# propodds: Proportional Odds Model for Ordinal Regression In VGAM: Vector Generalized Linear and Additive Models

 propodds R Documentation

## Proportional Odds Model for Ordinal Regression

### Description

Fits the proportional odds model to a (preferably ordered) factor response.

### Usage

``````propodds(reverse = TRUE, whitespace = FALSE,
thresholds = c("unconstrained", "equidistant",
"symmetric1", "symmetric0"), Treverse = reverse,
Tref = if (Treverse) "M" else 1)
``````

### Arguments

 `reverse, whitespace` Logical. Fed into arguments of the same name in `cumulative`. `thresholds, Treverse, Tref` Fed into arguments of the same name in `cumulative`.

### Details

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.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, and `vgam`.

### Warning

No check is made to verify that the response is ordinal if the response is a matrix; see `ordered`.

Thomas W. Yee

### References

See `cumulative`.

`cumulative`, `R2latvar`.

### Examples

``````# 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
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.