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Zhiyong Johnny Zhang

Professor of Quantitative Psychology
Director, Lab for Big Data Methodology
Fellow, Institute for Educational Initiatives
Fellow, American Psychological Association
Associate Editor, Multivariate Behavioral Research
Associate Editor, Neurocomputing
Editor, Journal of Behavioral Data Science

PhD, 2008, University of Virginia
438 Corbett Family Hall
Department of Psychology
University of Notre Dame

Tel: 574-631-2902
Voice: 574-626-8886
Fax: 574-631-8883
Email: ZhiyongZhang (at) nd.edu
Web: https://nd.psychstat.org
https://bigdatalab.nd.edu

Curriculum Vitae

Research interests

Our Lab for Big Data Methodology aims to develop better statistical methods and software in the areas of education, health, management and psychology. Our most recent research involves the development of new methods for social network and big data analysis. Particularly, we have contributed to the areas of Bayesian methods, Network analysis, Big data analysis, Structural equation modeling, Longitudinal data analysis, Mediation analysis, and Statistical computing and programming.

Publications

ResearchID Google Scholar
ORCID

Journal Articles

(students or post-doc fellows)

  1. Liu, H., Jin, I.-H., Zhang, Z., & Yuan, Y. (accepted). Social network mediation analysis: A latent space approach. Psychometrika.
  2. Che, C., Jin, I.-K., & Zhang, Z. (accepted). Network Mediation Analysis Using Model-based Eigenvalue Decomposition. Structural Equation Modeling.
  3. Kuang, Y., Zhang, Z., Duan, B., & Zhang, P. (2020). Fuzzy Cognitive Maps-based Switched-Mode Power Supply Design Assistant System. IEEE Access, 8, 183014-183024.
  4. Tong, X., & Zhang, Z. (2020). Robust Bayesian approaches in growth curve modeling: Using Student's t distributions versus semiparametric methods. Structural Equation Modeling, 27(4), 544-560.
  5. Qu, W., Liu, H., & Zhang, Z. (2020). A Method of Generating Multivariate Non-normal Random Numbers with Desired Multivariate Skewness and Kurtosis. Behavior Research Methods, 52, 939–946.
  6. Wilcox, K. T., Jacobucci, R. & Zhang, Z. (2019). Bayesian Supervised Topic Modeling with Covariates (Abstract). Multivariate Behavioral Research, DOI: 10.1080/00273171.2019.1695568
  7. Du, H., Edwards, M., & Zhang, Z. (2019). Bayes factor in one-sample tests of means with a sensitivity analysis: A discussion of separate prior distributions. Behavior Research Methods, 51(5), 1998–2021.
  8. Serang, S., Grimm, K. J., & Zhang, Z. (2019). On the Correspondence between the Latent Growth Curve and Latent Change Score Models. Structural Equation Modelling, 26(4), 623-635.
  9. Yuan, K., Zhang, Z., & Deng, L. (2019). Fit Indices for Mean Structures with Growth Curve Models. Psychological Methods, 24(1), 36-53.
  10. Cain, M., & Zhang, Z. (2019). Fit for a Bayesian: An evaluation of PPP and DIC for structural equation modeling.Structural Equation Modeling, 26(1), 39–50.
  11. Liu, H., Jin, I. K., & Zhang, Z.(2018). Structural Equation Modeling of Social Networks: Specification, Estimation, and Application. Multivariate Behavioral Research, 53(5), 714–730.
  12. Mai, Y., & Zhang, Z. (2018). Review of Software Packages for Bayesian Multilevel Modeling. Structural Equation Modeling, 25(4), 650–658. http://www.tandfonline.com/eprint/6u84fbxfzJPCGa6eUUgS/full
