I often work with survey datasets for which n<p(p+3)/2 but where the number of variables with missing data is a lot less than n. My intuition tells me that in these cases, there is no reason to impute from a model with p(p+3)/2 parameters. It seems excessive and requires that we fiddle with dropping variables. I know we could ridge the covariance matrix, but I'd like to bracket that for now to consider the question of whether we really need those p(p+3)/2 parameters in the first place. As an example, suppose we have data with 4 variables, A,B,C, and D. We have complete data for A and B. C and D exhibit arbitrary missingness (maybe monotone, maybe not). In this case, a full joint normal approach such as Amelia's algorithm would estimate parameters for a 4-dimensional normal distribution---that is, 4 means and 10 covariances, or 14 parameters. Suppose as an alternative, we impute using a bivariate normal model, where C and D are modeled as bivariate normal, with means that are regressions onto A and B, and conditional on A and B, C and D covary according to Cov(C,D) not zero. This distribution is thus characterized by 4 regression coefficients, Var(C), Var(D), and Cov(C,D)---that is, 7 parameters (i.e. half as many as in the full joint model) . Is there any reason that the second, bivariate, approach wouldn't be preferred? (If so, the obvious follow-up is, why are we trying to build more model than we need?) Thanks for any illumination! Cyrus -- Cyrus Samii Political Science Columbia University cds81(a)columbia.edu Burundi Survey: www.columbia.edu/~cds81/burundisurvey/ ISERP Statistical Consulting: www.iserp.columbia.edu/services/statistical_consulting.html Comparative Political Economy Blog: cpecolumbia.blogspot.com - Amelia mailing list served by Harvard-MIT Data Center [Un]Subscribe/View Archive: http://lists.gking.harvard.edu/?info=amelia More info about Amelia: http://gking.harvard.edu/amelia