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Data Mining

Tree-Structured Clustering in Fixed Effects Models

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Pages 380-392 | Received 01 Jan 2016, Published online: 17 May 2018

References

  • Agresti, A., Caffo, B., and Ohman-Strickland, P. (2004), “Examples in which Misspecification of a Random Effects Distribution Reduces Efficiency, and Possible Remedies,” Computational Statistics and Data Analysis, 47, 639–653.
  • Aitkin, M. (1999), “A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models,” Biometrics, 55, 117–128.
  • Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015), “Fitting Linear Mixed-Effects Models Using lme4,” Journal of Statistical Software, 67, 1–48.
  • Bates, D., Mäechler, M., and Bolker, B. (2014), mlmRev: Examples from Multilevel Modelling Software Review, R package version 1.0-6.
  • Berger, M. (2016), structree: Tree-Structured Clustering for the Identification of Latent Groups, R package version 1.1.5.
  • Bondell, H. D., and Reich, B. J. (2008), “Simultaneous Regression Shrinkage, Variable Selection and Clustering of Predictors With Oscar,” Biometrics, 64, 115–123.
  • Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, J. C. (1984), Classification and Regression Trees, Monterey, CA: Wadsworth.
  • Breslow, N. E., and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Model,” Journal of the American Statistical Association, 88, 9–25.
  • Bush, C. A., and MacEachern, S. N. (1996), “A Semiparametric Bayesian Model for Randomised Block Designs,” Biometrika, 83, 275–285.
  • Chen, J., and Davidian, M. (2002), “A Monte Carlo EM Algorithm for Generalized Linear Models with Flexible Random Effects Distribution,” Biostatistics, 3, 347–360.
  • Claeskens, G., and Hart, J. D. (2009), “Goodness-of-Fit Tests in Mixed Models,” TEST, 18, 213–239.
  • De Boeck, P., and Wilson, M. (2004), Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach, New York, NY: Springer Verlag.
  • Efron, B., and Tibshirani, R. (1994), An Introduction to the Bootstrap (Vol. 57), New York, NY: Chapman & Hall/CRC.
  • Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209–230.
  • Fisher, W. D. (1958), “On Grouping for Maximum Homogeneity,” Journal of the American Statistical Association, 53, 789–798.
  • Follmann, D., and Lambert, D. (1989), “Generalizing Logistic Regression by Non-Parametric Mixing,” Journal of the American Statistical Association, 84, 295–300.
  • Gertheiss, J., and Tutz, G. (2010), “Sparse Modeling of Categorial Explanatory Variables,” Annals of Applied Statistics, 4, 2150–2180.
  • Grilli, L., and Rampichini, C. (2011), “The Role of Sample Cluster Means in Multilevel Models: A View on Endogeneity and Measurement Error Issues,” Methodology: European Journal of Research Methods for the Behavioural and Social Sciences, 7, 121–133.
  • Grün, B., and Leisch, F. (2007), “Fitting Finite Mixtures of Generalized Linear Regressions in R,” Computational Statistics & Data Analysis, 51, 5247–5252.
  • ——— (2008), “FlexMix version 2: Finite Mixtures With Concomitant Variables and Varying and Constant Parameters,” Journal of Statistical Software, 28, 1–35.
  • Hajjem, A., Bellavance, F., and Larocque, D. (2011), “Mixed Effects Regression Trees for Clustered Data,” Statistics and Probability Letters, 81, 451–459.
  • Hastie, T., Tibshirani, R., and Friedman, J. H. (2009), The Elements of Statistical Learning (2nd ed.), New York, NY: Springer-Verlag.
  • Heagerty, P., and Kurland, B. F. (2001), “Misspecified Maximum Likelihood Estimates and Generalised Linear Mixed Models,” Biometrika, 88, 973–985.
  • Heinzl, F., and Tutz, G. (2013), “Clustering in Linear Mixed Models With Approximate Dirichlet Process Mixtures Using EM Algorithm,” Statistical Modelling, 13, 41–67.
