ordinalCont (version 0.4)

ocm: Ordinal regression for continuous scales

Description

Continuous ordinal regression with logit link using the generalized logistic function as g function.

Usage

ocm(formula, data = NULL, weights, start = NULL, link = c("logit"), gfun = c("glf"), method = c("optim", "ucminf"))

Arguments

formula

a formula expression as for regression models, of the form response ~ predictors. Only fixed effects are supported. The model must have an intercept: attempts to remove one will lead to a warning and will be ignored.

data

an optional data frame in which to interpret the variables occurring in the formulas

weights

optional case weights in fitting. Defaults to 1.

start

a vector of initial values for the regression coefficients and M, B, T, (offset, slope and symmetry of the g function)

link

link function, i.e. the type of location-scale distribution assumed for the latent distribution. The default ``logit'' link gives the proportional odds model and is the only link function currently supported.

gfun

A smooth monotonic function capable of capturing the non-linear nature of the ordinal measure. It defaults to the generalized logistic function, which is currently the only possibility.

method

The optimizer used to maximize the likelihood function.

Value

an object of type ocm with the components listed below. Parameter estimates are in coefficients. The last 3 elements of coefficients are the parameters of the g function: M, B, and T.

coefficients

parameter estimates

vcov

variance-covariance matrix

df

estimated degrees of freedom

logLik

value of the log-likelihood at the estimated optimum

len_beta

number of fixed-effects parameters of the model

len_gfun

number of parameters in the g function used in the model

fitted.values

fitted probabilities

residuals

residuals on the latent scale

v

vector of continuous scores

x

model matrix

sample.size

sample size (can differ from the number of observations if the weights are different from 1)

nobs

number of observations

call

call to fit the model

no.pars

total number of parameters estimated

data

data frame used

link

link function used

gfun

g function used

formula

formula used

Details

Fits a continuous ordinal regression model, with fixed effects. The g function is the generalized logistic function (see g_glf), and the link function is the logit, implying the standard logistic distribution for the latent variable. Maximum likelihood estimation is performed, using optim {stats} with a quasi-Newton method ("BFGS"). For continuous ordinal mixed modelling, see ocmm.

References

Manuguerra M, Heller GZ (2010). Ordinal Regression Models for Continuous Scales, The International Journal of Biostatistics: 6(1), Article 14.

See Also

For continuous ordinal mixed models, see ocmm

Examples

ANZ0001.ocm <- ANZ0001[ANZ0001$cycleno==0 | ANZ0001$cycleno==5,]
ANZ0001.ocm$cycleno[ANZ0001.ocm$cycleno==5] <- 1
fit.overall  <- ocm(overall  ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
fit.phys 	  <- ocm(phys 	  ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
fit.pain 	  <- ocm(pain 	  ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
fit.mood 	  <- ocm(mood 	  ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
fit.nausvom  <- ocm(nausvom  ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
fit.appetite <- ocm(appetite ~ cycleno + age + bsa + treatment, data=ANZ0001.ocm)
summary(fit.overall)
summary(fit.phys)
summary(fit.pain)
summary(fit.mood)
summary(fit.nausvom)
summary(fit.appetite)
par(mfrow=c(2,3))
plot(fit.overall, CIs='vcov', R=100)
plot(fit.phys, CIs='vcov', R=100)
plot(fit.pain, CIs='vcov', R=100)
plot(fit.mood, CIs='vcov', R=100)
plot(fit.nausvom, CIs='vcov', R=100)
plot(fit.appetite, CIs='vcov', R=100)
par(mfrow=c(1,1))