During social interactions an individual’s behavior is largely governed by the subset of signals emitted by others. Discrimination of ‘self’ from ‘other’ regulates the territorial urine countermarking behavior of mice. To identify the cues for this social discrimination and understand how they are interpreted, we designed an olfactory-dependent countermarking assay. We find Major Urinary Proteins (MUPs) sufficient to elicit countermarking, and unlike other vomeronasal ligands that are detected by specifically tuned sensory neurons, MUPs are detected by a combinatorial strategy. A chemosensory signature of ‘self’ that modulates behavior is developed via experience through exposure to a repertoire of MUPs. In contrast, aggression can be elicited by MUPs in an experience-independent but context dependent manner. These findings reveal that individual-emitted chemical cues can be interpreted based on their combinatorial permutation and relative ratios, and they can transmit both fixed and learned information to promote multiple behaviors.

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Summary. In this article, we propose a generalized estimating equations (GEE) approach for correlated ordinal or nominal multinomial responses using a local odds ratios parameterization. Our motivation lies upon observing that: (i) modeling the dependence between correlated multinomial responses via the local odds ratios is meaningful both for ordinal and nominal response scales and (ii) ordinary GEE methods might not ensure the joint existence of the estimates of the marginal regression parameters and of the dependence structure. To avoid (ii), we treat the so-called "working" association vector α as a "nuisance" parameter vector that defines the local odds ratios structure at the marginalized contingency tables after tabulating the responses without a covariate adjustment at each time pair. To estimate α and simultaneously approximate adequately possible underlying dependence structures, we employ the family of association models proposed by Goodman. In simulations, the parameter estimators with the proposed GEE method for a marginal cumulative probit model appear to be less biased and more efficient than those with the independence "working" model, especially for studies having time-varying covariates and strong correlation. Key words:Association models; Generalized estimating equations; Local odds ratios; Longitudinal data analysis; Multinomial responses. IntroductionLiang and Zeger (1986) originally proposed the generalized estimating equations (GEE) method as an extension of generalized linear models to handle longitudinal data. In contrast to ordinary maximum likelihood approaches, the GEE method provides consistent estimators of the marginal regression parameter vector β and of the covariance matrix of those estimates even if α, the parameter vector that describes the correlation/association pattern within the subjects, has been misspecified.Application of the GEE method for correlated multinomial responses with at least three response categories has been in need of further development. One reason relates to difficult issues in parameterizing the association structure in a way that is sensible for categorical response variables, and in particular, is suitable for both nominal and ordinal variables. In the relevant literature, a correlation coefficient Miller, Davis, and Landis, 1993;Parsons, Edmondson, and Gilmour, 2006) and a global odds ratios (Williamson, Kim, and Lipsitz, 1995;Lumley, 1996) parameterization for α have been proposed. The correlation coefficient parameterization is severely restricted by the marginal model even for bivariate multinomial responses, as we show in Section 2, while the use of a global odds ratios parameterization is limited to ordinal responses. To this end, note that the use of the GEE approach of Parsons et al. (2006) is restricted to ordinal responses under a marginal cumulative logistic model. Another difficult issue is

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