propodds {VGAM} | R Documentation |
Fits the proportional odds model to a (preferably ordered) factor response.
propodds(reverse = TRUE)
reverse |
Logical.
Fed into the |
The proportional odds model is a special case from the class of
cumulative link models.
It involves a logit link applied to cumulative probabilities and a
strong parallelism assumption.
A parallelism assumption means there is less chance of
numerical problems because the fitted probabilities will remain
between 0 and 1; however
the parallelism assumption ought to be checked,
e.g., via a likelihood ratio test.
This VGAM family function is merely a shortcut for
cumulative(reverse = reverse, link = "logit", parallel = TRUE)
.
Please see cumulative
for more details on this model.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
No check is made to verify that the response is ordinal;
see ordered
.
Thomas W. Yee
Agresti, A. (2010) Analysis of Ordinal Categorical Data, 2nd ed. New York: Wiley.
Yee, T. W. (2010) The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1–34. http://www.jstatsoft.org/v32/i10/.
Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
# Fit the proportional odds model, p.179, in McCullagh and Nelder (1989) pneumo = transform(pneumo, let = log(exposure.time)) (fit = vglm(cbind(normal, mild, severe) ~ let, propodds, pneumo)) fit@y # Sample proportions weights(fit, type = "prior") # Number of observations coef(fit, matrix = TRUE) constraints(fit) # Constraint matrices summary(fit) # Check that the model is linear in let ---------------------- fit2 = vgam(cbind(normal, mild, severe) ~ s(let, df = 2), propodds, pneumo) ## Not run: plot(fit2, se = TRUE, lcol = 2, scol = 2) # Check the proportional odds assumption with a LRT ---------- (fit3 = vglm(cbind(normal, mild, severe) ~ let, cumulative(parallel = FALSE, reverse = TRUE), pneumo)) pchisq(deviance(fit) - deviance(fit3), df = df.residual(fit) - df.residual(fit3), lower.tail = FALSE)