Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930's, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970's and continuing into the 1980's, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikeda's (1990) estimation strategy.In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.This research was supported by grants from the Australian Research Council and the National Science Foundation (#SBR93-10184). This paper was presented at the 1994 Annual Meeting of the Psychometric Society, Champaign, Illinois, June 1994. Special thanks go to Sarah Ardu for programming assistance, Laura Koehly and Garry Robins for help with this research, and to Shizuhiko Nishisato and three reviewers for their comments. INTERNETemail addresses:pattison@psych.unimelb.edu.au (PP);stanwass@uiuc.edu (SW). Affiliations: Department of Psychology, University of Melbourne (PP); Department of Psychology, Department of Statistics, and The Beckman Institute for Advanced Science and Technology, University of Illinois (SW).     

Models for letter cancellation performance and their implications for models of reading

Models for letter cancellation are developed, i.e. for tasks where subjects read a coherent piece of prose at the same time as trying to cancel every target letter they encounter. These models have two components (i) a model of how information is represented by the reader, (ii) a model of how this information is scanned to enable the reader to detect particular target letters. Models of representation range from a photographic image of the printed page to a sophisticated multi-level representation, and models of scanning range from a series of independent saccadic movements (like eye movements) to scans which take into account morphemic and syntactic structure.

Several predictions about the detailed pattern of letter cancellation data are developed on the basis of these models, and these are tested on a data base collected by Smith and Groat (1979). While some support for the simpler models is forthcoming, only the most elaborate models (multi-level representation, syntactically guided scan) can fully account for all the data. While instances can be found where the cancellation task is clearly disrupting the reading task, much of the data are consistent with the notion that the letter cancellation task is not excessively intrusive, and our analyses can thus give us significant information about normal reading.     

Conditional estimation of exponential random graph models from snowball sampling designs

A complete survey of a network in a large population may be prohibitively difficult and costly. So it is important to estimate models for networks using data from various network sampling designs, such as link-tracing designs. We focus here on snowball sampling designs, designs in which the members of an initial sample of network members are asked to nominate their network partners, their network partners are then traced and asked to nominate their network partners, and so on. We assume an exponential random graph model (ERGM) of a particular parametric form and outline a conditional maximum likelihood estimation procedure for obtaining estimates of ERGM parameters. This procedure is intended to complement the likelihood approach developed by  Handcock and Gile (2010) by providing a practical means of estimation when the size of the complete network is unknown and/or the complete network is very large. We report the outcome of a simulation study with a known model designed to assess the impact of initial sample size, population size, and number of sampling waves on properties of the estimates. We conclude with a discussion of the potential applications and further developments of the approach.     

Readers' Forum

The presence of intense and pervasive denial is a ubiquitous phenomenon in working with incest offenders and their families. This extraordinary defensiveness against acknowledging the occurrence of incest serves as a major resistance to the effective engagement of such families in rehabilitative efforts and often leads to the abandonment of the children and their families. This report is an attempt to illustrate clinically the working through of this denial in a group of incestuous fathers in a protective service setting in the community—a case management group work model designed to reach those children and their families who could not or would not testify in court against the sexually abusive father.     

Vowel quality changes produced by surrounding tone sequences

In three experiments, we examined whether energy at the same frequency as one of a vowel's harmonics in the F1 region can be captured by a preceding or following sequence of tones. The position of the /I/-/E/ phoneme boundary along an F1 continuum was used to assess the extent of capture. The first two experiments showed that a sequence of tones at 500 Hz (56-msec duration at 10/sec) can perceptually remove added energy at 500 Hz from a steady vowel (F0 = 125 Hz) that forms part of the sequence. The effect is detectable with one preceding tone, asymptotes with four, and is greater when two tones follow the vowel than when none do. Rising and falling sequences of tones (at 62.5-Hz intervals or at whole-tone intervals) differ in their effect. Falling sequences behave much like constant tones at 500 Hz but with less effect, whereas rising sequences show no evidence of removing the added tone. The second experiment replicated the first and also showed that when the vowel is embedded in a rising or a falling sequence of tones that continue after it, the following tones have no effect. The third experiment suggested that the different effects found with rising versus falling sequences are qualitatively predictable on the basis of the additive effects of their constituent tones rather than by virtue of their contour. The experiments indicated that sequences of repeating tones are much more effective at capturing a harmonic from a vowel than are sequences that follow a simple pattern. This result may reflect the operation of a principle of least commitment in auditory grouping.     

Statistical Evaluation of Algebraic Constraints for Social Networks

A multirelational social network on a set of individuals may be represented as a collection of binary relations. Compound relations constructed from this collection represent various labeled paths linking individuals in the network. Since many models of interest for social networks can be formulated in terms of orderings among these labeled paths, we consider the problem of evaluating an hypothesized set of orderings, termed algebraic constraints. Each constraint takes the form of an hypothesized inclusion relation for a pair of labeled paths. In this paper, we establish conditions under which sets of such constraints may be regarded as partial algebras. We describe the structure of constraint sets and show that each corresponds to a subset of consistent relation bundles between pairs of individuals. We thereby construct measures of fit for a given constraint set. Then, we show how, in combination with the assumption of various conditional uniform multigraph distributions, these measures lead to a flexible approach to the evaluation of fit of an hypothesized constraint set. Several applications are presented and some possible extensions of the approach are briefly discussed. Copyright 2000 Academic Press.     

Supervision in the Psychotherapy of Schizophrenia: Awareness of and Mutual Reflection upon Fragmentation

Historical and newly emerging models of schizophrenia suggest it is a disorder characterized by the fragmentation of the experience of the self and the world, leading to the interruption of how a unique life is unfolding in the world. It has been proposed that psychotherapy might therefore promote recovery by facilitating the development of a greater ability to integrate information about the self and others. In this paper we explore how the supervision of a metacognitively-oriented psychotherapy can assist therapists to experience and conceptualize fragmentation within sessions, join patients in the gradual process of making sense of their psychiatric problems and life challenges, and ultimately envision and achieve recovery. Common challenges and responses within supervision are described and discussed.