  • ——— (2014), “Clustering in Linear-Mixed Models With a Group Fused Lasso Penalty,” Biometrical Journal, 56, 44–68.
  • ——— (2015), “Additive Mixed Models With Approximate Dirichlet Process Mixtures: The EM Approach,” Statistics and Computing, 26, 73–92.
  • Hjort, N. L., Holmes, C., Müller, P., and Walker, S. G. (2010), Bayesian Nonparametrics (vol. 28), Cambridge, UK: Cambridge University Press.
  • Hothorn, T., Hornik, K., and Zeileis, A. (2006), “Unbiased Recursive Partitioning: A Conditional Inference Framework,” Journal of Computational and Graphical Statistics, 15, 651–674.
  • Huang, X. (2009), “Diagnosis of Random-Effect Model Misspecification in Generalized Linear Mixed Models for Binary Response,” Biometrics, 65, 361–368.
  • Khalili, A., and Chen, J. (2007), “Variable Selection in Finite Mixture of Regression Models,” Journal of the American Statistical Association, 102, 1025–1038.
  • Litière, S., Alonso, A., and Molenberghs, G. (2007), “Type I and Type II Error Under Random Effects Misspecification in Generalized Linear Mixed Models,” Biometrics, 63, 1038–1044.
  • Lombardía, M. J., and Sperlich, S. (2012), “A New Class of Semi-Mixed Effects Models and Its Application in Small Area Estimation,” Computational Statistics & Data Analysis, 56, 2903–2917.
  • Magder, L., and Zeger, S. (1996), “A Smooth Nonparametric Estimate of a Mixing Distribution Using Mixtures of Gaussians,” Journal of the American Statistical Association, 91, 1141–1151.
  • McCulloch, C., and Searle, S. (2001), Generalized, Linear, and Mixed Models, New York, NY: Wiley.
  • Molenberghs, G., and Verbeke, G. (2005), Models for Discrete Longitdinal Data, New York, NY: Springer–Verlag.
  • Morgan, J. N., and Sonquist, J. A. (1963), “Problems in the Analysis of Survey Data, and a Proposal,” Journal of the American Statistical Association, 58, 415–435.
  • Müller, P., and Rosner, G. L. (1997), “A Bayesian Population Model With Hierarchical Mixture Priors Applied to Blood Count Data,” Journal of the American Statistical Association, 92, 1279–1292.
  • Oelker, M.-R. (2015), gvcm.cat: Regularized Categorical Effects/Categorical Effect Modifiers/Continuous/Smooth Effects in GLMs, r package version 1.9.
  • Quinlan, J. R. (1986), “Industion of Decision Trees,” Machine Learning, 1, 81–106.
  • ——— (1993), Programs for Machine Learning, San Francisco: Morgan Kaufmann PublisherInc.
  • R Core Team (2016), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Ripley, B. D. (1996), Pattern Recognition and Neural Networks, Cambridge, UK: Cambridge University Press.
  • Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge, UK: Cambridge University Press.
  • Sela, R. J., and Simonoff, J. S. (2012), “RE-EM Trees: A Data Mining Approach for Longitudinal and Clustered Data,” Machine Learning, 86, 169–207.
  • Sethuraman, J. (1994), “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, 4, 639–650.
  • Städler, N., Bühlmann, P., and van de Geer, S. (2010), “L1-Penalization for Mixture Regression Models,” Test, 19, 209–256.
  • Strobl, C., Malley, J., and Tutz, G. (2009), “An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests,” Psychological Methods, 14, 323–348.
  • Tutz, G., and Gertheiss (2014), “Rating Scales as Predictors – The Old Question of Scale Level and Some Answers,” Psychometrika, 79, 357–376.
  • Tutz, G., and Oelker, M. (2015), “Modeling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures,” International Statistical Review[on-line], doi:10.1111/insr.12161.
  • Verbeke, G., and Molenberghs, G. (2000), Linear Mixed Models for Longitudinal Data, New York, NY: Springer–Verlag.
  • Zhang, H., and Singer, B. (1999), Recursive Partitioning in the Health Sciences, New York, NY: Springer–Verlag.

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