multgee (version 1.0)

ordLORgee: Marginal Models For Correlated Ordinal Multinomial Responses

Description

Solving the generalized estimating equations for correlated ordinal multinomial responses assuming a cumulative link model or an adjacent category logit model for the marginal probabilities.

Usage

ordLORgee(formula = formula, data = data, id = id, repeated = repeated, 
          link = "logistic", bstart = NULL, LORstr = "category.exch",
          LORem = "3way", LORterm = NULL, add = 0, homogeneous = TRUE, 
          restricted = FALSE, control = LORgee.control(), 
          ipfp.ctrl = ipfp.control(), IM = "solve")

Arguments

formula

a formula expression as for other regression models for multinomial responses. An intercept term must be included.

data

a mandatory data frame that should include the variables provided in the formula, id and repeated arguments.

id

a vector that identifies the subjects.

repeated

a vector that identifies the order of the observations within each subject.

link

a character string that specifies the link function. Options include "logistic", "probit", "cauchit", "cloglog" and "acl".

bstart

a vector that includes an initial estimate for the marginal regression parameter vector.

LORstr

a character string that indicates the local odds ratios structure. Options include "independence", "uniform", "category.exch", "time.exch", "RC" or "fixed".

LORem

a character string that indicates if the marginalized local odds ratios structure is estimated simultaneously ("3way") or seperately at each level pair of repeated ("2way").

LORterm

a matrix that contains the desired local odds ratios structure. It should be used when LORstr is "fixed".

add

a positive constant to be added at each cell of the full marginalized contingency table in the presence of zero observed counts.

homogeneous

a logical that indicates homogeneous score parameters when LORstr is "time.exch" or "RC".

restricted

a logical that indicates monotone score parameters when LORstr is "time.exch" or "RC".

control

a vector that specifies the control variables for the GEE solver.

ipfp.ctrl

a vector that specifies the control variables for the ipfp function.

IM

a character string that indicates the method used for inverting a matrix. Options include "solve", "qr.solve" or "cholesky".

Value

• Returns an object of the class "LORgee". Generic summary, print, fitted and residuals methods are available. The pvalue of the Null model corresponds to the hypothesis $H_0: \beta=0$ based on the Wald test statistic.

Details

The data must be provided in a subject level or equivalently in `long' format. See details about the `long' format in the reshape function. A term of the form offset(expression) is allowed in the formula. The id and the repeated do not need to be pre-sorted. Instead the function reshapes data in an ascending order of id and repeated. The default set for the response categories is $1,\ldots,I$, where $I>2$ is the maximum observed response category. If otherwise, the function recodes the observed response categories onto this set. The default set for the levels of repeated is $1,\ldots,T$, where $T$ is the number of observed levels. If otherwise, the function recodes the observed levels onto this set. The $I$-th response category is omitted. An adjacent category logit model is fitted if and only if link is "acl". Otherwise a cumulative link model is fitted. The linear predictor is of the form $$\beta_{0j} +\beta^{'} x_{it}$$ where $\beta_{0j}$ is the $j$-th intercept and $x_{it}$ is the covariate vector for the $i$-th subject at the $t$-th level of repeated. The LORterm argument must be an $L$ x $I^2$ matrix, where $L$ is the number of level pairs of repeated. These are ordered as $(1,2), (1,3), ...,(1,T), (2,3),...,(T-1,T)$ and the rows of LORterm are supposed to preserve this order. Each row is assumed to contain the vectorized form of a probability table that satisfies the desired local odds ratios structure.

References

Touloumis, A., Agresti, A. and Kateri, M. (2012). GEE for multinomial responses using a local odds ratios parameterization. Submitted.

See Also

For a nominal response scale use nomLORgee.

Examples

data(arthritis)
intrinsic.pars(arthritis$y,arthritis$id,arthritis$time,5)
fitmod <- ordLORgee(y~factor(trt)+factor(baseline)+factor(time),id="id",
                          repeated="time",data=arthritis, LORstr="uniform")
summary(fitmod)