cumulative {glmmLasso}

Family Object for Ordinal Regression with Cumulative Probabilities

Description

Provides necessary family components to fit a proportional odds regression model to an ordered response based on the corresponding (multivariate) binary design representation.

Usage

cumulative()

Details

For a response variable Y with ordered values 1,2,\ldots,M+1 the design of the corresponding (multivariate) binary response representation is automatically created by the glmmLasso function. The result is a linear predictor matrix \eta with n rows and M columns.

Based on this (n x M) predictor matrix \eta or on the corresponding (n x M) matrix \mu the below mentioned family components can be calculated.

Solely the logit link is implemented, hence, a proportional odds model is fitted.

Value

linkinv

function: the inverse of the link function as a function of eta. Solely the logit link is implemented, hence, the response function h(\eta)=exp(\eta)/(1+exp(\eta)) is used.

deriv.mat

function: derivative function as a function of the mean (not of eta as normally).

SigmaInv

function: the inverse of the variance as a function of the mean.

family

character: the family name.

multivariate

Logical. Is always set to TRUE if the family is used.

Author(s)

Andreas Groll [e-mail]

References

Agresti, A. (2013) Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.

Dobson, A. J. and Barnett, A. (2008) An Introduction to Generalized Linear Models, 3rd ed. Boca Raton: Chapman & Hall/CRC Press.

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

Simonoff, J. S. (2003) Analyzing Categorical Data, New York: Springer-Verlag.

Tutz, G. (2012) Regression for Categorical Data, Cambridge University Press.

Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.

See Also

acat, glmmLasso, knee

Examples

## Not run: 
data(knee)

knee[,c(2,4:6)]<-scale(knee[,c(2,4:6)],center=TRUE,scale=TRUE)
knee<-data.frame(knee)

## fit adjacent category model
glm.obj <- glmmLasso(pain ~ time + th + age + sex, rnd = NULL,  
        family = cumulative(), data = knee, lambda=10,
        switch.NR=TRUE, control=list(print.iter=TRUE)) 

summary(glm.obj)

## End(Not run)