Quasi Variances for Model Coefficients
Computes a set of quasi variances (and corresponding quasi standard errors) for estimated model coefficients relating to the levels of a categorical (i.e., factor) explanatory variable. For details of the method see Firth (2000), Firth (2003) or Firth and de Menezes (2004). Quasi variances generalize and improve the accuracy of “floating absolute risk” (Easton et al., 1991). This device for economical model summary was first suggested by Ridout (1989).
qvcalc(object, ...)
## Default S3 method:
qvcalc(object, factorname = NULL, coef.indices = NULL,
labels = NULL, dispersion = NULL,
estimates = NULL, modelcall = NULL, ...)
## S3 method for class 'lm'
qvcalc(object, factorname = NULL, coef.indices = NULL,
dispersion = NULL, ...)
## S3 method for class 'coxph'
qvcalc(object, factorname = NULL, coef.indices = NULL, ...)
## S3 method for class 'survreg'
qvcalc(object, factorname = NULL, coef.indices = NULL,
...)
## S3 method for class 'itempar'
qvcalc(object, ...)object |
For |
factorname |
Either |
coef.indices |
Either |
labels |
An optional vector of row names for the |
dispersion |
an optional scalar multiplier for the covariance matrix, to cope with overdispersion for example |
estimates |
an optional vector of estimated coefficients (redundant
if |
modelcall |
optional, the call expression for the model of interest
(redundant if |
... |
other arguments to pass to |
The qvcalc.default method is the computational backend for
all other, class-specific methods.
In qvcalc.default, none of the arguments other than
object is used in computing the result. The remaining
arguments are simply passed through to the result object as components
to help with record-keeping etc.
In qvcalc.lm, at least one of factorname or
coef.indices must be non-NULL. The value of
coef.indices, if non-NULL, determines which rows
and columns of the model's variance-covariance matrix to use. If
coef.indices contains a zero, then an extra row and column are
included at the indicated position, to represent the zero variances and
covariances associated with a reference level. If coef.indices
is NULL, then factorname should be the name of a factor
effect in the model, and is used in order to extract the necessary
variance-covariance estimates.
For qvcalc.itempar, the "itempar" object must have the
full variance-covariance matrix in its "vcov" attribute, and
must have its "alias" attribute be TRUE. These
attributes result from use of the default arguments
vcov = TRUE, alias = TRUE
when the itempar function is called.
Ordinarily the quasi variances are positive and so their square roots (the quasi standard errors) exist and can be used in plots, etc.
Occasionally one (and only one) of the quasi variances is negative, and
so the corresponding quasi standard error does not exist (it appears as
NaN). This is fairly rare in applications, and
when it occurs it is because the factor of interest is strongly
correlated with one or more other predictors in the model. It is not
an indication that quasi variances are inaccurate. An example is shown
below using
data from the car package: the quasi variance
approximation
is exact (since type has
only 3 levels), and there is a negative quasi variance. The quasi
variances remain perfectly valid (they can be used to obtain
inference on any contrast), but it makes no sense to plot
‘comparison intervals’ in the usual way since one of the quasi standard
errors is not a real number.
A list of class qv, with components
covmat |
the full variance-covariance matrix for the estimated coefficients corresponding to the factor of interest |
qvframe |
a data frame with variables
|
relerrs |
relative errors for approximating the standard errors of all simple contrasts |
factorname |
the factor name if given |
coef.indices |
the coefficient indices if given |
modelcall |
if |
David Firth, d.firth@warwick.ac.uk
Easton, D. F, Peto, J. and Babiker, A. G. A. G. (1991) Floating absolute risk: an alternative to relative risk in survival and case-control analysis avoiding an arbitrary reference group. Statistics in Medicine 10, 1025–1035.
Firth, D. (2000) Quasi-variances in Xlisp-Stat and on the web. Journal of Statistical Software 5.4, 1–13. At http://www.jstatsoft.org
Firth, D. (2003) Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1–18.
Firth, D. and de Mezezes, R. X. (2004) Quasi-variances. Biometrika 91, 65–80.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Menezes, R. X. de (1999) More useful standard errors for group and factor effects in generalized linear models. D.Phil. Thesis, Department of Statistics, University of Oxford.
Ridout, M.S. (1989). Summarizing the results of fitting generalized linear models to data from designed experiments. In: Statistical Modelling: Proceedings of GLIM89 and the 4th International Workshop on Statistical Modelling held in Trento, Italy, July 17–21, 1989 (A. Decarli et al., eds.), pp 262–269. New York: Springer.
## Overdispersed Poisson loglinear model for ship damage data
## from McCullagh and Nelder (1989), Sec 6.3.2
if (require(MASS)) {
data(ships)
ships$year <- as.factor(ships$year)
ships$period <- as.factor(ships$period)
shipmodel <- glm(formula = incidents ~ type + year + period,
family = quasipoisson,
data = ships,
subset = (service > 0),
offset = log(service))
shiptype.qv <- qvcalc(shipmodel, "type")
## We can plot "comparison intervals" as follows:
## plot(shiptype.qv, xlab = "ship type")
## An equivalent result by using the coef.indices argument instead:
## shiptype.qv2 <- qvcalc(shipmodel, coef.indices = c(0, 2:5))
summary(shiptype.qv, digits = 4)
}
## Example of a "coxph" model
if(require(survival)) {
data("veteran", package = "survival")
cancer_model <- coxph(Surv(time,status) ~ celltype, data = veteran)
celltype_qv <- qvcalc(cancer_model, "celltype")
summary(celltype_qv)
}
## Example of a "survreg" model
if(require(survival)) {
data("veteran", package = "survival")
cancer_model2 <- survreg(Surv(time,status) ~ celltype, data = veteran,
dist = "weibull")
celltype_qv2 <- qvcalc(cancer_model2, "celltype")
summary(celltype_qv2)
}
## Based on an example from ?itempar
if(require(psychotools)) {
data("VerbalAggression", package = "psychotools")
raschmod <- raschmodel(VerbalAggression$resp2)
ip1 <- itempar(raschmod)
qv1 <- qvcalc(ip1)
summary(qv1) }
## Example of a negative quasi variance
## Requires the "car" package
## Not run:
library(car)
data(Prestige)
attach(Prestige)
mymodel <- lm(prestige ~ type + education)
library(qvcalc)
type.qvs <- qvcalc(mymodel, "type")
## Warning message:
## In sqrt(qv) : NaNs produced
summary(type.qvs)
## Model call: lm(formula = prestige ~ type + education)
## Factor name: type
## estimate SE quasiSE quasiVar
## bc 0.000000 0.000000 2.874361 8.261952
## prof 6.142444 4.258961 3.142737 9.876793
## wc -5.458495 2.690667 NaN -1.022262
## Worst relative errors in SEs of simple contrasts (%): 0 0
## Worst relative errors over *all* contrasts (%): 0 0
plot(type.qvs)
## Error in plot.qv(type.qvs) : No comparison intervals available,
## since one of the quasi variances is negative. See ?qvcalc for more.
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