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Approximation Approaches to Inference

Logistic Regression Models for Aggregated Data

, ORCID Icon & ORCID Icon
Pages 1049-1067 | Received 08 Dec 2019, Accepted 22 Feb 2021, Published online: 20 Apr 2021

References

  • Albert, A., and Anderson, J. A. (1984), “On the Existence of Maximum Likelihood Estimates in Logistic Regression Models,” Biometrika, 71, 1–10. DOI: 10.1093/biomet/71.1.1.
  • Armstrong, B. (1985), “Measurement Error in the Generalized Linear Model,” Communication in Statistics—Simulation and Computation, 14, 529–544. DOI: 10.1080/03610918508812457.
  • Baldi, P., Sadowski, P., and Whiteson, D. (2014), “Searching for Exotic Particles in High-Energy Physics With Deep Learning,” Nature Communications, 5, 1–9. DOI: 10.1038/ncomms5308.
  • Beranger, B., Lin, H., and Sisson, S. A. (2018), “New Models for Symbolic Data Analysis,” arXiv no. 1809.03659.
  • Bhowmik, A., Ghosh, J., and Koyejo, O. (2016), “Generalized Linear Models for Aggregated Data,” arXiv no. 1605.04466.
  • Billard, L. (2011), “Brief Overview of Symbolic Data and Analytic Issues,” Statistical Analysis and Data Mining, 4, 149–156. DOI: 10.1002/sam.10115.
  • Billard, L., and Diday, E. (2003), “From the Statistics of Data to the Statistics of Knowledge,” Journal of the American Statistical Association, 98, 470–487. DOI: 10.1198/016214503000242.
  • (2006), Symbolic Data Analysis, Wiley Series in Computational Statistics, Chichester: Wiley.
  • Bock, H.-H., and Diday, E., eds. (2000), Analysis of Symbolic Data: Exploratory Methods For Extracting Statistical Information From Complex Data, Studies in Classification, Data Analysis, and Knowledge Organization, Berlin: Springer-Verlag.
  • Bowling, S. R., and Khasawneh, M. T. (2009), “A Logistic Approximation to the Cumulative Normal Distribution,” Journal of Industrial Engineering and Management, 2, 114–127. DOI: 10.3926/jiem.2009.v2n1.p114-127.
  • Brito, P., and Silva, A. P. D. (2012), “Modelling Interval Data With Normal and Skew-Normal Distributions,” Journal of Applied Statistics, 39, 3–20. DOI: 10.1080/02664763.2011.575125.
  • Cox, D. (1958), “The Regression Analysis of Binary Sequences,” Journal of the Royal Statistical Society, Series B, 20, 215–232. DOI: 10.1111/j.2517-6161.1958.tb00292.x.
  • Cramer, J. S. (2007), “Robustness of Logit Analysis: Unobserved Heterogeneity and Mis-Specified Disturbances,” Oxford Bulletin of Economics and Statistics, 69, 545–555. DOI: 10.1111/j.1468-0084.2007.00445.x.
  • de Souza, R. M., Cysneiros, F. J. A., Queiroz, D. C., and de Fagundes, R. A. (2008), “A Multi-Class Logistic Regression Model for Interval Data,” in Conference: Systems, Man and Cybernetics.
  • de Souza, R. M. C. R., Queiroz, D. C. F., and Cysneiros, F. J. A. (2011), “Logistic Regression-Based Pattern Classifiers for Symbolic Interval Data,” Pattern Analysis and Applications, 14, 273–282. DOI: 10.1007/s10044-011-0222-1.
  • Diday, E. (1989), “Introduction a l’approche symbolique en analyse des données,” RAIRO-Operations Research-Recherche Opérationnelle, 23, 193–236. DOI: 10.1051/ro/1989230201931.
  • Dua, D., and Graff, C. (2017), “UCI Machine Learning Repository.”
  • Eichelberger, R. K., and Sheng, V. S. (2013), “An Empirical Study of Reducing Multiclass Classification Methodologies,” in Machine Learning and Data Mining in Pattern Recognition. MLDM 2013, Lecture Notes in Computer Science (Vol. 7988), ed. P. Perner, Berlin, Heidelberg: Springer, pp. 505–519.
  • Hastie, T., Tibshirani, R., and Friedman, J. (2008), The Elements of Statistical Learning (2nd ed.), New York: Springer.
  • Hauser, R. P., and Booth, D. (2011), “Predicting Bankruptcy With Robust Logistic Regression,” Journal of Data Science, 9, 565–584. DOI: 10.6339/JDS.201110_09(4).0006.
  • Heitjan, D. F. (1989), “Inference From Grouped Continuous Data: A Review,” Statistical Science, 4, 164–183.
  • Hosmer, D. W., Lemeshow, S., and Sturdivant, R. X. (2013), Applied Logistic Regression (3rd ed.), Hoboken, NJ: Wiley.
  • Jeffress, L. A. (1973), “The Logistic Distribution as an Approximation to the Normal Curve,” The Journal of the Acoustical Society of America, 53, 1296. DOI: 10.1121/1.1913467.
