Sequences of regressions and their independences
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Ali RA, Richardson TS, Spirtes P (2009) Markov equivalence for ancestral graphs. Ann Stat 37:2808–2837
Anderson TW (1958) An introduction to multivariate statistical analysis. Wiley, New York (3rd edn, 2003)
Anderson TW (1973) Asymptotically efficient estimation of covariance matrices with linear structure. Ann Stat 1:135–141
Andersson SA, Perlman MD (2006) Characterizing Markov equivalence classes for AMP chain graph. Ann Stat 34:939–972
Andersson SA, Madigan D, Perlman MD, Triggs CM (1997) A graphical characterization of lattice conditional independence models. Ann Math Artif Intell 21:27–50
Andersson SA, Madigan D, Perlman MD (2001) Alternative Markov properties for chain graphs. Scand J Stat 28:33–86
Barndorff-Nielsen OE (1978) Information and exponential families in statistical theory. Wiley, Chichester
Birch MW (1963) Maximum likelihood in three-way contingency tables. J R Stat Soc B 25:220–233
Bishop YMM, Fienberg SF, Holland PW (1975) Discrete multivariate analysis. MIT Press, Cambridge
Blair JRS, Peyton BW (1993) An introduction to chordal graphs and clique trees. In: George JA, Gilbert JR, Liu JWH (eds) Graph theory and sparse matrix computations. IMA volumes in mathematics and its applications, vol 56. Springer, New York, pp 1–30
Brito C, Pearl J (2002) A new identification condition for recursive models with correlated errors. Struct Equ Model 9:459–474
Brown LD (1986) Fundamentals of statistical exponential families with applications in statistical decision theory. LNMS, vol 9. Inst Math Stat, Beachwood
Castelo R, Kocka T (2003) On inclusion-driven learning of Bayesian networks. J Mach Learn Res 4:527–574
Castelo R, Siebes A (2003) A characterization of moral transitive acyclic directed graph Markov models as labeled trees. J Stat Plan Inference 115:235–259
Caussinus H (1966) Contribution á l’analyse statistique des tableaux de corrélation. Ann Fac Sci Univ Toulouse 29:77–183
Cayley A (1889) A theorem on trees. Q J Math 23:376–378
Chaudhuri S, Drton M, Richardson TS (2007) Estimation of a covariance matrix with zeros. Biometrika 94:199–216
Cochran WG (1938) The omission or addition of an independent variate in multiple linear regression. Suppl J R Stat Soc 5:171–176
Chickering DM (1995) A transformational characterization of equivalent Bayesian networks. In: Besnard P, Hanks S (eds) Proc 10th UAI conf. Kaufman, San Mateo, pp 87–98
Cox DR (1966) Some procedures associated with the logistic qualitative response curve. In: David FN (ed) Research papers in statistics: Festschrift for J Neyman. Wiley, New York, pp 55–71
Cox DR, Wermuth N (1990) An approximation to maximum-likelihood estimates in reduced models. Biometrika 77:747–761
Cox DR, Wermuth N (1993) Linear dependencies represented by chain graphs (with discussion). Stat Sci 8:204–218; 247–277
Cox DR, Wermuth N (1994) Tests of linearity, multivariate normality and adequacy of linear scores. J R Stat Soc C 43:347–355
Cox DR, Wermuth N (1996) Multivariate dependencies: models, analysis, and interpretation. Chapman and Hall/CRC Press, London
Cox DR, Wermuth N (1999) Likelihood factorizations for mixed discrete and continuous variables. Scand J Stat 26:209–220
Cox DR, Wermuth N (2003) A general condition for avoiding effect reversal after marginalization. J R Stat Soc B 65:937–941
Darroch JN (1962) Interactions in multi-factor contingency tables. J R Stat Soc B 24:251–263
Darroch JN, Lauritzen SL, Speed TP (1980) Markov fields and log-linear models for contingency tables. Ann Stat 8:522–539
Dawid AP (1979) Conditional independence in statistical theory (with discussion). J R Stat Soc B 41:1–31
Dempster AP (1969) Elements of continuous multivariate analysis. Addison-Wesley, Reading
Dinitz Y (2006) Dinitz’ algorithm: the original version and even’s version. In: Even S, Goldreich O, Rosenberg AL, Selman AL (eds) Essays in memory of Shimon Even. Springer, New York, pp 218–240
Drton M, Richardson TS (2004) Multimodality of the likelihood in the bivariate seemingly unrelated regression model. Biometrika 91:383–392
Drton M, Richardson TS (2008b) Graphical methods for efficient likelihood inference in Gaussian covariance models, J. J Mach Learn Res 9:893–914
Foygel R, Draisma J, Drton M (2011) Half-trek criterion for generic identifiability of linear structural equation models (submitted). Available under http://arxiv.org/abs/1107.5552
Frydenberg M (1990) The chain graph Markov property. Scand J Stat 17:333–353
Geiger D, Verma TS, Pearl J (1990) Identifying independence in Bayesian networks. Networks 20:507–534
Glonek GFV, McCullagh P (1995) Multivariate logistic models. J R Stat Soc B 53:533–546
Goodman LA (1970) The multivariate analysis of qualitative data: interaction among multiple classifications. J Am Stat Assoc 65:226–256
Haavelmo T (1943) The statistical implications of a system of simultaneous equations. Econometrica 11:1–12
Hardt J, Sidor A, Nickel R, Kappis B, Petrak F, Egle UT (2008) Childhood adversities and suicide attempts: a retrospective study. J Fam Violence 23:713–718