  13. Cain, M., Zhang, Z., & Bergeman, C. S. (2018). Time and Other Considerations in Mediation Design. Educational and Psychological Measurement, 78(6), 952-972
  14. Ke, Z., & Zhang, Z. (2018). Testing Autocorrelation and Partial Autocorrelation: Asymptotic Methods versus Resampling Techniques. British Journal of Mathematical and Statistical Psychology, 71(1), 96–116.
  15. Mai, Y., Zhang, Z., & Wen, Z. (2018). Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables. Structural Equation Modeling, 25(5), 737-749. https://www.tandfonline.com/eprint/6u84fbxfzJPCGa6eUUgS/full
  16. Tong, X., & Zhang, Z. (2017). Outlying Observation Diagnostics in Growth Curve Modeling. Multivariate Behavioral Research, 52(6), 768–788. http://www.tandfonline.com/eprint/43NdXgKr7Pywnv8SKYie/full
  17. Zhang, Z., Jiang, K., Liu, H., & Oh, I.-S. (2017). Bayesian meta-analysis of correlation coefficients through power prior. Communications in Statistics – Theory and Methods, 46(24)-11988-12007. http://www.tandfonline.com/eprint/avPtpSNV8Y4S5HwZGcc9/full
  18. Cain, M., Zhang, Z., & Yuan, K. (2017). Univariate and Multivariate Skewness and Kurtosis for Measuring Nonnormality: Prevalence, Influence and Estimation. Behavior Research Methods, 49(5), 1716–1735.
  19. Liu, H., & Zhang, Z. (2017). Logistic Regression with Misclassification in Binary Outcome Variables: A Method and Software. Behaviormetrika, 44(2), 447–476.
  20. Yuan, K.-H., Zhang, Z., & Zhao, Y. (2017). Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling. Structural Equation Modeling, 24(3), 315-330
  21. Cheung, R. Y. M., Cummings, E. M., Zhang, Z., & Davies, P. (2016) Trivariate Modeling of Interparental Conflict and Adolescent Emotional Security: An Examination of Mother-Father-Child Dynamics. Journal of Youth and Adolescence, 45(11), 2336–2352.
  22. Liu, H., Zhang, Z., & Grimm, K. J. (2016). Comparison of Inverse-Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis. Structural Equation Modeling, 23 (3), 354-367.
  23. Zhang, Z. (2016). Modeling Error Distributions of Growth Curve Models through Bayesian Methods. Behavior Research Methods, 48(2), 427-444.
  24. Zhang, Z. & Yuan, K.-H. (2016). Robust Coefficients Alpha and Omega and Confidence Intervals with Outlying Observations and Missing Data: Methods and Software. Educational and Psychological Measurement, 76(3), 387–411. http://files.eric.ed.gov/fulltext/ED575032.pdf
  25. Merluzzi, T.V., Philip, E.J., Zhang, Z., & Sullivan, C. (2015). Perceived discrimination, coping, and quality of life for African-American and Caucasian persons with cancer. Cultural Diversity and Ethnic Minority Psychology, 21(3), 337-344.
  26. Bernard, K., Peloso, E., Laurenceau, J-P, Zhang, Z., & Dozier, M. (2015). Examining Change in Cortisol Patterns During the 10-week Transition to a New Childcare Setting. Child Development, 86(2), 456–71.
  27. Serang, S., Zhang, Z., Helm, J., Steele, J. S., & Grimm, K. J. (2015). Evaluation of a Bayesian Approach to Estimating Nonlinear Mixed-Effects Mixture Models. Structural Equation Modelling, 22(2), 202–215.
  28. Yuan, K.-H., Tong, X., & Zhang, Z. (2015). Bias and Efficiency for SEM with Missing Data and Auxiliary Variables: Two-Stage Robust Method versus Two-Stage ML. Structural Equation Modeling, 22(2), 178–192.
  29. Zhang, Z., Hamagami, F., Grimm, K. J., & McArdle, J. J. (2015). Using R Package RAMpath for Tracing SEM Path Diagrams and Conducting Complex Longitudinal Data Analysis. Structural Equation Modeling, 22(1), 132–147. Download
