qvcalc {qvcalc} | R Documentation |
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 Menezes (2004). Quasi variances generalize and improve the accuracy of “floating absolute risk” (Easton et al., 1991).
qvcalc(object, factorname=NULL, labels = NULL, dispersion = NULL, estimates=NULL, modelcall=NULL)
object |
A model (of class lm, glm, etc.), or the covariance (sub)matrix for the estimates of interest |
factorname |
If object is a model, the name of the factor of
interest |
labels |
An optional vector of row names for the qvframe
component of the result (redundant if object is a model) |
dispersion |
an optional scalar multiplier for the covariance matrix, to cope with overdispersion for example |
estimates |
an optional vector of estimated coefficients (redundant
if object is a model) |
modelcall |
optional, the call expression for the model of interest
(redundant if object is a model) |
If object
is a Bradley-Terry model of class
BTm
, of the standard,
unstructured kind that is specified using
the special BTm
formula ~ ..
, the factorname
argument can be omitted, in which case the factorname
component of the resulting qv
object will be ""
.
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
estimate , SE , quasiSE and quasiVar ,
the last two being a quasi standard error and quasi-variance
for each level of the factor of interest |
relerrs |
relative errors for approximating the standard errors of all simple contrasts |
factorname |
the factor name if given |
modelcall |
if object is a model, object$call ;
otherwise NULL |
David Firth, d.firth@warwick.ac.uk
Easton, D. F, Peto, J. and Babiker, A. G. A. G. (1991) Floating absolute risk: an alternative to relative risk in survival and case-control analysis avoiding an arbitrary reference group. Statistics in Medicine 10, 1025–1035.
Firth, D. (2000) Quasi-variances in Xlisp-Stat and on the web. Journal of Statistical Software 5.4, 1–13. At http://www.jstatsoft.org
Firth, D. (2003) Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1–18.
Firth, D. and Mezezes, R. X. de (2004) Quasi-variances. Biometrika 91, 65–80.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Menezes, R. X. (1999) More useful standard errors for group and factor effects in generalized linear models. D.Phil. Thesis, Department of Statistics, University of Oxford.
## Overdispersed Poisson loglinear model for ship damage data ## from McCullagh and Nelder (1989), Sec 6.3.2 library(MASS) data(ships) ships$year <- as.factor(ships$year) ships$period <- as.factor(ships$period) shipmodel <- glm(formula = incidents ~ type + year + period, family = quasipoisson, data = ships, subset = (service > 0), offset = log(service)) shiptype.qvs <- qvcalc(shipmodel, "type") summary(shiptype.qvs, digits=4) plot(shiptype.qvs) ## A Bradley-Terry model example ## For details and references see help(BTm) library(BradleyTerry) ## ## Baseball data from Agresti (2002) p438 data(baseball) ## Fit the Bradley-Terry model with home advantage effect baseballModel <- BTm(baseball ~ .., order.effect = baseball$home.adv) baseball.qv <- qvcalc(baseballModel, factorname = "team") plot(baseball.qv, main = "Bradley-Terry analysis of baseball data") ## Not run: ## Example of a negative quasi variance ## Requires the "car" package library(car) data(Prestige) attach(Prestige) mymodel <- lm(prestige ~ type + education) library(qvcalc) type.qvs <- qvcalc(mymodel, "type") ## Warning message: ## NaNs produced in: sqrt(qv) 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. ## End(Not run)