mathematics of marital conflict: Qualitative dynamic mathematical modeling of marital interaction . Journal of Family Psychology , 9 ( 2 ) : 110 – 130 .
   Web of Science ®Google Scholar
• Duncan , B.L. , Miller , S.D. , Wampold , B.E. , & Hubble , M.A. 2010 The heart and soul of change: Delivering what works in therapy. , (2nd ed.) Washington , DC : American Psychological Association.
   Google Scholar
• Gardener , B.C , Burr , K.B. , & Wiedower , S.E. 2006 . Reconceptualizing strategic family therapy: Insights from a dynamic systems perspective . Contemporary Family Therapy , 28 , 339 – 352 . doi: 10.1007/s10591-006-9007-x .
   Google Scholar
• Gelso , C.J. 2009 The real relationship in a postmodern world: Theoretical and empirical explorations . Psychotherapy Research , 19 3 , 253 – 264 . doi: 10.1080/10503300802389242 .
   PubMed Web of Science ®Google Scholar
• Gelso , C.J. and Hayes , J.A. 2002 . “ The management of countertransferrence ” . In Psychotherapy relationships that work: therapist contributions and responsiveness to patient needs , Edited by: Norcross , J.C. 267 – 284 . New York , NY : Oxford University Press .
   Google Scholar
• Gottman , J.M. , Carrère , S. , Swanson , C. and Coan , J.A. 2000 . Reply to “From basic research to interventions” . Journal of Marriage and the Family , 62 : 265 – 273 .
   Web of Science ®Google Scholar
• Gottman , J.M. , Coan , J.A. , Carrère , S. and Swanson , C. 1998 . Predicting marital happiness and stability from newlywed interactions . Journal of Marriage and the Family , 60 : 5 – 22 .
   Web of Science ®Google Scholar
• Gottman , J.M. , McCoy , K. , Coan , J. and Collier , H. 1996 . “ The Specific Affect Coding System (SPAFF) ” . In What predicts divorce? The measures , Edited by: Gottman , J.M. Mahwah , NJ : Lawrence Erlbaum .
   Google Scholar
• Gottman , J. , Murray , J. , Swanson , C. , Tyson , R. and Swanson , K. 2002 . The mathematics of marriage: dynamic nonlinear models , Cambridge , MA : MIT Press .
   Google Scholar
• Gottman , J.M. and Notarius , C. 2000 . Decade review: Observing marital interaction . Journal of Marriage and the Family , 62 : 927 – 947 .
   Web of Science ®Google Scholar
• Gottman , J.M. and Notarius , C. 2002 . Marital research in the 20th Century and a research agenda for the 21st Century . Family Process , 41 : 159 – 197 .
   PubMed Web of Science ®Google Scholar
• Gottman , J.M. , Swanson , C. and Swanson , K. 2002 . A general systems theory of marriage: Nonlinear difference modeling of marital interaction . Personality and Social Psychology Review , 6 : 326 – 340 .
   Web of Science ®Google Scholar
• Granic , I. , & Hollenstein , T. 2003 Dynamic systems methods for models of developmental psychopathology . Development and Psychopathology , 15 , 641 – 669 . doi: 10.1017.S0954579403000324 .
   PubMed Web of Science ®Google Scholar
• Granic , I. and Lamey , A.V. 2002 . Combining dynamic systems and multivariate analyses to compare the mother-child interactions of externalizing subtypes . Journal of Abnormal Child Psychology , 30 : 265 – 283 .
   PubMed Web of Science ®Google Scholar
• Greenson , R.R. 1965 . The working alliance and the transference neurosis . Psychoanalysis Quarterly , 34 : 155 – 181 .
   PubMed Web of Science ®Google Scholar
• Greenson , R.R. 1967 . The technique and practice of psychoanalysis , Vol. 1 , Madison , CT : International Universities Press .
