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@Book{brazzale07,
author = {A R Brazzale and A C Davison and N Reid},
title = {Applied Asymptotics---case studies in small-sample
statistics} ,
publisher = {Cambridge University Press},
year = 2007}
@Book{pawitan01,
author = {Yudi Pawitan},
title = {{In All Likelihood---Statistical Modelling and
Inference Using Likelihood}},
publisher = {Oxford University Press},
year = 2001
}
@Manual{R11,
title = {R: A Language and Environment for Statistical Computing},
author = {{R Development Core Team}},
organization = {R Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2011},
note = {{ISBN} 3-900051-07-0},
url = {http://www.R-project.org/},
}
@Article{tutz96,
author = {Gerhard Tutz and Wolfgang Hennevogl},
title = {Random effects in ordinal regression models},
journal = {Computational Statistics \& Data Analysis},
year = 1996,
volume = 22,
pages = {537-557}
}
@Article{efron78,
author = {Bradley Efron and David V Hinkley},
title = {{Assessing the accuracy of the maximum likelihood
estimator: Observed versus expected Fisher information}},
journal = {Biometrika},
year = 1978,
volume = 65,
number = 3,
pages = {457-487}}
@article{bauer09,
author = {Bauer, Daniel},
affiliation = {University of North Carolina Department of
Psychology Chapel Hill NC 27599-3270 USA},
title = {A Note on Comparing the Estimates of Models
for†Cluster-Correlated or Longitudinal Data with
Binary or Ordinal†Outcomes},
journal = {Psychometrika},
publisher = {Springer New York},
issn = {0033-3123},
keyword = {Humanities, Social Sciences and Law},
pages = {97-105},
volume = {74},
issue = {1},
url = {http://dx.doi.org/10.1007/s11336-008-9080-1},
year = {2009}
}
@article{fielding04,
author = {Fielding, Antony},
title = {Scaling for Residual Variance Components of Ordered
Category Responses in Generalised Linear Mixed
Multilevel Models},
journal = {Quality \& Quantity},
publisher = {Springer Netherlands},
issn = {0033-5177},
keyword = {Humanities, Social Sciences and Law},
pages = {425-433},
volume = {38},
issue = {4},
url = {http://dx.doi.org/10.1023/B:QUQU.0000043118.19835.6c},
year = {2004}
}
@article{winship84,
jstor_articletype = {research-article},
title = {Regression Models with Ordinal Variables},
author = {Winship, Christopher and Mare, Robert D.},
journal = {American Sociological Review},
jstor_issuetitle = {},
volume = {49},
number = {4},
jstor_formatteddate = {Aug., 1984},
pages = {512-525},
url = {http://www.jstor.org/stable/2095465},
ISSN = {00031224},
abstract = {Most discussions of ordinal variables in the
sociological literature debate the suitability of
linear regression and structural equation methods
when some variables are ordinal. Largely ignored in
these discussions are methods for ordinal variables
that are natural extensions of probit and logit
models for dichotomous variables. If ordinal
variables are discrete realizations of unmeasured
continuous variables, these methods allow one to
include ordinal dependent and independent variables
into structural equation models in a way that (1)
explicitly recognizes their ordinality, (2) avoids
arbitrary assumptions about their scale, and (3)
allows for analysis of continuous, dichotomous, and
ordinal variables within a common statistical
framework. These models rely on assumed probability
distributions of the continuous variables that
underly the observed ordinal variables, but these
assumptions are testable. The models can be
estimated using a number of commonly used
statistical programs. As is illustrated by an
empirical example, ordered probit and logit models,
like their dichotomous counterparts, take account of
the ceiling and floor restrictions on models that
include ordinal variables, whereas the linear
regression model does not.},
language = {English},
year = {1984},
publisher = {American Sociological Association},
copyright = {Copyright © 1984 American Sociological Association},
}
@article{thompson81,
jstor_articletype = {research-article},
title = {Composite Link Functions in Generalized Linear Models},
author = {Thompson, R. and Baker, R. J.},
journal = {Journal of the Royal Statistical Society. Series C
(Applied Statistics)},
jstor_issuetitle = {},
volume = {30},
number = {2},
jstor_formatteddate = {1981},
pages = {125-131},
url = {http://www.jstor.org/stable/2346381},
ISSN = {00359254},
abstract = {In generalized linear models each observation is
linked with a predicted value based on a linear
function of some systematic effects. We sometimes
require to link each observation with a linear
function of more than one predicted value. We embed
such models into the generalized linear model
