Univariate cumulative link regression models

Ordinal regression models

Usage

ordreg(
  formula,
  data = parent.frame(),
  offset,
  family = stats::binomial("probit"),
  start,
  fast = FALSE,
  ...
)

Arguments

formula

formula

data

data.frame

offset

offset

family

family (default proportional odds)

start

optional starting values

fast

If TRUE standard errors etc. will not be calculated

...

Additional arguments to lower level functions

Details

Let \(Y\in\{1,...,J\}\) be the ordinal outcome and \(X\) a vector of covariates. The cumulative link model is given by $$ P(Y\leq j|X=x) = g(a_j - b^\top x), j=1,...,J-1.$$ The default link function is the Probit function, i.e. where \(g\) is equal to the standard normal cumulative distribution function. The proportional odds model is obtained with family=binomial(logit).

Note, the intercept parameters are parametrized such that they are monotone increasing \(a_1 < \cdots < a_{J-1}\). To get the parameter estimates of the actual \(a_j\)'s use the summary method.

Author

Klaus K. Holst

Examples

m <- lvm(y~x)
ordinal(m,K=3) <- ~y
d <- sim(m,100)
e <- ordreg(y~x,d)
summary(e)
#> AIC:  145.3235 
#> 
#>     Estimate Std.Err    2.5%   97.5%   P-value
#> 0|1  -1.0227  0.1491 -1.3150 -0.7305 6.892e-12
#> 1|2  -0.5031  0.1441 -0.7855 -0.2207 4.798e-04
#> x     0.9674  0.1675  0.6391  1.2957 7.674e-09
#>