nomLORgee: Marginal Models For Correlated Nominal Multinomial Responses In multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses

Description

Solving the generalized estimating equations for correlated nominal multinomial responses assuming a baseline category logit model for the marginal probabilities.

Usage

 1 2 3 4 nomLORgee(formula, data, id = id, repeated = NULL, bstart = NULL, LORstr = "time.exch", LORem = "3way", LORterm = NULL, add = 0, homogeneous = TRUE, 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 an optional data frame containing the variables provided in formula, id and repeated. id a vector that identifies the clusters. repeated an optional vector that identifies the order of the observations within each cluster. bstart a vector that includes an initial estimate for the marginal regression parameter vector. LORstr a character string that indicates the marginalized local odds ratios structure. Options include "independence", "time.exch", "RC" or "fixed". LORem a character string that indicates if the marginalized local odds ratios structure is estimated simultaneously ("3way") or independently at each level pair of repeated ("2way"). LORterm a matrix that satisfies the user-defined local odds ratios structure. It is ignored unless LORstr="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="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 function ipfp. IM a character string that indicates the method used for inverting a matrix. Options include "solve", "qr.solve" or "cholesky".

Details

The data must be provided in case level or equivalently in ‘long’ format. See details about the ‘long’ format in the function reshape.

A term of the form offset(expression) is allowed in the right hand side of formula.

The default set for the response categories is \{1,…,J\}, where J>2 is the maximum observed response category. If otherwise, the function recodes the observed response categories onto this set.

The J-th response category is treated as baseline.

The default set for the id labels is \{1,…,N\}, where N is the sample size. If otherwise, the function recodes the given labels onto this set.

The argument repeated can be ignored only when data is written in such a way that the t-th observation in each cluster is recorded at the t-th measurement occasion. If this is not the case, then the user must provide repeated. The suggested set for the levels of repeated is \{1,…,T\}, where T is the number of observed levels. If otherwise, the function recodes the given levels onto this set.

The variables id and repeated do not need to be pre-sorted. Instead the function reshapes data in an ascending order of id and repeated.

The fitted marginal baseline category logit model is

log \frac{Pr(Y_{it}=j |x_{it})}{Pr(Y_{it}=J |x_{it})}=β_{j0} +β^{'}_j x_{it}

where Y_{it} is the t-th multinomial response for cluster i, x_{it} is the associated covariates vector, β_{j0} is the j-th response category specific intercept and β_{j} is the j-th response category specific parameter vector.

The formula is easier to read from either the Vignette or the Reference Manual (both available here).

The LORterm argument must be an L x J^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.

Value

Returns an object of the class "LORgee". This has components:

 call the matched call. title title for the GEE model. version the current version of the GEE solver. link the marginal link function. local.odds.ratios the marginalized local odds ratios structure variables. terms the terms structure describing the marginal model. contrasts the contrasts used for the factors. nobs the number of observations. convergence the values of the convergence variables. coefficients the estimated regression parameter vector of the marginal model. linear.pred the estimated linear predictor of the marginal regression model. The j-th column corresponds to the j-th response category. fitted.values the estimated fitted values of the marginal regression model. The j-th column corresponds to the j-th response category. residuals the residuals of the marginal regression model based on the binary responses. The j-th column corresponds to the j-th response category. y the multinomial response variables. id the id variable. max.id the number of clusters. clusz the number of observations within each cluster. robust.variance the estimated "robust" covariance matrix. naive.variance the estimated "naive" or "model-based" covariance matrix. xnames the regression coefficients' symbolic names. categories the number of observed response categories. occasions the levels of the repeated variable. LORgee.control the control values for the GEE solver. ipfp.control the control values for the function ipfp. inverse.method the method used for inverting matrices. adding.constant the value used for add. pvalue the p-value based on a Wald test that no covariates are statistically significant.

Generic coef, summary, print, fitted and residuals methods are available. The pvalue of the Null model corresponds to the hypothesis H_0: β_1=...=β_{J-1}=0 based on the Wald test statistic.

Author(s)

Anestis Touloumis

References

Touloumis, A. (2011) GEE for multinomial responses. PhD dissertation, University of Florida.

Touloumis, A., Agresti, A. and Kateri, M. (2013) GEE for multinomial responses using a local odds ratios parameterization. Biometrics, 69, 633-640.

Touloumis, A. (2015) R Package multgee: A Generalized Estimating Equations Solver for Multinomial Responses. Journal of Statistical Software, 64, 1-14.

 1 2 3 4 ## See the interpretation in Touloumis (2011). data(housing) fitmod <- nomLORgee(y~factor(time)*sec,data=housing,id=id, repeated=time) summary(fitmod)