R: Cumulative Link Location-Scale Models

clls-deprecated {sensR}

R Documentation

Cumulative Link Location-Scale Models

Description

IMPORTANT: This function and its methods are no longer supported. The user is adviced to use clm() from package ordinal instead.

Fits a cumulative link location-scale model to an ordered response variable. When the scale part is left unspecified, the model reduces to a cumulative link model assuming a constant scale. With the default logistic link function, the model reduces to the famous Proportional Odds Model. With the probit link and a single two-level factor in both location and scale parts, the model is known as the Binormal model in the Signal Detection Theory and the Psychometric literature.

Usage

  clls(location, scale, data, weights, start, ..., subset,
           na.action, contrasts = NULL, Hess = FALSE, model = TRUE,
           method = c("logistic", "probit", "cloglog", "cauchit"))

Arguments

`location`	a formula expression as for regression models, of the form `response ~ predictors`. The response should be a factor (preferably an ordered factor), which will be interpreted as an ordinal response, with levels ordered as in the factor. The model must have an intercept: attempts to remove one will lead to a warning and be ignored. An offset may be used. See the documentation of `formula` for other details.
`scale`	a optional formula expression as for the location part, of the form `~ predictors`, ie. with an empty left hand side. If left unspecified, the model assumes a constant scale and reduces to the cumulative link model. An offset may be used. See the documentation of `formula` for other details.
`data`	an optional data frame in which to interpret the variables occurring in `formula`.
`weights`	optional case weights in fitting. Default to 1.
`start`	initial values for the parameters. This is in the format `c(beta, theta, sigma)`: see the Values section.
`...`	additional arguments to be passed to `optim`, most often a `control` argument.
`subset`	expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
`na.action`	a function to filter missing data.
`contrasts`	a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.
`Hess`	logical for whether the Hessian (the observed information matrix) should be returned. Use this if you intend to call `summary` or `vcov` on the fit.
`model`	logical for whether the model matrix should be returned.
`method`	logistic or probit or complementary log-log or cauchit (corresponding to a Cauchy latent variable).

Details

The implementation is highly inspired by polr in package MASS and should give compatible results, if scale is left unspecified.

Note that standard errors are appropriate for tau = log sigma and not for sigma, because the profile likelihood is usually more symmetric for tau than for sigma. Therefore vcov will give the variance-covariance matrix of the parameters with tau rather than sigma and summary.clls will report standard errors for log sigma. Notice also that a relevant test for sigma is H_0: sigma = 1, so the relevant test for log sigma is H_0: log(sigma) = 0. This is reflected in the z value for sigma returned by summary.clls.

There are methods for the standard model-fitting functions, including summary, vcov, anova, and an extractAIC method.

Value

A object of class "clls". This has components

`coefficients`	the coefficients of the location (`beta`), the intercepts (`theta`) and the scale (`sigma`).
`beta`	the parameter estimates of the location part.
`theta`	the intercepts/thresholds for the class boundaries.
`sigma`	the parameter estimates of the scale part.
`tau`	parameter estimates of the scale part on the log scale; ie. `tau` = log `sigma`.
`deviance`	the residual deviance.
`fitted.values`	a matrix, with a column for each level of the response with the fitted probabilities.
`fitted.case`	a vector of same length as `response`, with the fitted probabilities on a case-by-case basis.
`lev`	the names of the response levels.
`terms.location`	a `terms` structure describing the location part.
`terms.scale`	a `terms` structure describing the scale part.
`df.residual`	the number of residual degrees of freedoms, calculated using the weights.
`edf`	the (effective) number of degrees of freedom used by the model
`n`, `nobs`	the (effective) number of observations, calculated using the weights.
`call`	the matched call.
`method`	the matched method used.
`convergence`	the convergence code returned by `optim`.
`niter`	the number of function and gradient evaluations used by `optim`.
`Hessian`	if `Hess` is true, the observed Fisher information matrix.
`location`	if `model` is true, the `model.frame` for the location part.
`scale`	if `model` is true, the `model.frame` for the scale part.

References

Agresti, A. (2002) Categorical Data. Second edition. Wiley.

Christensen, R.H.B., Cleaver, G. and Brockhoff, P.B. (2011). Statistical and Thurstonian models for the A-not A protocol with and without sureness. Food Quality and Preference, 22(6), pp.542-549.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

  old <- options(contrasts = c("contr.treatment", "contr.poly"))
  ## Extend example from polr in package MASS:
  ## Fit model from polr example:
  data(housing, package = "MASS")
  fm1 <- clls(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
  fm1
  summary(fm1)
  ## With probit link:
  summary(update(fm1, method = "probit"))

  ## Allow scale to depend on Cont-variable
  summary(fm2 <- update(fm1, scale =~ Cont))
  anova(fm1, fm2)
  ## which seems to improve the fit
  options(old)

[Package sensR version 1.5-3 Index]