Rank-order relational data, in which each actor ranks other actors according to some criterion, often arise from sociometric measurements of judgment or preference. The authors propose a general framework for representing such data, define a class of exponential-family models for rank-order relational structure, and derive sufficient statistics for interdependent ordinal judgments that do not require the assumption of comparability across raters. These statistics allow estimation of effects for a variety of plausible mechanisms governing rank structure, both in a cross-sectional context and evolving over time. The authors apply this framework to model the evolution of liking judgments in an acquaintance process and to model recall of relative volume of interpersonal interaction among members of a technology education program.
AndersonCameronSrivastavaSanjayBeerJennifer S.SpataroSandra E.ChatmanJennifer A.2006. “Knowing Your Place: Self-perceptions of Status in Face-to-face Groups.” Journal of Personality and Social Psychology91(6):1094–1110.
2.
ArabiePhippsBoormanScott A.LevittPaul R.1978. “Constructing Blockmodels: How and Why.” Journal of Mathematical Psychology17(1):21–63.
3.
AschSolomon E.1951. “Effects of Group Pressure upon the Modification and Distortion of Judgments.” Pp. 177–90 in Groups, Leadership and Men, edited by GuetzkowHarold. Oxford, UK: Carnegie Press.
4.
Barndorff-NielsenOle E.1978. Information and Exponential Families in Statistical Theory. New York: John Wiley.
5.
BergerJosephCohenBernard P.ZelditchMorris. 1972. “Status Characteristics and Social Interaction.” American Sociological Review37(3):241–55.
6.
BergerJosephFisekM. HamitNormanRobert Z.ZelditchMorris. 1977. Status Characteristics and Social Interaction: An Expectation States Approach. New York: Elsevier.
7.
BernardH. RussellKillworthPeterKronenfeldDavidSailerLee. 1984. “The Problem of Informant Accuracy: The Validity of Retrospective Data.” Annual Review of Anthropology13:495–517.
8.
BernardH. RussellKillworthPeter D.1977. “Informant Accuracy in Social Network Data II.” Human Communication Research4(1):3–18.
9.
BordieuPierre. 1968. “Outline of a Sociological Theory of Art Perception.” International Social Science Journal20(4):589–612.
10.
BreigerRonald L.BoormanScott A.ArabiePhipps. 1975. “An Algorithm for Clustering Relational Data with Applications to Social Network Analysis and Comparison with Multidimensional Scaling.” Journal of Mathematical Psychology12:323–83.
11.
BrownLawrence D.1986. Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. Vol. 9, Lecture Notes—Monograph Series. Hayward, CA: Institute of Mathematical Statistics.
12.
ButtsCarter T.2007a. “Models for Generalized Location Systems.” Pp. 283–348 in Sociological Methodology, Vol. 37, edited by XieYu. Hoboken, NJ: Wiley-Blackwell.
13.
ButtsCarter T.2007b. “Permutation Models for Relational Data.” Pp. 257–81 in Sociological Methodology, Vol. 37, edited by XieYu. Hoboken, NJ: Wiley-Blackwell.
14.
ButtsCarter T.2011. “Bernoulli Graph Bounds for General Random Graphs.” Pp. 299–345 in Sociological Methodology, Vol. 41, edited by LiaoTim Futing. Hoboken, NJ: Wiley-Blackwell.
15.
CaimoAlbertoFrielNial. 2011. “Bayesian Inference for Exponential Random Graph Models.” Social Networks33(1):41–55.
DekkerDavidKrackhardtDavidSnijdersTom A. B.2007. “Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions.” Psychometrika72(4):563–81.
18.
DoreianP.1990. “Network Autocorrelation Models: Problems and Prospects.” Pp. 369–89 in Spatial Statistics: Past, Present, and Future, edited by GriffithI. D. A.Ann Arbor, MI: Institute of Mathematical Geography.
19.
