Ordinal Regression with Adjacent Categories Probabilities
Fits an adjacent categories regression model to an ordered (preferably) factor response.
acat(link = "loglink", parallel = FALSE, reverse = FALSE,
zero = NULL, whitespace = FALSE)link |
Link function applied to the ratios of the
adjacent categories probabilities.
See |
parallel |
A logical, or formula specifying which terms have equal/unequal coefficients. |
reverse |
Logical.
By default, the linear/additive predictors used are
eta_j = log(P[Y=j+1]/P[Y=j])
for j=1,…,M.
If |
zero |
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,...,M}. |
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.
By default, the log link is used because the ratio of two probabilities is positive.
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 an ordered 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: Springer-Verlag.
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, acat, data = pneumo)) coef(fit, matrix = TRUE) constraints(fit) model.matrix(fit)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.