glmmLasso (version 1.6.3)

cumulative: 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()

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

Andreas Groll

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.

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

if (FALSE) {
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)
}