geeasy (version 0.1.3)

geelm.fit: Fit Generalized Estimating Equation-based Linear Models

Description

Estimate mean structure parameters and their corresponding standard errors for generalized linear models with clustered or correlated observations by use of generalized estimating equations.

Usage

geelm.fit(x, y, id, offset, family, weights, control, corstr, start = NULL)
geelm(
  formula,
  id = NULL,
  waves = NULL,
  data = parent.frame(),
  family = gaussian,
  corstr = "independence",
  Mv = 1,
  weights = NULL,
  corr.mat = NULL,
  offset = NULL,
  engine = "geeasy",
  output = "geelm",
  control = geelm.control()
)

Value

An object of class geelm (inherits from geeglm) representing the fit. It contains the following slots:

$coefficients: Coefficients from the mean structure model (betas) on their original scales

$residuals: Pearson residuals, in the order of the inputted dataset (with NAs omitted).

$fitted.values: Fitted values (response scale), in the order of the inputted dataset (with NAs omitted).

$rank: The rank of the model matrix, i.e. the number of estimated mean structure coefficients.

$qr: QR decomposition of the model matrix (NA omitted).

$family: A family object specifying which exponential family was used for fitting the mean structure model, see family for more information.

$linear.predictors: The linear predictor on the original scale.

$weights: Weights used for computations, in the order of the inputted dataset (NAs omitted).

$prior.weights: The original weights used to produce this geeglm object (set by user or defaulted to 1 for all observations).

$df.residuals: Residual degrees of freedom.

$y: Outcome variable, in the order of the inputted dataset (NAs omitted).

$model: The model.frame, ordered as the original inputted data with NAs omitted.

$call: The original function call that produced this geeglm object.

$formula: The formula used in the original call.

$terms: The terms of the formula used in the original call.

$data: The original dataset that was used for producing this geeglm object.

$offset: Offset used for fitting the model, ordered as the original inputted data with NAs omitted.

$control: Value of control parameters used for fitting the model.

$method: Internal function used for fitting the model.

$contrasts: Contrasts used in the model matrix.

$xlevels: Levels of factor variables used in the model formula (if any).

$geese: An object containing further information about the variance estimation, including a variance matrix for the beta-coefficients ($vbeta), the estimated coefficients for the working correlation matrix ($alpha), the estimated dispersion parameter ($gamma), and the individual cluster sizes ($clusz). See geese for more information.

$modelInfo: Information about the link functions used for fitting the mean, variance and scale structures of the model.

$id: IDs used for identifying the clusters, ordered as the original inputted data with NAs omitted.

$corstr: Name of the correlation structured imposed on the model. If the correlation structure requires further information, it is stored in a suitably named attribute. For example, for m-dependent correlation structures, the m scalar is available in an attribute named Mv.

$cor.link: Link function used for the correlation structure.

$std.err: Method used to estimate the standard error of the mean structure coefficients (betas).

Arguments

x, y

For glm: logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value.

For glm.fit: x is a design matrix of dimension n * p, and y is a vector of observations of length n.

id

A vector identifying the clusters. If NULL, then each observation is assigned its own cluster.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset.

family

A description of the error distribution and link function to be used in the model. The argument can be one of three options: a family object, a character string, or a list of functions. For more information on how to use family objects, see Details below.

weights

an optional vector of ‘prior weights’ to be used in the fitting process. Should be NULL or a numeric vector.

control

A list of parameters for controlling the fitting process.

corstr

A character string specifying the correlation structure. The default is "independence". Allowed structures are: "independence", "exchangeable", "ar1", "m-dependent", "unstructured", "fixed", and "userdefined". Any unique substring may be supplied. If "fixed" or "userdefined", then corr.mat must be specified. If "m-dependent", then Mv is relevant.

start

starting values for the parameters in the linear predictor.

formula

A formula expression similar to that for glm,

waves

An numeric vector identifying the time ordering within clusters (i.e. levels of id). By default, data are assumed to be sorted such that observations in a cluster are in consecutive rows and higher numbered rows in a cluster are assumed to be later. Note that only the ordering of the values in waves is used, NOT the numeric values themselves. This means that e.g. having waves equal to c(1, 2, 3) or c(1, 2, 7) within a cluster results in the same model.

data

An optional data frame containing the variables in the model.

