Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 | ```
ordLORgee(formula, data, id = id, repeated = NULL,
link = "logit", bstart = NULL, LORstr = "category.exch",
LORem = "3way", LORterm = NULL, add = 0, homogeneous = TRUE,
restricted = FALSE, control = LORgee.control(),
ipfp.ctrl = ipfp.control(), IM = "solve")
``` |

`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 |

`id` |
a vector that identifies the clusters. |

`repeated` |
an optional vector that identifies the order of observations within each cluster. |

`link` |
a character string that specifies the link function. Options include |

`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 |

`LORem` |
a character string that indicates if the marginalized local odds ratios structure is estimated simultaneously ( |

`LORterm` |
a matrix that satisfies the user-defined local odds ratios structure. It is ignored unless |

`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 |

`restricted` |
a logical that indicates monotone score parameters when |

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

`ipfp.ctrl` |
a vector that specifies the control variables for the function |

`IM` |
a character string that indicates the method used for inverting a matrix. Options include |

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 omitted.

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 cumulative link model is

*Pr(Y_{it}≤ j |x_{it})=F(β_{j0} +β^{'} x_{it})*

where *Y_{it}* is the *t*-th multinomial response for cluster *i*, *x_{it}* is the associated covariates vector, *F* is the cumulative distribution function determined by `link`

, *β_{j0}* is the *j*-th response category specific intercept and *β* is the marginal regression parameter vector excluding intercepts.

The marginal adjacent categories logit model

*log \frac{Pr(Y_{it}=j |x_{it})}{Pr(Y_{it}=j+1 |x_{it})}=β_{j0} +β^{'} x_{it}*

is fitted if and only if `link="acl"`

. In contrast to a marginal cumulative link model, here the intercepts do not need to be monotone increasing.

The formulae are 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.

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 |

`contrasts` |
the |

`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 |

`fitted.values` |
the estimated fitted values of the marginal regression model. The |

`residuals` |
the residuals of the marginal regression model. The |

`y` |
the multinomial response variables. |

`id` |
the |

`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 |

`LORgee.control` |
the control values for the GEE solver. |

`ipfp.control` |
the control values for the function |

`inverse.method` |
the method used for inverting matrices. |

`adding.constant` |
the value used for |

`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=0* based on the Wald test statistic.

Anestis Touloumis

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.

For a nominal response scale use the function nomLORgee.

1 2 3 4 5 |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.