Ordinal Regression with Stopping Ratios
Fits a stopping ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
sratio(link = "logitlink", parallel = FALSE, reverse = FALSE,
zero = NULL, whitespace = FALSE)link |
Link function applied to the M
stopping ratio probabilities.
See |
parallel |
A logical, or formula specifying which terms have equal/unequal coefficients. |
reverse |
Logical.
By default, the stopping ratios used are
eta_j = logit(P[Y=j|Y>=j])
for j=1,…,M.
If |
zero |
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. |
whitespace |
See |
In this help file the response Y is assumed to be a factor with ordered values 1,2,…,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
logitlink(P[Y>j|Y>=j]).
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.
The response should be either a matrix of counts (with row sums that
are all positive), or a factor. In both cases, the y slot
returned by vglm/vgam/rrvglm is the matrix
of counts.
For a nominal (unordered) factor response, the multinomial
logit model (multinomial) is more appropriate.
Here is an example of the usage of the parallel argument.
If there are covariates x1, x2 and x3, then
parallel = TRUE ~ x1 + x2 -1 and
parallel = FALSE ~ x3 are equivalent. This would constrain
the regression coefficients for x1 and x2 to be
equal; those of the intercepts and x3 would be different.
Thomas W. Yee
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. https://www.jstatsoft.org/v32/i10/.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.