   Google Scholar
• Hamaker , E.L. , Zhang Z. , & Van der Maas , H.L. J. 2009 Using threshold autoregressive models to study dyadic interactions . Psychometrika , 74 , 727 – 745 . doi: 10.1007/s11336-009-9113-4 .
   Web of Science ®Google Scholar
• Heyman , R.E. 2001 . Observation of couple conflicts: Clinical assessment applications, stubborn truths, and shaky foundations . Psychological Assessment , 13 ( 1 ) : 5 – 35 .
   PubMed Web of Science ®Google Scholar
• Heyman , R.E. and Slep , A.M. 2001 . The hazards of predicting divorce without crossvalidation . Journal of Marriage and the Family , 63 : 473 – 479 .
   PubMed Web of Science ®Google Scholar
• Hill , C.E. , & Knox , S. 2009 Processing the therapeutic relationship . Psychotherapy Research , 19 1 , 13 – 29 . doi: 10.1080/10503300802621206 .
   PubMed Web of Science ®Google Scholar
• Horvath , A.O. and Bedi , R.P. 2002 . “ The alliance ” . In Psychotherapy relationships that work: therapist contributions and responsiveness to patient needs , Edited by: Norcross , J.C. 37 – 70 . New York , NY : Oxford University Press .
   Google Scholar
• Horvath , A.O. , Del Re , A.C. , Fluckiger , C. , & Symonds , D. 2011 Alliance in individual psychotherapy . Psychotherapy , 48 1 , 9 – 16 . doi: 10.1037/a0022186 .
   PubMed Web of Science ®Google Scholar
• Kazdin , A.E. 2008 Evidence-Based treatment and Practice: New opportunities to bridge clinical research and practice, enhance the knowledge base, and improve patient care . American Psychologist. 63 146 – 159 . doi: 10.1037/0003–066X.63.3.146 .
   PubMed Web of Science ®Google Scholar
• Lambert , M.J. and Barley , D.E. 2002 . “ Research summary on the therapeutic relationship and psychotherapy outcomes ” . In Psychotherapy relationships that work: therapist contributions and responsiveness to patient needs , Edited by: Norcross , J.C. 17 – 32 . New York , NY : Oxford University Press .
   Google Scholar
• Liebovitch , L.S. , Naudot , V. , Vallacher , R. , Nowak , A. Bui-Wrzosinska , L. , and Coleman , P. 2008 Dynamics of two-actor cooperation-competition conflict models . Physica A , 387 , 6360 – 6378 . doi: 10.1016/j.physa.2008.07.020 .
   Web of Science ®Google Scholar
• Liebovitch , L.S. , Peluso , P.R. , Norman , M.D. , Su , J. , & Gottman , J.M. (in press). Mathematical model of the dynamics of psychotherapy . Cognitive Neurodynamics .
   Google Scholar
• Madhyastha T.M. , Hamaker , E.L. , and Gottman , J.M. 2011 Investigating spousal influence using moment to moment affect data from marital conflict . Journal of Family Psychology , 25 2 , 292 – 300 . doi: 10.1037/a0023028 .
   PubMed Web of Science ®Google Scholar
• Martin , D.J. , Garske , M.P. and Davis , M.K. 2000 . Relation of the therapeutic alliance with outcome and other variables: A meta-analytic review . The Journal of Consulting and Clinical Psychology , 68 : 438 – 450 .
   PubMed Web of Science ®Google Scholar
• Miller , W.R. and Rollnick , S. 2002 . Motivational interviewing: preparing people for change , 2nd ed. , New York , NY : Guilford Press .
   Google Scholar
• Mozdzierz , G. , Peluso , P.R. and Lisiecki , J. 2009 . Principles of counseling and psychotherapy: learning the essential domains and nonlinear thinking of master practitioners , New York , NY : Routledge .
