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.