glmmLasso (version 1.5.1)

acat: Family Object for Ordinal Regression with Adjacent Categories Probabilities

Description

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

Usage

acat()

Value

linkinv

function: the inverse of the link function as a function of eta.

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.

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.

References

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

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

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

See Also

cumulative, 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 = acat(), data = knee, lambda=10,
        switch.NR=TRUE, control=list(print.iter=TRUE)) 

summary(glm.obj)
# }