   Google Scholar
• Muran , J.C. , Gorman , B.S. , Eubanks-Carter , C. , et al. 2009 The relationship of early alliance ruptures and their resolution to process and outcome in three time-limited psychotherapies for personality disorders . Psychotherapy Theory, Research, Practice, Training , 46 2 , 233 – 248 . doi: 10.1037/a0016085 .
   PubMed Web of Science ®Google Scholar
• National Institutes of Mental Health 2010 The numbers count: Mental disorders in America . Retrieved from http://www.nimh.nih.gov/health/publications/the-numbers-count-mental-disorders-in-america/index.shtml.
   Google Scholar
• Norcross , J.C. 2002 Psychotherapy relationships that work: therapist contributions and responsiveness to patient needs . New York , NY : Oxford University Press .
   Google Scholar
• Norcross , J.C. 2010 . “ The therapeutic relationship ” . In The heart and soul of change: delivering what works in therapy , 2nd ed , Edited by: Duncan , B.L. , Miller , S.D. , Wampold , B.E. and Hubble , M.A. 113 – 142 . Washington , DC : American Psychological Association .
   Google Scholar
• Norcross , J.C. , & Wampold , B.E. 2011 Evidence-based therapy relationship: Research conclusions and clinical practices . Psychotherapy , 48 1 , 98 – 102 . doi: 10.1037/a0022161 .
   PubMed Web of Science ®Google Scholar
• Orlinsky , D.E. , Grave , K. and Parks , B.K. 1994 . “ Process and outcome in psychotherapy ” . In Handbook of psychotherapy and behavior change , Edited by: Bergin , A.E. and Garfield , S.L. 257 – 310 . New York , NY : Wiley .
   Google Scholar
• Orlinsky , D.E. and Howard , K.E. 1977 . “ The thrapists's experience of psychotherapy ” . In Effective psychotherapy: a handbook of research , Edited by: Gurman , A.S. and Razin , A.M. 566 – 589 . New York , NY : Pergamon .
   Google Scholar
• Prochaska , J.O. and DiClemente , C.C. 2003 . “ The transtheoretical approach ” . In Handbook of psychotherapy integration , 2nd ed. , Edited by: Norcross , J.C. and Goldfried , M.R. 147 – 171 . New York , NY : Oxford University Press .
   Google Scholar
• Safran , J.D. , Muran , J.C. , & Eubanks-Carter , C. 2011 Repairing alliance ruptures . Psychotherapy , 48 1 , 80 – 87 . doi: 10.1037/a0022140 .
   PubMed Web of Science ®Google Scholar
• Safran , J.D. , Muran , J.C. , Samstang , L.W. and Stevens , C. 2002 . “ Repairing alliance ruptures ” . In Psychotherapy relationships that work: Therapist contributions and responsiveness to patient needs , Edited by: Norcross , J.C. 235 – 254 . New York : Oxford University Press .
   Google Scholar
• Skovholt , T.M. and Jennings , L. 2004 . Master therapists: exploring expertise in therapy and counseling , Boston : Allyn & Bacon .
   Google Scholar
• Stanley , S.M. , Bradbury , T.N. and Markman , H.J. 2000 . Structural flaws in the bridge from basic research on marriage interventions for couples . Journal of Marriage and the Family , 62 : 256 – 264 .
   Web of Science ®Google Scholar
• Vallacher , R.R. , Coleman , P.T. , Nowak , A. , and Bui-Wrzosinska , L. 2010 Rethinking intractable conflict: The perspective of dynamical systems . American Psychologist , 65 4 , 262 – 278 . doi: 10.137/a0019290 .
   PubMed Web of Science ®Google Scholar
• Wampold , B.E. 2010 . “ The research evidence for common factors models: A historically situated perspective ” . In The heart and soul of change: delivering what works in therapy , 2nd ed , Edited by: Duncan , B.L. , Miller , S.D. , Wampold , B.E. and Hubble , M.A. 49 – 81 . Washington , DC : American Psychological Association .
   Google Scholar