DoreianPatrickKapuscinskiRomanKrackhardtDavidSzczypulaJanusz. 1996. “A Brief History of Balance through Time.” Journal of Mathematical Sociology21(1–2):113–31.
20.
DunbarRobin. 1997. Grooming, Gossip, and the Evolution of Language. Cambridge, MA: Harvard University Press.
21.
EnelowJames M.HinichMelvin J.1984. The Spatial Theory of Voting: An Introduction. Cambridge, UK: Cambridge University Press.
22.
GeyerCharles J.ThompsonElizabeth A.1992. “Constrained Monte Carlo Maximum Likelihood for Dependent Data.” Journal of the Royal Statistical Society, Series B54(3):657–99.
23.
GoodreauSteven M.KittsJamesMorrisMartina. 2008a[b]. “Birds of a Feather, or Friend of a Friend? Using Exponential Random Graph Models to Investigate Adolescent Social Networks.” Demography46(1):103–25.
GormleyIsobel ClaireMurphyThomas Brendan. 2008. “Exploring Voting Blocs within the Irish Electorate: A Mixture Modeling Approach.” Journal of the American Statistical Association103(483):1014–27.
26.
HandcockMark S.GileKrista J.2010. “Modeling Social Networks from Sampled Data.” Annals of Applied Statistics4(1):5–25.
27.
HandcockMark S.HunterDavid R.ButtsCarter T.GoodreauSteven M.KrivitskyPavel N.MorrisMartina. 2014. “ergm: Fit, Simulate and Diagnose Exponential-family Models for Networks.” The Statnet Project. R Package Version 3.2.4. Retrieved (http://www.statnet.org).
28.
HannekeSteveFuWenjieXingEric P.2010. “Discrete Temporal Models of Social Networks.” Electronic Journal of Statistics4:585–605.
29.
HarrisKathleen M.FloreyF.TaborJoyceBearmanPeter S.JonesJ.UdryJ. Richard. 2003. “The National Longitudinal Study of Adolescent Health: Research Design.” Technical report, University of North Carolina.
30.
HollandPaul W.LeinhardtSamuel. 1981. “An Exponential Family of Probability Distributions for Directed Graphs.” Journal of the American Statistical Association76(373):33–65.
31.
HubertLawrence J.1987. Assignment Methods in Combinatorial Data Analysis. New York: Marcel Dekker.
32.
HummelRuth M.HunterDavid R.HandcockMark S.2012. “Improving Simulation-based Algorithms for Fitting ERGMs.” Journal of Computational and Graphical Statistics21(4):920–39.
33.
HunterDavid R.GoodreauSteven M.HandcockMark S.2008. “Goodness of Fit for Social Network Models.” Journal of the American Statistical Association103:248–58.
34.
HunterDavid R.HandcockMark S.2006. “Inference in Curved Exponential Family Models for Networks.” Journal of Computational and Graphical Statistics15(3):565–83.
35.
HunterDavid R.HandcockMark S.ButtsCarter T.GoodreauSteven M.MorrisMartina. 2008. “ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks.” Journal of Statistical Software24(1):1–29.
36.
JohnsonJeffrey C.BosterJames S.PalinkasLawrence A.2003. “Social Roles and the Evolution of Networks.” Journal of Mathematical Sociology27(1):89–121.
37.
KrackhardtDavid. 1987. “QAP Partialling as a Test of Spuriousness.” Social Networks9(2):171–86.
38.
KrackhardtDavidHandcockMark S.2007. “Heider versus Simmel: Emergent Features in Dynamic Structures.” Pp. 14Ą27 In Statistical Network Analysis: Models, Issues, and New Directions: ICML 2006 Workshop on Statistical Network Analysis, Pittsburgh, PA, USA, June 29, 2006, Revised Selected Papers, edited by AiroldiEdoardoBleiDavid M.FienbergStephen E.GoldenbergAnnaXingEric P.ZhengAlice X.New York: Springer.
39.
