Fits the proportional odds model to a (preferably ordered) factor response.
propodds(reverse = TRUE, whitespace = FALSE)
Fed into arguments of the same name in
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).
cumulative for more details on this
An object of class
The object is used by modelling functions
No check is made to verify that the response is ordinal if the
response is a matrix; see
Thomas W. Yee
# Fit the proportional odds model, McCullagh and Nelder (1989,p.179) pneumo <- transform(pneumo, let = log(exposure.time)) (fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, pneumo)) depvar(fit) # 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) lrtest(fit3, fit) # Easier
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