Fits a stopping ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
sratio(link = "logit", parallel = FALSE, reverse = FALSE,
zero = NULL, whitespace = FALSE)
Link function applied to the \(M\)
stopping ratio probabilities.
See Links
for more choices.
A logical, or formula specifying which terms have equal/unequal coefficients.
Logical.
By default, the stopping ratios used are
\(\eta_j = logit(P[Y=j|Y \geq j])\)
for \(j=1,\dots,M\).
If reverse
is TRUE
, then
\(\eta_j = logit(P[Y=j+1|Y \leq j+1])\)
will be used.
Can be an integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,…,\(M\)}. The default value means none are modelled as intercept-only terms.
See CommonVGAMffArguments
for information.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
rrvglm
and vgam
.
No check is made to verify that the response is ordinal if the
response is a matrix;
see ordered
.
In this help file the response \(Y\) is assumed to be a factor with ordered values \(1,2,\dots,M+1\), so that \(M\) is the number of linear/additive predictors \(\eta_j\).
There are a number of definitions for the continuation ratio
in the literature. To make life easier, in the VGAM package,
we use continuation ratios (see cratio
)
and stopping ratios.
Continuation ratios deal with quantities such as
logit(P[Y>j|Y>=j])
.
Agresti, A. (2013) Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.
Simonoff, J. S. (2003) Analyzing Categorical Data, New York, USA: Springer-Verlag.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Yee, T. W. (2010) The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1--34. http://www.jstatsoft.org/v32/i10/.
cratio
,
acat
,
cumulative
,
multinomial
,
margeff
,
pneumo
,
logit
,
probit
,
cloglog
,
cauchit
.
# NOT RUN { pneumo <- transform(pneumo, let = log(exposure.time)) (fit <- vglm(cbind(normal, mild, severe) ~ let, sratio(parallel = TRUE), data = pneumo)) coef(fit, matrix = TRUE) constraints(fit) predict(fit) predict(fit, untransform = TRUE) # }
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