  30. Zhang, Z. (2014b). Monte Carlo Based Statistical Power Analysis for Mediation Models: Methods and Software. Behavior Research Methods, 46(4), 1184-1198 Download
  31. Tong, X., Zhang, Z., & Yuan, K.-H. (2014). Evaluation of Test Statistics for Robust Structural Equation Modeling with Nonnormal Missing Data. Structural Equation Modeling, 21, 553–565. http://www.tandfonline.com/doi/pdf/10.1080/10705511.2014.919820
  32. Zhang, Z. (2014a). WebBUGS: Conducting Bayesian Analysis online. Journal of Statistical Software, 61(7),1-30. http://www.jstatsoft.org/v61/i07/paper
  33. Hardy, S. A., Zhang, Z., Skalski, J. E., Melling, B. S., & Brinton, C. T. (2014). Daily religious involvement, spirituality, and moral emotions. Psychology of Religion and Spirituality, 6(4), 338-348.
  34. Tong, X., & Zhang, Z. (2014). Abstract: Semiparametric Bayesian Modeling With Application in Growth Curve Analysis. Multivariate Behavioral Research, 49, 299-299.
  35. Song, H., & Zhang, Z. (2014). Analyzing Multiple Multivariate Time Series Data Using Multilevel Dynamic Factor Models. Multivariate Behavioral Research, 49(1), 67-77. http://www.tandfonline.com/eprint/G84HgvCIskMS9P3SkRvG/full
  36. Lu, Z., & Zhang, Z. (2014). Robust Growth Mixture Models with Non-ignorable Missingness: Models, Estimation, Selection, and Application. Computational Statistics and Data Analysis, 71, 220-240. Download
  37. Zhang, Z. (2013). Bayesian Growth Curve Models with the Generalized Error Distribution. Journal of Applied Statistics, 40(8), 1779-1795. download
  38. Grimm, K. J., Kuhl, A. P., & Zhang, Z. (2013). Measurement Models, Estimation, and the Study of Change. Structural Equation Modeling, 20(3), 504-517, DOI: http://dx.doi.org/10.1080/10705511.2013.797837.
  39. Philip, E. J., Merluzzi, T. V., Zhang, Z. & Heitzmann, C. (2013). Depression and Cancer Survivorship: Importance of Coping Self-Efficacy in Post-Treatment Survivors. Psycho-Oncology, 22(5), 987-994.
  40. Grimm, K. J., Zhang, Z., Hamagami, F., & Mazzocco, M. (2013). Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories. Multivariate Behavioral Research, 48, 117-143. http://www.tandfonline.com/eprint/4XE3CQai8dTixwY2tPKv/full
  41. Zhang, Z., Lai, K., Lu, Z., & Tong, X. (2013). Bayesian inference and application of robust growth curve models using student’s t distribution. Structural equation modeling, 20(1), 47-78. Manuscript http://www.tandfonline.com/eprint/bI5aVbVq2uwI7Xs8HiBq/full
  42. Zhang, Z., & Wang, L. (2013). Methods for mediation analysis with missing data. Psychometrika, 78(1), 154-184. Manuscript Additional information
  43. Yuan, K.-H., & Zhang, Z. (2012). Structural equation modeling diagnostics using R package semdiag and EQS. Structural Equation Modeling: An Interdisciplinary Journal, 19(4), 683-702. Manuscript
  44. Yuan, K.-H., & Zhang, Z. (2012). Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika, 77(4), 803-826. Manuscript
  45. Tong, X., and Zhang, Z. (2012). Diagnostics of Robust Growth Curve Modeling using Student's t Distribution. Multivariate Behavioral Research,47(4), 493-518. Manuscript Software
  46. Zhang, Z., & Wang, L. (2012). A note on the robustness of a full Bayesian method for non-ignorable missing data analysis. Brazilian Journal of Probability and Statistics, 26(3), 244-264. Manuscript