framework using composite link functions. The
computer program GLIM-3 can be used to fit these
models. Illustrative examples are given including a
mixed-up contingency table and grouped normal
data.},
language = {English},
year = {1981},
publisher = {Blackwell Publishing for the Royal Statistical Society},
copyright = {Copyright © 1981 Royal Statistical Society},
}
@article{burridge81,
jstor_articletype = {research-article},
title = {A Note on Maximum Likelihood Estimation for Regression
Models Using Grouped Data},
author = {Burridge, J.},
journal = {Journal of the Royal Statistical Society. Series B
(Methodological)},
jstor_issuetitle = {},
volume = {43},
number = {1},
jstor_formatteddate = {1981},
pages = {41-45},
url = {http://www.jstor.org/stable/2985147},
ISSN = {00359246},
abstract = {The estimation of parameters for a class of
regression models using grouped or censored data is
considered. It is shown that with a simple
reparameterization some commonly used distributions,
such as the normal and extreme value, result in a
log-likelihood which is concave with respect to the
transformed parameters. Apart from its theoretical
implications for the existence and uniqueness of
maximum likelihood estimates, this result suggests
minor changes to some commonly used algorithms for
maximum likelihood estimation from grouped data. Two
simple examples are given.},
language = {English},
year = {1981},
publisher = {Blackwell Publishing for the Royal Statistical Society},
copyright = {Copyright © 1981 Royal Statistical Society},
}
@article{pratt81,
jstor_articletype = {research-article},
title = {Concavity of the Log Likelihood},
author = {Pratt, John W.},
journal = {Journal of the American Statistical Association},
jstor_issuetitle = {},
volume = {76},
number = {373},
jstor_formatteddate = {Mar., 1981},
pages = {103-106},
url = {http://www.jstor.org/stable/2287052},
ISSN = {01621459},
abstract = {For a very general regression model with an ordinal
dependent variable, the log likelihood is proved
concave if the derivative of the underlying response
function has concave logarithm. For a binary
dependent variable, a weaker condition suffices,
namely, that the response function and its
complement each have concave logarithm. The normal,
logistic, sine, and extreme-value distributions,
among others, satisfy the stronger condition, the t
(including Cauchy) distributions only the
weaker. Some converses and generalizations are also
given. The model is that which arises from an
ordinary linear regression model with a continuous
dependent variable that is partly unobservable,
being either grouped into intervals with unknown
endpoints, or censored, or, more generally, grouped
in some regions, censored in others, and observed
exactly elsewhere.},
language = {English},
year = {1981},
publisher = {American Statistical Association},
copyright = {Copyright © 1981 American Statistical Association},
}
@Manual{christensen11,
title = {Analysis of ordinal data with cumulative link models
--- estimation with the \textsf{ordinal} package},
author = {Rune Haubo Bojesen Christensen},
note = {R-package version 2011.09-13},
year = 2011}
@Book{agresti10,
author = {Alan Agresti},
title = {Analysis of ordinal categorical data},
publisher = {Wiley},
year = 2010,
edition = {2nd}}
@Book{agresti02,
author = {Alan Agresti},
title = {Categorical Data Analysis},
publisher = {Wiley},
year = 2002,
edition = {2nd}
}
@Article{mccullagh80,
author = {Peter McCullagh},
title = {Regression Models for Ordinal Data},
journal = {Journal of the Royal Statistical Society, Series B},
year = 1980,
volume = 42,
pages = {109-142}
}
@Article{randall89,
author = {J.H. Randall},
title = {The Analysis of Sensory Data by Generalised Linear Model},
journal = {Biometrical journal},
year = 1989,
volume = 7,
pages = {781-793}
}
@Book{fahrmeir01,
author = {Ludwig Fahrmeir and Gerhard Tutz},
title = {Multivariate Statistical Modelling Based on
Generalized Linear Models},
publisher = {Springer-Verlag New York, Inc.},
year = 2001,
series = {Springer series in statistics},
edition = {2nd}
}
@Book{greene10,
author = {William H Greene and David A Hensher},
title = {Modeling Ordered Choices: A Primer},
publisher = {Cambridge University Press},
year = 2010}
@Book{mccullagh89,
author = {Peter McCullagh and John Nelder},
title = {Generalized Linear Models},
publisher = {Chapman \& Hall/CRC},
year = 1989,
edition = {Second}
}
@Book{collett02,
author = {David Collett},
title = {Modelling binary data},
publisher = {London: Chapman \& Hall/CRC},
year = 2002,
edition = {2nd}
}
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