  • Johnson, T. R. (2006), “Generalized Linear Models With Ordinally-Observed Covariates,” British Journal of Mathematical and Statistical Psychology, 59, 275–300. DOI: 10.1348/000711005X65762.
  • Johnson, T. R., and Wiest, M. M. (2014), “Generalized Linear Models With Coarsened Covariates: A Practical Bayesian Approach,” Psychological Methods, 19, 281–299. DOI: 10.1037/a0034274.
  • Kim, H., and Gu, Z. (2010), “A Logistic Regression Analysis for Predicting Bankruptcy in the Hospitality Industry,” Journal of Hospitality Financial Management, 14, 24.
  • Knottnerus, J. A. (1992), “Application of Logistic Regression to the Analysis of Diagnostic Data: Exact Modeling of a Probability Tree of Multiple Binary Variables,” Medical Decision Making, 12, 93–108. DOI: 10.1177/0272989X9201200202.
  • Le Rademacher, J., and Billard, L. (2011), “Likelihood Functions and Some Maximum Likelihood Estimators for Symbolic Data,” Journal of Statistical Planning and Inference, 141, 1593–1602. DOI: 10.1016/j.jspi.2010.11.016.
  • Lin, H., Caley, M. J., and Sisson, S. A. (2017), “Estimating Global Species Richness Using Symbolic Data Meta-Analysis,” arXiv no. 1711. 03202.
  • Lindsay, B. G. (1988), “Composite Likelihood Methods,” in Statistical Inference From Stochastic Processes (Ithaca, NY, 1987), Contemporary Mathematics (Vol. 80), Providence, RI: American Mathematical Society, pp. 221–239.
  • Lipsitz, S., Parzen, M., Natarajan, S., Ibrahim, J., and Fitzmaurice, G. (2004), “Generalized Linear Models With a Coarsened Covariate,” Journal of the Royal Statistical Society, Series C, 53, 279–292. DOI: 10.1046/j.1467-9876.2003.05009.x.
  • Merlo, J., Chaix, B., Ohlsson, H., Beekman, A., Johnell, K., Hjerpe, P., Rstam, L., and Larsen, K. (2006), “A Brief Conceptual Tutorial of Multilevel Analysis in Social Epidemiology: Using Measures of Clustering in Multilevel Logistic Regression to Investigate Contextual Phenomena,” Journal of Epidemiology and Community Health, 60, 290–297. DOI: 10.1136/jech.2004.029454.
  • Min, H. (2013), “Ordered Logit Regression Modeling of the Self-Rated Health in Hawaii, With Comparisons to the OLS Model,” The Journal of Modern Applied Statistical Methods, 12, 371–380. DOI: 10.22237/jmasm/1383279720.
  • Pampel, F. C. (2000), Logistic Regression: A Primer (Vol. 1), Thousand, CA: SAGE Publications.
  • Pavlopoulos, D., Muffels, R., and Vermunt, J. (2010), “Wage Mobility in Europe. A Comparative Analysis Using Restricted Multinomial Logit Regression,” Quality and Quantity, 44, 115–129. DOI: 10.1007/s11135-008-9185-8.
  • Pingel, R. (2014), “Some Approximations of the Logistic Distribution With Application to the Covariance Matrix of Logistic Regression,” Statistics and Probability Letters, 85, 63–68. DOI: 10.1016/j.spl.2013.11.007.
  • QUT (2016), “Technical Report on Classification Methods for Crop Types,” Technical Report, Queensland University of Technology.
  • Rahman, P., Beranger, B., Roughan, M., and Sisson, S. A. (2020), “Likelihood-Based Inference for Modelling Packet Transit From Thinned Flow Summaries,” arXiv no. 2008.13424.
  • Tranmer, M. H., and Steel, D. (1997), “Logistic Regression Analysis With Aggregate Data: Tackling the Ecological Fallacy,” Paper Presented at the American Statistical Association Conference.
  • Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
  • Wang, H., Zhu, R., and Ma, P. (2018), “Optimal Subsampling for Large Sample Logistic Regression,” Journal of the American Statistical Association, 113, 829–844. DOI: 10.1080/01621459.2017.1292914.
  • Whitaker, T., Beranger, B., and Sisson, S. A. (2020), “Composite Likelihood Methods for Histogram-Valued Random Variables,” Statistics and Computing, 30, 1459–1477. DOI: 10.1007/s11222-020-09955-5.
  • Wooldridge, J. M. (2002), Econometric Analysis of Cross Section and Panel Data, Cambridge, MA: MIT Press.
  • Zhang, X., Beranger, B., and Sisson, S. A. (2020), “Constructing Likelihood Functions for Interval-Valued Random Variables,” Scandinavian Journal of Statistics, 47, 1–35. DOI: 10.1111/sjos.12395.

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