  47. Zhang, Z., McArdle, J. J., & Nesselroade, J. R. (2012). Growth Rate Models: Emphasizing Growth Rate Analysis through Growth Curve Modeling. Journal of Applied Statistics, 39(6), 1241-1262. Manuscript http://www.tandfonline.com/eprint/7pWwYdzgIsEcTSQF4CHp/full
  48. Wang, L. & Zhang, Z. (2011). Estimating and testing mediation effects with censored data. Structural Equation Modeling, 18(1), 18-34. Download http://www.tandfonline.com/eprint/gR8X6zdCYk8UP2n58Y5d/full
  49. Hardy, S. A., White, J., Zhang, Z., & Ruchty, J.(2011). Parenting and the socialization of religiousness and spirituality. Psychology of Religion and Spirituality, 3(3), 217-230. doi: 10.1037/a0021600. Manuscript
  50. Lu, Z., Zhang, Z., & Lubke, G. (2011). Bayesian Inference For Growth Mixture Models With Latent Class Dependent Missing Data. Multivariate Behavioral Research, 46(4), 567-597. Manuscript http://www.tandfonline.com/eprint/448QBknPccekgTn7FvbB/full
  51. Tong, X., Zhang, Z., & Yuan, K.-H. (2011). Evaluation of Test Statistics for Robust Structural Equation Modeling with Non-normal Missing Data (Abstract). Multivariate Behavioral Research, 46(6), 1016-1016.
  52. Zhang, Z., Browne, M. W., & Nesselroade, J. R. (2011). Higher–order factor invariance and idiographic mapping of constructs to observables. Applied Developmental Sciences, 15(4), 186-200. Manuscript
  53. Lu, L., Zhang, Z., & Lubke, G. (2010). Bayesian Inference For Growth Mixture Models With Non-ignorable Missing Data (Abstract). Multivariate Behavioral Research, 45(6), 1028–1028.
  54. Winter, W. C., Hammond, W. R., Zhang, Z., & Green, N. H. (2009). Measuring circadian advantage in Major League Baseball: A 10-year retrospective study. International. Journal of Sports Physiology and Performance, 4(3) 394-401.
  55. Hamaker, E. L., Zhang, Z., & van der Maas, H. L. J. (2009). Dyads as dynamic systems: Using threshold autoregressive models to study dyadic interactions. Psychometrika, 74(4) 727-745. Download
  56. Zhang, Z., & Wang, L. (2009). Statistical power analysis for growth curve models using SAS. Behavior Research Methods, 41(4), 1083-1094. Download PDF
  57. Zhang, Z., Hamaker, E. L., & Nesselroade, J. R. (2008). Comparisons of four methods for estimating dynamic factor models. Structural Equation Modeling, 15(3), 377-402. Download
  58. Zhang, Z., McArdle, J. J., Wang, L., & Hamagami, F. (2008). A SAS interface for Bayesian analysis with WinBUGS. Structural Equation Modeling, 15(4), 705–728. Download NOTE: Some SAS codes were not shown exactly during the final publishing process. Please download the final draft instead of the published one. Final Draft http://www.tandfonline.com/eprint/bCBAPfGTvNXQkJAHCdph/full
  59. Wang, L., Zhang, Z., McArdle, J. J., & Salthouse, T. A. (2008). Investigating ceiling effects in longitudinal data analysis. Multivariate Behavioral Research, 43(3), 476–496. Download
  60. Zhang, Z., Davis, H. P., Salthouse, T. A., & Tucker-Drob, E. A. (2007). Correlates of individual, and age-related, differences in short-term learning. Learning and Individual Differences, 17(3), 231–240. Download
  61. Zhang, Z., Hamagami, F., Wang, L., Grimm, K. J., & Nesselroade, J. R. (2007). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Development, 31(4), 374-383.Download
  62. Zhang, Z., & Nesselroade J. R. (2007). Bayesian estimation of categorical dynamic factor models. Multivariate Behavioral Research, 42(4), 729-756. Download

