ordDisp-class {ordDisp}

Separating Location and Dispersion in Ordinal Regression Models

Description

A function to estimate the location-shift model or rating-scale model accounting for response styles (RSRS) for the regression analysis of ordinal responses. The model allows to account for differing variability in subgroups of the population. The model explicitely links varying disperion (or response behaviour) to explanatory variables (metric, binary, ordinal and/or nominal). The basic models are described in Tutz and Berger (2016) and Tutz and Berger (2017).

Usage

ordDisp(formula, data, family = c("cumulative", "acat"),
  scaling = TRUE, middle = TRUE, m = NULL, n_bs = 6,
  reverse = FALSE, ...)

Arguments

formula

Object of class formula: a symbolic description of the model to be fitted. See details.

data

Data.frame of class data.frame containing the variables of the model.

family

Type of link function that is used to link the mean responses to the linear predictors of the model; ordDisp currently allows only one out of "cumulative" and "acat". See details.

scaling

If true, the thresholds of the location-shift model are shifting by using scale values for the widening of the intervals between two thresholds.

middle

If true, the model expects a symmetric response of the form 'strongly disagree','moderatly disagree',..., 'moderatly agree','strongly agree'.

m

Middle category of the (non-symmetric) response, chosen for the model. Only relevant, if middle=FALSE.

n_bs

Number of inner B-spline basis functions for smooth components (see details).

reverse

Argument of the family function passed to vglm.

...

Further arguments passed to or from other methods

Details

The formula has to have the form response ~ x-variables|z-variables, where response is the name of the ordinal response variable, x-variables are the terms that specify the location (or content-related) effects of the model and z-variables are the terms that specify the dispersion (or response-style) effects.

If all the variables are entered in both parts of the model, the right hand side of the formula can, for example, have the form x1+...+xp|x1+...+xp. If the second part is omitted, a simple model without dispersion (or response-style) effects is fitted.

The function allows for smooth (non-linear) effects in the x-variables and/or the z-variables. Smooth effects are specified by entering s(x) and/or s(z) into the formula. The functions are fitted using n_bs B-spline basis functions.

Function ordDisp internally calls vglm from package VGAM. Argument family is passed to vglm. Currently two link functions are implemented

• "cumulative" to estimate a cumulative model of the form

  P(y\leq r)/P(y>r)=eta_r

• "acat" to estimate a adjacent-categories model of the form

  P(y=r+1)/P(y=r)=eta_r

Value

Object of class ordDisp which inherits from vglm. The object comprises all the slots of an "vglm"-object and in addition the following components:

outercall

The matched call of ordDisp.

X

Design matrix of x-variables.

Z

Design matrix of z-variables.

All the methods implemented for objects of class vglm, like print, summary, predict and plot can be applied.

Author(s)

Moritz Berger <[e-mail]>
https://www.imbie.uni-bonn.de/personen/dr-moritz-berger/

References

Tutz, Gerhard and Berger, Moritz (2016): Response Styles in Rating Scales - Simultaneous Modelling of Content-Related Effects and the Tendency to Middle or Extreme Categories, Journal of Educational and Behavioral Statistics 41(3), 239-268.

Tutz, Gerhard and Berger, Moritz (2017): Seperating Location and Dispersion in Ordinal Regression Models, Econometrics and Statistics 2, 131-148.

See Also

summaryvglm, predictvglm, plotordDisp

Examples

data(reti)

mod <- ordDisp(RET~SM+DIAB+GH+BP|SM+DIAB,data=reti,family="cumulative")
summary(mod)

mod2 <- ordDisp(RET~SM+s(DIAB)+GH+BP|SM+DIAB+GH+BP, data=reti, 
family="cumulative", n_bs=4, scaling=FALSE)
summary(mod2)