Fits an adjacent categories regression model to an ordered (preferably) factor response.
acat(link = "loge", parallel = FALSE, reverse = FALSE,
zero = NULL, whitespace = FALSE)Link function applied to the ratios of the
adjacent categories probabilities.
See Links for more choices.
A logical, or formula specifying which terms have equal/unequal coefficients.
Logical.
By default, the linear/additive predictors used are
\(\eta_j = \log(P[Y=j+1]/P[Y=j])\)
for \(j=1,\ldots,M\).
If reverse is TRUE then
\(\eta_j = \log(P[Y=j]/P[Y=j+1])\)
will be used.
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,…,\(M\)}.
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 \(1,2,\ldots,M+1\), so that \(M\) is the number of linear/additive predictors \(\eta_j\).
By default, the log link is used because the ratio of two probabilities is positive.
Agresti, A. (2013) Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.
Simonoff, J. S. (2003) Analyzing Categorical Data, New York: Springer-Verlag.
Yee, T. W. (2010) The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1--34. http://www.jstatsoft.org/v32/i10/.
# NOT RUN {
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let, acat, data = pneumo))
coef(fit, matrix = TRUE)
constraints(fit)
model.matrix(fit)
# }
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