Bayesian joint modeling of binomial and rank response with non-ignorable missing data for primate cognition. (English) Zbl 07859031
Summary: A random effects model for analyzing mixed rank and binomial data with considering the missing values is presented. Occurring of missing data is an important problem in all research fields. The most common approach to dealing with missing data is to delete cases containing missing observations. However, this approach reduces statistical power and mislead us to biased statistical results. This paper aims to prepare guidance for researchers facing missing data problems and to provide techniques for jointly modeling of binomial and rank responses. We compare the cognitive abilities of different primates based on their performance on 17 cognitive assessments obtained on either a rank or binomial scale using Bayesian latent variable with random effects models. Random effects are used to take into account the correlation between responses of the same individual.
MSC:
| 62-XX | Statistics |
Keywords:
hierarchical Bayes; latent performance; mixed responses; non-ignorable missing values; rank responseReferences:
| [1] | Agresti, A.2002. Categorical data analysis. New York: John Wiley. · Zbl 1018.62002 |
| [2] | Albert, J. H., and Chib, S.. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association88 (422):669-79. doi:. · Zbl 0774.62031 |
| [3] | Alvo, M., and Yu, P. L.. 2014. Statistical methods for ranking data. New York: Springer-Verlag. · Zbl 1341.62001 |
| [4] | Amici, F., Barney, B., Johnson, V. E., Call, J., and Aureli, F.. 2012. A modular mind? A test using individual data from seven primate species. PLoS One7 (12):e51918. doi:. |
| [5] | Barney, B. J., Amici, F., Aureli, F., Call, J., and Johnson, V. E.. 2015. Joint Bayesian modeling of binomial and rank data for primate cognition. Journal of the American Statistical Association110 (510):573-82. doi:. |
| [6] | Böckenholt, U.1992. Thurstonian representation of ranking data. British Journal of Mathematical and Statistical Psychology45 (1):31-49. doi:. |
| [7] | Böckenholt, U.1993. Applications of Thurstonian models to ranking data. In Probability models and statistical analyses for ranking data, ed. Fligner, M. A. and Verducci, J. S., 157-72. New York: Springer-Verlag. · Zbl 0764.62097 |
| [8] | Bradley, R. A., and Terry, M. E.. 1952. The rank analysis of incomplete block designs: 1, the method of paired comparisons. Biometrika39 (3-4):324-45. doi:. · Zbl 0047.12903 |
| [9] | Catalano, P., and Ryan, L. M.. 1992. Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association50:1078-95. |
| [10] | Cox, D. R., and Wermuth, N.. 1992. Response models for mixed binary and quantitative variables. Biometrika79 (3):441-61. doi:. · Zbl 0766.62042 |
| [11] | Critchlow, D. E., Fligner, M. A., and Verducci, J. S.. 1991. Probability models on rankings. Journal of Mathematical Psychology35 (3):294-318. doi:. · Zbl 0741.62024 |
| [12] | Daniels, H. E.1950. Rank correlation and population models. Journal of the Royal Statistical Society, Series B12 (2):171-81. doi:. · Zbl 0040.22302 |
| [13] | David, H. A.1988. The method of paired comparisons (2nd ed.). London: Chapman and Hall. · Zbl 0665.62075 |
| [14] | Davidson, R. R.1970. On extending the Bradley-Terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association65 (329):317-28. doi:. |
| [15] | Davidson, R. R., and Beaver, R. J.. 1977. On extending the Bradley-Terry model to incorporate withen-pair order effects. Biometrics33 (4):693-702. doi:. · Zbl 0377.62071 |
| [16] | DeConde, R. P., Hawley, S., Falcon, S., Clegg, N., Knudsen, B., and Etzioni, R.. 2006. Combining results of microarray experiments: A rank aggregation approach. Statistical Applications in Genetics and Molecular Biology5 (1):213-34. doi:. · Zbl 1166.92306 |
| [17] | Diaconis, P.1988. Group representations in probability and statistics. Lecture Notes Monograph Series11:1-192. · Zbl 0695.60012 |
| [18] | Diggle, P. J., and Kenward, M. G.. 1994. Informative drop-out in longitudinal data analysis. Applied Statistics43 (1):49-93. doi:. · Zbl 0825.62010 |
| [19] | Dittrich, R., Hatzinger, R., and Katzenbeisser, W.. 2002. Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings. Journal of the Royal Statistical Society: Series C (Applied Statistics)47 (4):511-25. doi:. · Zbl 0915.62063 |
| [20] | Dwork, C., Kumar, R., Naor, M., and Sivakumar, D.. 2001. Rank aggregation methods for the web. In Proceedings of the 10th International Conference on World Wide Web, . 613-22. ACM. |
| [21] | Francis, B., Dittrich, R., Hatzinger, R., and Penn, R.. 2002. Analysing partial ranks by using smoothed paired comparison methods: An investigation of value orientation in Europe. Journal of the Royal Statistical Society: Series C (Applied Statistics)51 (3):319-36. doi:. · Zbl 1111.62383 |
| [22] | Fienberg, S. E.1979. Graphical methods in statistics. The American Statistician33 (4):165-78. |
