clmmOld: Cumulative link mixed models

In ordinal: Regression Models for Ordinal Data

Cumulative link mixed models

Description

Fits cumulative link mixed models, i.e. cumulative link models with random effects via the Laplace approximation or the standard and the adaptive Gauss-Hermite quadrature approximation. The functionality in clm2 is also implemented here. Currently only a single random term is allowed in the location-part of the model.

A new implementation is available in clmm that allows for more than one random effect.

Usage

clmm2(location, scale, nominal, random, data, weights, start, subset,
     na.action, contrasts, Hess = FALSE, model = TRUE, sdFixed,
     link = c("logistic", "probit", "cloglog", "loglog",
     "cauchit", "Aranda-Ordaz", "log-gamma"), lambda,
     doFit = TRUE, control, nAGQ = 1,
     threshold = c("flexible", "symmetric", "equidistant"), ...)

Arguments

location	as in clm2.
scale	as in clm2.
nominal	as in clm2.
random	a factor for the random effects in the location-part of the model.
data	as in clm2.
weights	as in clm2.
start	initial values for the parameters in the format c(alpha, beta, log(zeta), lambda, log(stDev)) where stDev is the standard deviation of the random effects.
subset	as in clm2.
na.action	as in clm2.
contrasts	as in clm2.
Hess	logical for whether the Hessian (the inverse of the observed information matrix) should be computed. Use Hess = TRUE if you intend to call summary or vcov on the fit and Hess = FALSE in all other instances to save computing time.
model	as in clm2.
sdFixed	If sdFixed is specified (a positive scalar), a model is fitted where the standard deviation for the random term is fixed at the value of sdFixed. If sdFixed is left unspecified, the standard deviation of the random term is estimated from data.
link	as in clm2.
lambda	as in clm2.
doFit	as in clm2 although it can also be one of c("no", "R" "C"), where "R" use the R-implementation for fitting, "C" (default) use C-implementation for fitting and "no" behaves as FALSE and returns the environment.
control	a call to clmm2.control.
threshold	as in clm2.
nAGQ	the number of quadrature points to be used in the adaptive Gauss-Hermite quadrature approximation to the marginal likelihood. Defaults to 1 which leads to the Laplace approximation. An odd number of quadrature points is encouraged and 3, 5 or 7 are usually enough to achive high precision. Negative values give the standard, i.e. non-adaptive Gauss-Hermite quadrature.
...	additional arguments are passed on to clm2.control and possibly further on to the optimizer, which can lead to surprising error or warning messages when mistyping arguments etc.

Details

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

A Newton scheme is used to obtain the conditional modes of the random effects for Laplace and AGQ approximations, and a non-linear optimization is performed over the fixed parameter set to get the maximum likelihood estimates. The Newton scheme uses the observed Hessian rather than the expected as is done in e.g. glmer, so results from the Laplace approximation for binomial fits should in general be more precise - particularly for other links than the "logistic".

Core parts of the function are implemented in C-code for speed.

The function calls clm2 to up an environment and to get starting values.

Value

If doFit = FALSE the result is an environment representing the model ready to be optimized. If doFit = TRUE the result is an object of class "clmm2" with the following components:

stDev	the standard deviation of the random effects.
Niter	the total number of iterations in the Newton updates of the conditional modes of the random effects.
grFac	the grouping factor defining the random effects.
nAGQ	the number of quadrature points used in the adaptive Gauss-Hermite Quadrature approximation to the marginal likelihood.
ranef	the conditional modes of the random effects, sometimes referred to as "random effect estimates".
condVar	the conditional variances of the random effects at their conditional modes.
beta	the parameter estimates of the location part.
zeta	the parameter estimates of the scale part on the log scale; the scale parameter estimates on the original scale are given by exp(zeta).
Alpha	vector or matrix of the threshold parameters.
Theta	vector or matrix of the thresholds.
xi	vector of threshold parameters, which, given a threshold function (e.g. "equidistant"), and possible nominal effects define the class boundaries, Theta.
lambda	the value of lambda if lambda is supplied or estimated, otherwise missing.
coefficients	the coefficients of the intercepts (theta), the location (beta), the scale (zeta), and the link function parameter (lambda).
df.residual	the number of residual degrees of freedoms, calculated using the weights.
fitted.values	vector of fitted values conditional on the values of the random effects. Use predict to get the fitted values for a random effect of zero. An observation here is taken to be each of the scalar elements of the multinomial table and not a multinomial vector.
convergence	TRUE if the optimizer terminates wihtout error and FALSE otherwise.
gradient	vector of gradients for the unit-variance random effects at their conditional modes.
optRes	list with results from the optimizer. The contents of the list depends on the choice of optimizer.
logLik	the log likelihood of the model at optimizer termination.
Hessian	if the model was fitted with Hess = TRUE, this is the Hessian matrix of the parameters at the optimum.
scale	model.frame for the scale model.
location	model.frame for the location model.
nominal	model.frame for the nominal model.
edf	the (effective) number of degrees of freedom used by the model.
start	the starting values.
method	character, the optimizer.
y	the response variable.
lev	the names of the levels of the response variable.
nobs	the (effective) number of observations, calculated as the sum of the weights.
threshold	character, the threshold function used in the model.
estimLambda	1 if lambda is estimated in one of the flexible link functions and 0 otherwise.
link	character, the link function used in the model.
call	the matched call.
contrasts	contrasts applied to terms in location and scale models.
na.action	the function used to filter missing data.

Author(s)

Rune Haubo B Christensen

References

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

Examples

options(contrasts = c("contr.treatment", "contr.poly"))

## More manageable data set:
dat <- subset(soup, as.numeric(as.character(RESP)) <=  24)
dat$RESP <- dat$RESP[drop=TRUE]

m1 <- clmm2(SURENESS ~ PROD, random = RESP, data = dat, link="probit",
           Hess = TRUE, method="ucminf", threshold = "symmetric")

m1
summary(m1)
logLik(m1)
vcov(m1)
extractAIC(m1)
anova(m1, update(m1, location = SURENESS ~ 1, Hess = FALSE))
anova(m1, update(m1, random = NULL))

## Use adaptive Gauss-Hermite quadrature rather than the Laplace
## approximation:
update(m1, Hess = FALSE, nAGQ = 3)

## Use standard Gauss-Hermite quadrature:
update(m1, Hess = FALSE, nAGQ = -7)

##################################################################
## Binomial example with the cbpp data from the lme4-package:
if(require(lme4)) {
    cbpp2 <- rbind(cbpp[,-(2:3)], cbpp[,-(2:3)])
    cbpp2 <- within(cbpp2, {
        incidence <- as.factor(rep(0:1, each=nrow(cbpp)))
        freq <- with(cbpp, c(incidence, size - incidence))
    })

    ## Fit with Laplace approximation:
    fm1 <- clmm2(incidence ~ period, random = herd, weights = freq,
                 data = cbpp2, Hess = 1)
    summary(fm1)

    ## Fit with the adaptive Gauss-Hermite quadrature approximation:
    fm2 <- clmm2(incidence ~ period, random = herd, weights = freq,
                 data = cbpp2, Hess = 1, nAGQ = 7)
    summary(fm2)
}

ordinal documentation built on Sept. 11, 2024, 7:44 p.m.