The authors develop regression models with cross- classified responses, generalizing logistic regression beyond binary data. Absent of covariates, cross-classified data are typically aggregated into contingency tables, for which log-linear models are among the standard analytical tools. With the proposed log-linear regression models, one effectively "disaggregates" contingency tables along an x-axis, allowing the modeling of table probabilities as functions of covariates. The problem is formulated as a special case of penalized likelihood conditional density estimation on a generic domain X times Y, but beyond the basic formulation, modeling tools are developed that only make sense for an all discrete Y, which include the Bayesian confidence intervals for odds ratios among margins of tables and the mixed-effect models for correlated data. Also discussed are cross-validation for smoothing parameter selection and "hypothesis testing" via Kullback-Leibler projection. The modeling and data analytical tools are implemented in the ssllrm suite of the R package gss, whose usage is described in an appendix.

Chong Gu is a Professor in the Department of Statistics at Purdue University. After receiving his PhD degree (Statistics, 1989) from University of Wisconsin-Madison, he spent one year as a postdoctoral fellow at the University of British Columbia before joining the faculty at Purdue in 1990. Gu's main research interests are in multivariate smoothing using roughness penalties, and he has worked on the methodology, the theory, and the computation in the settings of Gaussian and non-Gaussian regression, density estimation, and hazard estimation. He is the author of the 2002 Springer book Smoothing Spline ANOVA Models, of which the second edition is forthcoming. Gu recognizes the importance of the dissemination of methodological innovations via open-source software, and takes pride in the creation and the continuing development of the R package gss.

Ping Ma is an Associate Professor in the Department of Statistics at University of Illinois at Urbana-Champaign. He received his PhD in statistics from Purdue University in 2003 and was a postdoctoral fellow at Jun Liu's lab at Harvard University from 2003 to 2005. Ping's research focuses on nonparametric estimation, bioinformatics and geophysics. He was Beckman Fellow at the Center for Advanced Study at University of Illinois at Urbana-Champaign and a recipient of the National Science Foundation CAREER Award. He is an elected member of International Statistical Institute.

The award-winning paper was presented by the authors at the 40th Annual Meeting of the Statistical Society of Canada held in Guelph, Ontario, June 3 to 6, 2012.