Jensen ST (1988) Covariance hypotheses which are linear in both the covariance and the inverse covariance. Ann Stat 16:302–322
Jöreskog KG (1981) Analysis of covariance structures. Scand J Stat 8:65–92
Kang C, Tian J (2009) Markov properties for linear causal models with correlated errors. J Mach Learn Res 10:41–70
Kappesser J (1997) Bedeutung der Lokalisation für die Entwicklung und Behandlung chronischer Schmerzen. Thesis, Department of Psychology, University of Mainz
Kauermann G (1996) On a dualization of graphical Gaussian models. Scand J Stat 23:115–116
Kiiveri HT (1987) An incomplete data approach to the analysis of covariance structures. Psychometrika 52:539–554
Kline RB (2006) Principles and practice of structural equation modeling, 3rd edn. Guilford Press, New York
Lauritzen SL (1996) Graphical models. Oxford University Press, Oxford
Lauritzen SL, Wermuth N (1989) Graphical models for association between variables, some of which are qualitative and some quantitative. Ann Stat 17:31–57
Lehmann EL, Scheffé H (1955) Completeness, similar regions and unbiased estimation. Sankhya 14:219–236
Lněnička R, Matúš F (2007) On Gaussian conditional independence structures. Kybernetika 43:323–342
Lupparelli M, Marchetti GM, Bergsma WP (2009) Parameterization and fitting of discrete bi-directed graph models. Scand J Stat 36:559–576
Mandelbaum A, Rüschendorf L (1987) Complete and symmetrically complete families of distributions. Ann Stat 15:1229–1244
Marchetti GM, Lupparelli M (2011) Chain graph models of multivariate regression type for categorical data. Bernoulli 17:845–879
Marchetti GM, Wermuth N (2009) Matrix representations and independencies in directed acyclic graphs. Ann Stat 47:961–978
McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman and Hall/CRC Press, London
Nelder JA, Wedderburn R (1972) Generalized linear models. J R Stat Soc, A 135:37–384
Pearl J (1988) Probabilistic reasoning in intelligent systems. Kaufmann, San Mateo
Pearl J (2009) Causality: models, reasoning, and inference, 2nd edn. Cambridge University Press, New York
Pearl J, Paz A (1987) Graphoids: a graph based logic for reasoning about relevancy revelations. In: Boulay BD, Hogg D, Steel L (eds) Advances in artificial intelligence II. North Holland, Amsterdam, pp 357–363
Pearl J, Wermuth N (1994) When can association graphs admit a causal interpretation? In: Cheeseman P, Oldford W (eds) Models and data, artificial intelligence and statistics IV. Springer, New York, pp 205–214
Roverato A (2005) A unified approach to the characterisation of Markov equivalence classes of directed acyclic graphs, chain graphs with no flags and chain graphs. Scand J Stat 32:295–312
Roverato A, Studený M (2006) A graphical representation of equivalence classes of AMP chain graphs. J Mach Learn Res 7:1045–1078
Rudas T, Bergsma WP, Nemeth R (2010) Marginal log-linear parameterization of conditional independence models. Biometrika 97:1006–1012
Sadeghi K (2009) Representing modified independence structures. Transfer thesis, Oxford University
Sadeghi K, Lauritzen SL (2012) Markov properties of mixed graphs (submitted). Also available on http://arxiv.org/abs/1109.5909
San Martin E, Mouchart M, Rolin JM (2005) Ignorable common information, null sets and Basu’s first theorem. Sankhya 67:674–698
Stanghellini E, Wermuth N (2005) On the identification of path analysis models with one hidden variable. Biometrika 92:337–350
Studený M (2005) Probabilistic conditional independence structures. Springer, London
Sundberg R (2010) Flat and multimodal likelihoods and model lack of fit in curved exponential families. Scand J Stat 37:632–643
Tarjan RE, Yannakakis M (1984) Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J Comput 13:566–579
Verma T, Pearl J (1990) Equivalence and synthesis of causal models. In: Bonissone PP, Henrion M, Kanal LN, Lemmer JF (eds) Proc 6th UAI conf. Elsevier, Amsterdam, pp 220–227
Wermuth N (1976a) Analogies between multiplicative models for contingency tables and covariance selection. Biometrics 32:95–108
Wermuth N (1980) Linear recursive equations, covariance selection, and path analysis. J Am Stat Assoc 75:963–997
Wermuth N, Cox DR (1998) On association models defined over independence graphs. Bernoulli 4:477–495
Wermuth N, Cox DR (2004) Joint response graphs and separation induced by triangular systems. J R Stat Soc B 66:687–717
Wermuth N, Lauritzen SL (1983) Graphical and recursive models for contingency tables. Biometrika 70:537–552
Wermuth N, Lauritzen SL (1990) On substantive research hypotheses, conditional independence graphs and graphical chain models (with discussion). J R Stat Soc B 52:21–75
Wermuth N, Wiedenbeck M, Cox DR (2006b) Partial inversion for linear systems and partial closure of independence graphs. BIT Numer Math 46:883–901
Wermuth N, Marchetti GM, Cox DR (2009) Triangular systems for symmetric binary variables. Electron J Stat 3:932–955
Whittaker J (1990) Graphical models in applied multivariate statistics. Wiley, Chichester
Wiedenbeck M, Wermuth N (2010) Changing parameters by partial mappings. Stat Sin 20:823–836
Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J Am Stat Assoc 57:348–368