Mv

For "m-dependent", the value for m.

corr.mat

The correlation matrix for "fixed". Matrix should be symmetric with dimensions >= the maximum cluster size. If the correlation structure is "userdefined", then this is a matrix describing which correlations are the same.

engine

Engine used to fit the model. The default, "geeasy" uses this package (built on the geeM package), while "geepack" uses the function geeglm from geepack to fit the model. Note that if the geepack engine is used, the data are sorted according to id (and possibly waves within id) and NAs are dropped before the data is used (this differs from the standard in geepack).

output

Output object type. There are two options; 1) "geelm" (default), resulting in an output that inherits the structure of geepacks geeglm object, or 2) "geem" (or its alias "geeM") which results in an output that has the structure of geeMs geem object.

Functions

• geelm.fit():

Author

Anne Helby Petersen, Lee McDaniel & Nick Henderson

Details

Users may specify functions for link and variance functions, but the functions must be vectorized functions.

Offsets can be specified in the model formula, as in glm() or they may be specified using the offset argument. If offsets are specified in both ways, their sum is used as an offset.

For the "userdefined" correlation option, the function accepts a matrix with consecutive integers. Each such integer represent a distinct parameter that will be estimated. All entries given as 1 will be assumed to be the same as each other and will be assumed to be possibly different from entries with a 2, and so on.geelm only looks at the upper triangle of the matrix. Any entry given as 0 will be fixed at 0.

If observations are dropped because they have a weight of 0, then the denominator for the moment estimates of the correlation matrices are calculated using the number of non-zero Pearson residuals for the correlation structures unstructured, userdefined and m-dependent with Mv>1. Therefore, residuals numerically equal to 0 may cause problems in the calculation of correlation parameters.

Concerning the family argument: If the supplied argument is a character string, then the string should correspond to one of the family objects. In order to define a link function, a list must be created with the components (LinkFun, VarFun, InvLink, InvLinkDeriv), all of which are vectorized functions. If the components in the list are not named as (LinkFun, VarFun, InvLink, InvLinkDeriv), then geelm assumes that the functions are given in that order. LinkFun and VarFun are the link and variance functions. InvLink and InvLinkDeriv are the inverse of the link function and the derivative of the inverse of the link function and so are decided by the choice of the link function.

See Also

glm, formula, family

Examples

# load data
data("respiratory")
respiratory$useid <- interaction(respiratory$center, respiratory$id)

# fit model
m <- geelm(outcome ~ treat + sex + age + baseline, 
           data = respiratory, id = useid,
                      family = "binomial", corstr = "exchangeable")

if (FALSE) {
get_jack_se <- function(object, dat){
    parm <- sapply(1:nrow(dat),
                   function(i){
                       dat.i <- dat[-i,]
                       coef(update(object, data=dat.i))
                   })
    parm <- t(parm)
    parm.mean <- apply(parm, 2, mean)
    
    parm.cent <- sapply(1:nrow(parm),
                        function(i){
                            parm[i, ] - parm.mean
                        })
    parm.cent <- t(parm.cent) 
    
    jack.var <- ((nrow(dat)-1) / nrow(dat)) * t(parm.cent) %*% parm.cent
    jack.se <- sqrt(diag(jack.var))
    jack.se
}


# load data
data("respiratory")
respiratory$useid <- interaction(respiratory$center, respiratory$id)

# fit model
obj <- geelm(outcome ~ treat + sex + age + baseline, 
           data = respiratory, id = useid,
                      family = "binomial", corstr = "exchangeable")

dat <- respiratory
get_jack_se(obj, dat)
summary(obj) |> coef()
}