[Ando, T. 2007. “Bayesian Predictive Information Criterion for the Evaluation of Hierarchical Bayesian and Empirical Bayes Models.” Biometrika 94: 443-458. Doi: http://dx.doi.org/10.1093/biomet/asm017.10.1093/biomet/asm017]Search in Google Scholar
[Bedrick, E.J. 1983. “Adjusted Chi-Squared Tests for Cross-Classified Tables of Survey Data.” Biometrika 70: 591-595. Doi: http://dx.doi.org/10.1093/biomet/70.3.591.10.1093/biomet/70.3.591]Search in Google Scholar
[Brier, S.S. 1980. “Analysis of Contingency Tables Under Cluster Sampling.” Biometrika 67: 591-596. Doi: http://dx.doi.org/10.1093/biomet/67.3.591.10.1093/biomet/67.3.591]Search in Google Scholar
[Calsyn, C., P. Gonzales, and M. Frase. 1999. “Highlights from TIMSS.” National Center for Education Statistics, Washington, DC. Doi: http://mces.ed.gov/timss.]Search in Google Scholar
[Datta, G.S. and M. Ghosh. 1991. “Bayesian Prediction in Linear Models: Applications to Small Area Estimation.” Annals of Statistics 19: 1748-1770.10.1214/aos/1176348369]Search in Google Scholar
[Foy, P., K. Rust, and A. Schleicher. 1996. “Sample Design.” In TIMMS Technical Report, Volume I: Design and Development, edited by M.O. Martin and D.L. Kelly, pagenumber. Chestnut Hill, MA: Boston College.]Search in Google Scholar
[Fuller, W.A. and G.E. Battese. 1973. “Transformations for Estimation of Linear Models with Nested-Error Structure.” Journal of the American Statistical Association 68: 626-632. Doi: http://dx.doi.org/10.1080/01621459.1973.10481396.10.1080/01621459.1973.10481396]Search in Google Scholar
[Gelfand, A., D. Dey, and H. Chang. 1992. “Model Determination using Predictive Distributions with Implementation via Sampling-based Methods.” In Bayesian Statistics 4, 147-168. New York: Oxford University Press.]Search in Google Scholar
[Geisser, S. and W. Eddy. 1979. “A Predictive Approach to Model Selection.” Journal of the American Statistical Association 74: 153-160. Doi: http://dx.doi.org/10.1080/01621459.1979.10481632.10.1080/01621459.1979.10481632]Search in Google Scholar
[Gelman, A., J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin. 2013. Bayesian Data Analysis, 3rd ed. New York: Chapman & Hall/CRC.10.1201/b16018]Search in Google Scholar
[Ghosh, M. and P. Lahiri. 1988. “Bayes and Empirical Bayes Analysis in Multistage Sampling.” In Statistical Decision Theory and Related Topics IV, Vol. 1, edited by S.S. Gupta and J.O. Berger. 195-212. New York: Springer.10.1007/978-1-4613-8768-8_22]Search in Google Scholar
[Hamilton, J. 2009. President Obama, U.S. Secretary of Education Duncan Announce National Competition to Advance School Reform. U.S. Department of Education: Available at: http://www.ed.gov/news/pressreleases/2009/07/07242009.html.]Search in Google Scholar
[Holt, D., A.J. Scott, and P.D. Ewings. 1980. “Chi-Squared Tests with Survey Data.” Journal of the Royal Statistical Society, Series A 143: 303-320. Doi: http://dx.doi.org/10.2307/2982131.10.2307/2982131]Search in Google Scholar
[Malec, D. and J. Sedransk. 1985. “Bayesian Inference for Finite Population Parameters in Multistage Cluster Sampling.” Journal of the American Statistical Association 80: 897-902. Doi: http://dx.doi.org/10.1080/01621459.1985.10478200.10.1080/01621459.1985.10478200]Search in Google Scholar
[Molina, I., B. Nandram, and J.N.K. Rao. 2014. “Small Area Estimation of General Parameters with Application to Poverty Indicators: A Hierarchical Bayes Approach.” Annals of Applied Statistics 8: 852-885. Doi: http://dx.doi.org/10.1214/13-AOAS702.10.1214/13-AOAS702]Search in Google Scholar
