Log-Mean Linear Parameterizations for Smooth Independence Models Monia Lupparelli, Luca La Rocca and Alberto Roverato Key words: marginal independence, smooth model, sparse table 1 Introduction In categorical data analysis the choice of suitable parameterizations is a relevant aspect for several reasons: (i) the parameter space is often involved, (ii) its dimen- sion rapidly increases with the number of variables, (iii) tables are sparse for high dimensional data, (iv) models specified by non-linear constraints on joint probabil- ities can result in non-smooth models. There is, in particular, an interest in parame- terizations defining smooth and interpretable models by means of linear constraints on the parameter space. These considerations motivate the increasing attention for novel parameterizations; see [5], [1] and [9]. We focus on the log-mean linear (LML) parameterization recently introduced by [9] for the binary case and then generalized by [8], which is suitable for mod- els of marginal independence, also known as bi-directed graph or covariance graph models; see [3] and [4]. These models investigate the marginal independence struc- tures of the variables and are very useful in high dimensional data analysis, where working in low-dimension sub-spaces is highly desirable. Monia Lupparelli University of Bologna, Department of Statistical Sciences, Via Belle Arti 41, 40126 Bologna, Italy, e-mail: monia.lupparelli@unibo.it Luca La Rocca University of Modena and Reggio Emilia, Department of Computer, Mathematical and Physical Sciences, Via Campi 213/b, 41125 Modena, Italy, e-mail: luca.larocca@unimore.it Alberto Roverato University of Bologna, Department of Statistical Sciences, Via Belle Arti 41 40126 Bologna, Italy, e-mail: alberto.roverato@unibo.it 1