dfbeta.glmgee {glmtoolbox}

Dfbeta for Generalized Estimating Equations

Description

Produces an approximation, better known as the one-step approximation, of the effect on the parameter estimates of deleting each cluster/observation in turn. This function also can produce an index plot of the Dfbeta Statistic for some parameters via the argument coefs.

Usage

## S3 method for class 'glmgee'
dfbeta(
  model,
  level = c("clusters", "observations"),
  method = c("Preisser-Qaqish", "full"),
  coefs,
  identify,
  ...
)

Arguments

model

an object of class glmgee.

level

an (optional) character string indicating the level for which the Dfbeta statistic is required. The options are: cluster-level ("clusters") and observation-level ("observations"). As default, level is set to "clusters".

method

an (optional) character string indicating the method of calculation for the one-step approximation. The options are: the one-step approximation described by Preisser and Qaqish (1996) in which the working-correlation matrix is assumed to be known ("Preisser-Qaqish"); and the "authentic" one-step approximation ("full"). As default, method is set to "Preisser-Qaqish".

coefs

an (optional) character string which (partially) match with the names of some parameters in the linear predictor.

identify

an (optional) integer indicating the number of clusters/observations to identify on the plot of the Dfbeta statistic. This is only appropriate if coefs is specified.

...

further arguments passed to or from other methods. If coefs is specified then ... may be used to include graphical parameters to customize the plot. For example, col, pch, cex, main, sub, xlab, ylab.

Details

The one-step approximation (with the method "full") of the estimates of the parameters in the linear predictor of a GEE when the i-th cluster is excluded from the dataset is given by the vector obtained as the result of the first iteration of the fitting algorithm of that GEE when it is performed using: (1) a dataset in which the i-th cluster is excluded; and (2) a starting value which is the solution to the same GEE but based on the dataset inluding all clusters.

Value

A matrix with so many rows as clusters/observations in the sample and so many columns as parameters in the linear predictor. For clusters, the i-th row of that matrix corresponds to the difference between the estimates of the parameters in the linear predictor using all clustersand the one-step approximation of those estimates when the i-th cluster is excluded from the dataset.

References

Pregibon D. (1981). Logistic regression diagnostics. The Annals of Statistics 9, 705-724.

Preisser J.S., Qaqish B.F. (1996) Deletion diagnostics for generalised estimating equations. Biometrika 83:551–562.

Hammill B.G., Preisser J.S. (2006) A SAS/IML software program for GEE and regression diagnostics. Computational Statistics & Data Analysis 51:1197-1212.

Vanegas L.H., Rondon L.M., Paula G.A. (2023) Generalized Estimating Equations using the new R package glmtoolbox. The R Journal 15:105-133.

Examples

###### Example 1: Effect of ozone-enriched atmosphere on growth of sitka spruces
data(spruces)
mod1 <- size ~ poly(days,4) + treat
fit1 <- glmgee(mod1, id=tree, family=Gamma(log), corstr="AR-M-dependent", data=spruces)
dfbs1 <- dfbeta(fit1, method="full", coefs="treat", col="red", lty=1, lwd=1, col.lab="blue",
         col.axis="blue", col.main="black", family="mono", cex=0.8, main="treat")

### Calculation by hand of dfbeta for the tree labeled by "N1T01"
onestep1 <- glmgee(mod1, id=tree, family=Gamma(log), corstr="AR-M-dependent",
            data=spruces, start=coef(fit1), subset=c(tree!="N1T01"), maxit=1)

coef(fit1)-coef(onestep1)
dfbs1[rownames(dfbs1)=="N1T01",]

###### Example 2: Treatment for severe postnatal depression
data(depression)
mod2 <- depressd ~ visit + group
fit2 <- glmgee(mod2, id=subj, family=binomial(logit), corstr="AR-M-dependent",
               data=depression)

dfbs2 <- dfbeta(fit2, method="full", coefs="group" ,col="red", lty=1, lwd=1, col.lab="blue",
         col.axis="blue", col.main="black", family="mono", cex=0.8, main="group")

### Calculation by hand of dfbeta for the woman labeled by "18"
onestep2 <- glmgee(mod2, id=subj, family=binomial(logit), corstr="AR-M-dependent",
            data=depression, start=coef(fit2), subset=c(subj!=18), maxit=1)

coef(fit2)-coef(onestep2)
dfbs2[rownames(dfbs2)==18,]

###### Example 3: Treatment for severe postnatal depression (2)
mod3 <- dep ~ visit*group
fit3 <- glmgee(mod3, id=subj, family=gaussian(identity), corstr="AR-M-dependent",
               data=depression)

dfbs3 <- dfbeta(fit3, method="full", coefs="visit:group" ,col="red", lty=1, lwd=1, col.lab="blue",
         col.axis="blue", col.main="black", family="mono", cex=0.8, main="visit:group")

### Calculation by hand of dfbeta for the woman labeled by "18"
onestep3 <- glmgee(mod3, id=subj, family=gaussian(identity), corstr="AR-M-dependent",
            data=depression, start=coef(fit3), subset=c(subj!=18), maxit=1)

coef(fit3)-coef(onestep3)
dfbs3[rownames(dfbs3)==18,]