Books

  1. Zhang, Z. (2018). Text Mining for Social and Behavioral Research Using R: A Case Study on Teaching Evaluation. Retrievable from https://books.psychstat.org/textmining.
  2. Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R. Granger, IN: ISDSA Press.
  3. Zhang, Z. & Wang, L. (2017). Advanced statistics using R. [https://advstats.psychstat.org]. Granger, IN: ISDSA Press. ISBN: 978-1-946728-01-2.

Book Chapters

  1. Zhang, Z., Ye, M., Huang, Y., & Sun, N. (2018). A Longitudinal Social Network Clustering Method Based on Tie Strength. 2018 IEEE International Conference on Big Data (Big Data). (pp. 1690–1697)
  2. Mai, Y., & Zhang, Z. (in press). Statistical Power Analysis for Comparing Means with Binary or Count Data Based on Analogous ANOVA. In L. A. van der Ark, M. Wiberg, S. A. Culpepper, J. A. Douglas, and W.-C. Wang (Eds.) Quantitative Psychology - The 81st Annual Meeting of the Psychometric Society, Asheville, North Carolina, 2016. Springer Proceedings in Mathematics & Statistics. (pp. 381–393)
  3. Du, H., Zhang, Z., & Yuan, K.-H. (2017). Power analysis for t-test with non-normal data and unequal variances. In L. A. van der Ark, M. Wiberg, S. A. Culpepper, J. A. Douglas, and W.-C. Wang (Eds.) Quantitative Psychology - The 81st Annual Meeting of the Psychometric Society, Asheville, North Carolina, 2016. Springer Proceedings in Mathematics & Statistics. (pp. 373–380)
  4. Zhang, Z., Wang, L., & Tong, X. (2015). Mediation Analysis with Missing Data through Multiple Imputation and Bootstrap. In L. A. van der Ark, D. M. Bolt, W.-C. Wang, J. A. Douglas, & S.-M. Chow (Eds.) Quantitative Psychology Research: the 79th Annual Meeting of the Psychometric Society. Springer Proceedings in Mathematics & Statistics. (pp. 341–355).
  5. Lu, Z., & Zhang, Z. (2015). Issues in Aggregating Time Series: Illustration through an AR(1) Model. In L. A. van der Ark, D. M. Bolt, W.-C. Wang, J. A. Douglas, & S.-M. Chow (Eds.) Quantitative Psychology Research: the 79th Annual Meeting of the Psychometric Society. Springer Proceedings in Mathematics & Statistics. (pp. 357–370).
  6. Lu, Z., Zhang, Z., & Cohen, A. (2014). Model selection criteria for latent growth models using Bayesian methods. In R. E. Millsap, D. M. Bolt, L. A. van der Ark, & W.-C. Wang (Eds.), Quantitative Psychology Research, volume 89 of Springer Proceedings in Mathematics & Statistics (pp. 319–341). Springer International Publishing.
  7. Lu, Z., Zhang, Z., & Cohen, A. (2013). Bayesian methods and model selection for latent growth curve models with missing data. In R. E. Millsap, L. A. van der Ark, D. M. Bolt, & C. M. Woods (Eds.), New Developments in Quantitative Psychology, volume 66 of Springer Proceedings in Mathematics & Statistics (pp.275–304). Springer New York.
  8. Hamagami, F., Zhang, Z., & McArdle, J. J. (2009). A Bayesian Discrete Dynamic System by Latent Difference Score Structural Equations Models for Multivariate Repeated Measures Data. In S.-M. Chow, E. Ferrer, & F. Hsieh (Eds), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 319-348). New Jersey: Lawrence Erlbaum Associates.
  9. Wang, L., Zhang, Z., & Estabrook, R. (2009). Longitudinal mediation analysis of training intervention effects. In S.-M. Chow, E. Ferrer, & F. Hsieh (Eds), Statistical methods for modeling human dynamics: An interdisciplinary dialogue(pp. 349-380). New Jersey: Lawrence Erlbaum Associates.
  10. Zhang, Z., & Wang, L. (2008). Methods for evaluating mediation effects: Rationale and comparison. In K. Shigemasu, A. Okada, T. Imaizumi, & T. Hoshino (Eds.), New trends in psychometrics(pp. 585-594). Tokyo: Universal Academy Press.Download

Encyclopedia Entries

  1. Liu, H., & Zhang, Z. (2018). Probit Transformation. The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. (p.1300)
  2. Zhang, Z. (2018). Moments of a Distribution. The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. (p.1084-1085)
  3. Cain, M., & Zhang, Z. (2018). Posterior. The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. (p.1274-1275)

