The symmetric difference between sets of qualitative elements
(features) forms the basis of a distance model that can be used for
fitting a particular class of networks, called feature graphs.
Weighted counting of the elements in the symmetric set difference
implies a city-block model with binary coordinates (Hamming
distance). It is shown how to parametrize the network fitting
problem in terms of a lattice of subsets, using an earlier result
which relates the Hamming distance to the pathlength distance
along geodesics in a feature graph. Each node of the network
corresponds to a row (column) entry of a given symmetric
proximity matrix, and the aim of the method is to find weighted
edges so that the total pathlength distance between nodes
approximates the pairwise proximities in a least squares sense.
Actual construction of the network is achieved by using the
observation that inclusion relations between feature sets lead to
additivity of distance along geodesics.
The approach is general enough to include additive trees, hierarchical trees and circumplex structures as special cases. Intermediate feature sets that do not correspond to actual nodes may be included as latent nodes to enhance the simplicity of the network. An algorithm based on alternating least squares and combinatorial optimization methods is described, and illustrated with examples from cognitive psychology.
The survey interview may be viewed as a longitudinal sequence of
conversational exchanges between an interviewer and a respondent.
Interviewer and respondent behavior across interview exchanges reflect
the dynamics of the interview and the mutual effects of interviewer
behavior on respondents, and respondents on interviewer behavior. Event
history models can be used to examine the timing of these behaviors and
whether respondents modify the way they answer questions in response to
interviewer behaviors, or whether interviewers modify their
interviewing techniques in response to respondent behaviors.
A total of 297 interviews from a sample survey of members of a health maintenance organization in a metropolitan area in the United States were, with subject permission, tape recorded. Survey interviewers not participating in the survey interviews were trained to listen to the tapes and record the presence of approximately 30 different types of interviewer and respondent behaviors at each question asked in the interview. Two respondent behaviors, laughter during an exchange and interrupting the reading of the question, are examined as events occurring during the interview using standard event history analysis methods. Duration times to laughter or interruption vary across gender and race of respondents, and by the occurrence of the event (i.e., first, second, third, etc.). Cox proportional hazard models will be presented to illustrate the association of a number of respondent and interviewer characteristics on duration times. Findings will also be presented on analysis of interviewer behavior as time varying covariates. These latter analyses can indicate whether respondent behaviors, such as laughter or interruption, are related to interviewer behavior such as reading questions accurately or probing responses that cannot be adequately coded.
The proportional hazards model is the most commonly used model in analyzing survival data. The model differs from a number of classical rivals in that all our conclusions based on the data (inferences) remain identical when the observed survival times are replaced by their ranks. The model is therefore partially non parametric and is sometimes referred to as being semi-parametric. This invariance property underlies the wide applicability of the model. Nonetheless, as in any modelling setup, assumptions need to be tested and the ability of the model to successfully predict needs to be evaluated. By considering the framework for inference behind the model it is possible to address many questions; ranging from estimation in the presence of time dependent effects to more accurate inference for small samples.