KrivitskyPavel N.2012. “Exponential-family Random Graph Models for Valued Networks.” Electronic Journal of Statistics6:1100–28.
40.
KrivitskyPavel N.HandcockMark S.2014. “A Separable Model for Dynamic Networks.” Journal of the Royal Statistical Society, Series B76(1):29–46.
41.
LevineJoel H.1993. Exceptions Are the Rule: Inquiries on Method in the Social Sciences. Boulder, CO: Westview.
42.
MorseStanley J.ReisHarry T.GruzenJoanWolffEllen. 1974. “The Eye of the Beholder: Determinants of Physical Attractiveness Judgments in the U.S. and South Africa.” Journal of Personality42(4):528–42.
43.
NakaoKeikoRomneyA. Kimball. 1993. “Longitudinal Approach to Subgroup Formation: Re-analysis of Newcomb’s Fraternity Data.” Social Networks15(2):109–31.
44.
NewcombTheodore M.1956. “The Prediction of Interpersonal Attraction.” American Psychologist11(11):575–86.
45.
NewcombTheodore M.1961. The Acquaintance Process. New York: Holt, Rinehart.
46.
PattisonPhilippa E.1982. “The Analysis of Semigroups of Multirelational Systems.” Journal of Mathematical Psychology25(1):87–118.
47.
PlackettRobin L.1975. “The Analysis of Permutations.” Journal of the Royal Statistical Society, Series C (Applied Statistics)24(2):193–202.
48.
R Core Team. 2014. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
49.
RinaldoAlessandroFienbergStephen E.ZhouYi. 2009. “On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models.” Electronic Journal of Statistics3:446–84.
50.
RobinsGarryPattisonPhilippaWassermanStanley S.1999. “Logit Models and Logistic Regressions for Social Networks: III. Valued Relations.” Psychometrika64(3):371–94.
51.
SampsonSamuel F.1968. “A Novitiate in a Period of Change: An Experimental and Case Study of Social Relationships.” PhD dissertation, Department of Sociology, Cornell University.
52.
SchweinbergerMichael. 2011. “Instability, Sensitivity, and Degeneracy of Discrete Exponential Families.” Journal of the American Statistical Association106(496):1361–70.
53.
SnijdersTom A. B.1996. “Stochastic Actor-oriented Models for Network Change.” Journal of Mathematical Sociology21(1–2):149–72.
54.
SnijdersTom A. B.PattisonPhilippa E.RobinsGarry L.HandcockMark S.2006. “New Specifications for Exponential Random Graph Models.” Pp. 99–153 in Sociological Methodology, Vol. 36, edited by StolzenbergRoss M.Boston, MA: Blackwell.
55.
StraussDavidIkedaMichael. 1990. “Pseudolikelihood Estimation for Social Networks.” Journal of the American Statistical Association85(409):204–12.
56.
ThomasAndrew C.BlitzsteinJoseph K.2011. “Valued Ties Tell Fewer Lies: Why Not to Dichotomize Network Edges with Thresholds.” Retrieved February 3, 2017 (https://arxiv.org/pdf/1101.0788.pdf).
57.
van DuijnMarijtje A. J.SnijdersTom A. B.ZijlstraBonne J. H.2004. “p2: A Random Effects Model with Covariates for Directed Graphs.” Statistica Neerlandica58(2):234–54.
58.
WassermanStanley. 1980. “Analyzing Social Networks as Stochastic Processes.” Journal of the American Statistical Association75(370):280–94.
59.
WassermanStanley S.PattisonPhilippa. 1996. “Logit Models and Logistic Regressions for Social Networks: I. An Introduction to Markov Graphs and p∗.” Psychometrika61(3):401–25.
60.
WebsterMurrayDriskellJames E.1983. “Beauty as Status.” American Journal of Sociology89(1):140–65.
61.
WhiteHarrison C.BoormanScott A.BreigerRonald L.1976. “Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions.” American Journal of Sociology81(4):730–80.
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