[Nandram, B. 2014. Bayesian Predictive Inference for a Proportion Under a Two-Fold Small Area Model. Technical Report, Department of Mathematical Sciences, Worcester Polytechnic Institute, 1-43. (Available on request.) Nandram, B., D.R. Bhatta, J. Sedransk, and D. Bhadra. 2013. “A Bayesian Test of Independence in a Two-Way Contingency Table Using Surrogate Sampling.” Journal of Statistical Planning and Inference 143: 1392-1408. Doi: http://dx.doi.org/10.1016/j.jspi.2013.03.011.10.1016/j.jspi.2013.03.011]Search in Google Scholar
[Nandram, B. 1998. “A Bayesian Analysis of the Three-Stage Hierarchical Multinomial Model.” Journal of Statistical Computation and Simulation 61: 97-126. Doi: http://dx.doi.org/10.1080/00949659808811904.10.1080/00949659808811904]Search in Google Scholar
[Nandram, B. and J. Sedransk. 1993. “Bayesian Predictive Inference for a Finite Population Proportion: Two-Stage Cluster Sampling.” Journal of the Royal Statistical Society, Series B 55: 399-408.10.1111/j.2517-6161.1993.tb01910.x]Search in Google Scholar
[Natarajan, R. and R.E. Kass. 2000. “Reference Bayesian Methods for Generalized Linear Mixed Models.” Journal of the American Statistical Association 95: 227-237. Doi: http://dx.doi.org/10.1080/01621459.2000.10473916.10.1080/01621459.2000.10473916]Search in Google Scholar
[Rao, J.N.K. 2003. Small Area Estimation. New York: Wiley.10.1002/0471722189]Search in Google Scholar
[Rao, J.N.K. and A.J. Scott. 1981. “The Analysis of Categorical Data from Complex Sample Surveys: Chi-squared Tests for Goodness of Fit and Independence in Two-Way Tables.” Journal of the American Statistical Association 76: 221-230. Doi: http://dx.doi.org/10.1080/01621459.1981.10477633.10.1080/01621459.1981.10477633]Search in Google Scholar
[Rao, J.N.K. and A.J. Scott. 1984. “On Chi-Squared Tests for Multi-way Tables with Cell Proportions Estimated from Survey Data.” Annals of Statistics 12: 46-60.10.1214/aos/1176346391]Search in Google Scholar
[Scott, A.J. and D. Holt. 1982. “The Effect of Two-Stage Sampling on Ordinary Least Squares Methods.” Journal of the American Statistical Association 77: 848-854. Doi: http://dx.doi.org/10.1080/01621459.1982.10477897.10.1080/01621459.1982.10477897]Search in Google Scholar
[Scott, A. and T.M.F. Smith. 1969. “Estimation in Multi-Stage Surveys.” Journal of the American Statistical Association 101: 1387-1397. Doi: http://dx.doi.org/10.1080/01621459.1969.10501015.10.1080/01621459.1969.10501015]Search in Google Scholar
[Silverman, B.W. 1986. Density Estimation for Statistics and Data Analysis. New York: Chapman & Hall.]Search in Google Scholar
[Stukel, D.M. and J.N.K. Rao. 1997. “Estimation of Regression Models with Nested Error Regression Structure and Unequal Error Variances Under Two and Three Stage Cluster Sampling.” Statistics & Probability Letters 35: 401-407. Doi: http://dx.doi.org/10.1016/S0167-7152(97)86602-3.10.1016/S0167-7152(97)86602-3]Search in Google Scholar
[Stukel, D.M. and J.N.K. Rao. 1999. “On Small-Area Estimation Under Two-Fold Nested Error Regression Models.” Journal of Statistical Planning and Inference 78: 131-147. Doi: http://dx.doi.org/10.1016/S0378-3758(98)00211-0.10.1016/S0378-3758(98)00211-0]Search in Google Scholar
[Toto, M.C.S. and B. Nandram. 2010. “A Bayesian Predictive Inference for Small Area Means Incorporating Covariates and Sampling Weights.” Journal of Statistical Planning and Inference 140: 2963-2979. Doi: http://dx.doi.org/10.1016/j.jspi.2010.03.043.10.1016/j.jspi.2010.03.043]Search in Google Scholar
[Yan, G. and J. Sedransk. 2007. “Bayesian Diagnostic Techniques for Detecting Hierarchical Structure.” Bayesian Analysis 2: 735-760. Doi: http://dx.doi.org/10.1214/07-BA230.10.1214/07-BA230]Search in Google Scholar
[Yan, G. and J. Sedransk. 2010. “A Note on Bayesian Residuals as a Hierarchical Model Diagnostic Technique.” Statistical Papers 51: 1-10. Doi: http://dx.doi.org/10.1007/s00362-007-0111-2. 10.1007/s00362-007-0111-2]Search in Google Scholar