| [23] | Fitzmaurice, G. M., and Laird, N. M.. 1995. Regression models for bivariate discrete and continuous outcome with clustering. Journal of the American Statistical Association90 (431):845-52. doi:. · Zbl 0851.62083 |
| [24] | Fitzmaurice, G. M., and Laird, N. M.. 1997. Regression models for mixed discrete and continuous responses with potentially missing value. Biometrics53 (1):110-22. doi:. · Zbl 0904.62082 |
| [25] | Guo, X., and Carlin, B. P.. 2004. Separate and joint modeling of longitudinal and event time data using standard computer packages. The American Statistician58 (1):16-24. doi:. |
| [26] | Hoff, P. D.2007. Extending the rank likelihood for semiparametric copula estimation. The Annals of Applied Statistics1:265-83. [574] · Zbl 1129.62050 |
| [27] | Johnson, T. R., and Kuhn, K. M.. 2013. Bayesian Thurstonian models for ranking data using JAGS. Behavior Research Methods45 (3):857-72. doi:. |
| [28] | Johnson, V. E.2007. Bayesian model assessment using pivotal quantities. Bayesian Analysis2 (4):719-34. [579] doi:. · Zbl 1331.62147 |
| [29] | Johnson, V. E., Deaner, R. O., and van Schaik, C. P.. 2002. Bayesian analysis of rank data with application to primate intelligence experiments. Journal of the American Statistical Association97 (457):8-17. doi:. · Zbl 1073.62519 |
| [30] | Kendall, M., and Smith, B.. 1940. On the method of paired comparisons. Biometrika31 (3-4):324-45. doi:. · Zbl 0023.14803 |
| [31] | Kousgaard, N.1976. Models for paired comparisons with ties. Scandinavian Journal of Statistics3 (1):1-14. · Zbl 0336.62065 |
| [32] | Lam, K. F., Xue, H., and Cheung, Y. B.. 2006. Semiparametric analysis of zero-inflated count data. Biometrics62 (4):996-1003. doi:. · Zbl 1117.62125 |
| [33] | Lee, A. H., Wang, K., Scott, J. A., Yau, K. K. W., and McLachlan, G. J.. 2006. Multi-level zero-inflated Poisson regression modeling of correlated count data with excess zeros. Statistical Methods in Medical Research15 (1):47-61. doi:. · Zbl 1152.62083 |
| [34] | Leon, A. R. D., and Carri’ere, K. C.. 2013. Analysis of mixed data: Methods and Application. New York: CRC Press. · Zbl 1318.62006 |
| [35] | Lin, S.2010. Rank aggregation methods. Wiley Interdisciplinary Reviews: Computational Statistics2 (5):555-70. doi:. |
| [36] | Little, R. J., and Schluchter, M.. 1985. Maximum likelihood estimation for mixed continuous and categorical data with missing values. Biometrika72 (3):497-512. doi:. · Zbl 0609.62082 |
| [37] | Little, R. J., and Rubin, D.. 2002. Statistical analysis with missing data. 2nd ed. New York: Wiley. · Zbl 1011.62004 |
| [38] | Marden, J. I.1995. Analyzing and modeling rank data. London: Chapman and Hall. · Zbl 0853.62006 |
| [39] | Matthews, J. N. S., and Morris, K. P.. 1995. An application of Bradley-Terry-type models to the measurement of pain. Journal of the Royal Statistical Society: Series C (Applied Statistics)44 (2):243-55. doi:. · Zbl 0821.62081 |
| [40] | McFadden, D.1980. Econometric models for probabilistic choice among products. The Journal of Business53 (S3):S13-S29. doi:. |
| [41] | Murray, J. S., Dunson, D. B., Carin, L., and Lucas, J. E.. 2013. Bayesian Gaussian copula factor models for mixed data. Journal of the American Statistical Association108 (502):656-65. [574] doi:. · Zbl 06195968 |
| [42] | Olkin, L., and Tate, R. F.. 1961. Multivariate correlation models with mixed discrete and continuous variables. The Annals of Mathematical Statistics32 (2):448-65. doi:. · Zbl 0113.35101 |
| [43] | R Core Team. 2019. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/. |
| [44] | Rao, P. V., and Kupper, L. L.. 1967. Ties in paired-comparison experiments: A generalization of the Bradley-Terry model. Journal of the American Statistical Association62 (317):194-204. doi:. |
| [45] | Rubin, D. B.1976. Inference and missing data. Biometrika63 (3):581-92. doi:. · Zbl 0344.62034 |
| [46] | Stern, H.1990. Models for distributions on permutations. Journal of the American Statistical Association85 (410):558-64. doi:. |
| [47] | Sunethra, A., and Sooriyarachchi, R.. 2018. A joint model for exponential survival data and Poisson count data. American Journal of Applied Mathematics and Statistics6 (2):72-9. |
| [48] | Sweeting, M., and Thompson, G.. 2011. Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture. Biometrical Journal. Biometrische Zeitschrift53 (5):750-63. doi:. · Zbl 1226.62130 |
| [49] | Tanner, M. A., and Wong, W. H.. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association82 (398):528-40. doi:. · Zbl 0619.62029 |
| [50] | Thurstone, L. L.1927. A law of comparative judgement. Psychological Review15:284-97. |
| [51] | Thurstone, L. L.1931. Rank order as a psychological method. Journal of Experimental Psychology14 (3):187-201. doi:. |
| [52] | Wulfsohn, M., and Tsiatis, A.. 1997. A joint model for survival and longitudinal data measured with error. Biometrics53 (1):330-9. · Zbl 0874.62140 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