Software

  1. Zhang, Z., Yuan, K.-H., & Cain, M. (2016). Software for estimating univariate and multivariate skewness and kurtosis. Retrieved from http://psychstat.org/nonnormal
  2. Ke, Z., & Zhang, Z. (2016). pautocorr: Testing Autocorrelation and Partial Autocorrelation Through Bootstrap and Surrogate Methods. R package retrievialbe from https://r-forge.r-project.org.
  3. Liu, H., & Zhang, Z. (2016). logistic4p: Logistic Regression with Misclassification in Dependent Variables. R package retrievialbe from https://cran.r-project.org/package=logistic4p. Usage statistics
  4. Mai, Y., Zhang, Z., & Yuan, K.-H. (2015) An Online Interface for Drawing Path Diagrams for Structural Equation Modeling. Retrieved from http://semdiag.psychstat.org
  5. Zhang, Z., Yuan, K.-H., & Mai, Y. (2015-2016). WebPower: Statistical power analysis online. Retrieved from http://webpower.psychstat.org.
  6. Zhang, Z., & Yuan, K.-H. (2015). coefficientalpha: Robust Cronbach's alpha and McDonald's omega for non-normal and missing data. http://CRAN.R-project.org/package=coefficientalpha Usage statistics
  7. Zhang, Z. (2014). WebBUGS: Conducting Bayesian Analysis online. Retrievable from http://webbugs.psychstat.org.
  8. Zhang, Z., Jiang, J., & Liu, H. (2013). An online software for meta-analysis of correlation. Available at http://webbugs.psychstat.org/modules/metacorr/.
  9. Zhang, Z., McArdle, J. J., Hamagami, F., & Grimm, K. J. (2013). RAMpath: Structural Equation Modeling using RAM Notation. R package version 0.3.6. http://CRAN.R-project.org/package=RAMpath Usage statistics
  10. Zhang, Z., Yuan, K.-H., & Mai, Y. (2012-2016). WebSEM: Structural equation modeling online. Retrievable from https://websem.psychstat.org.
  11. Zhang, Z., & Tong, X. (2011). Online software of distribution diagnostics for robust growth curve models. Available at http://nd.psychstat.org/research/mbr2012.
  12. Yuan, K.-H., & Zhang, Z. (2011). rsem: An R package for Robust non-normal SEM with Missing Data. Available at http://CRAN.R-project.org/package=rsem. Usage statistics
  13. Zhang, Z. & Yuan, K.-H. (2011). semdiag: An R package for structural equation modeling diagnostics. Retrievable from http://CRAN.R-project.org/package=semdiag. Usage statistics
  14. Zhang, Z., & Wang, L. (2011). bmem: An R packages for mediation analysis with ignorable and non-ignorable missing data. Retrievable from http://CRAN.R-project.org/package=bmem. Usage statistics
  15. Zhang, Z., Tong, X., & Lu, Z. (2010). Bayesian estimation of robust growth curve models using Student's t distribution. Available at http://webstats.psychstat.org/semrgcm/..
  16. Zhang, Z., & Wang, L. (2009). SAS macros for power analysis of growth curve models, Version 1.0. Retrievable from http://saspower.psychstat.org
  17. Zhang, Z., & Wang, L. (2008). BAUW as an OpenBUGS plugin, Version 1.0. Retrievable from http://bauw.psychstat.org
  18. Zhang, Z., & Wang, L. (2007). MedCI: Mediation Confidence Intervals, Version 3.0. Retrievable from http://medci.psychstat.org
  19. Zhang, Z., & Wang, L. (2006). BAUW: Bayesian Analysis Using WinBUGS, Version 1.0. Retrievable from http://bauw.psychstat.org Citations
  20. Zhang, Z. (2006). LDSM: A C++ program for generating codes for analyzing latent difference score model in Mplus. Retrievable from http://www.psychstat.org/us/article.php/38
  21. Zhang, Z., & Nesselroade, J. R. (2005). Selection: A C++ program for analyzing selection effects. Retrievable from http://www.psychstat.org/us/article.php/64
  22. Zhang, Z., & Nesselroade, J. R. (2004). DFA: Dynamic Factor Analysis, Version 2.0. Retrievable from http://dfa.psychstat.org

Other Publications

  1. Zhang, Z. (2018). A Review of Bayesian Psychometric Modeling. Journal of Educational and Behavioral Statistics.
  2. Winter, W., Potenziano, B., Zhang, Z., Green, N., & Hammond, W.(2010). Chronotype as a predictor of performance in major league baseball pitchers, Sleep, 2010, 33, A188-A189.

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