| Version: | 1.0.4 |
| Date: | 2025-01-24 |
| Title: | Quasi Variances for Factor Effects in Statistical Models |
| Maintainer: | David Firth <d.firth@warwick.ac.uk> |
| URL: | https://davidfirth.github.io/qvcalc/ |
| BugReports: | https://github.com/DavidFirth/qvcalc/issues |
| Description: | Functions to compute quasi variances and associated measures of approximation error. |
| Suggests: | relimp, MASS, testthat (≥ 3.0.0) |
| Enhances: | psychotools, survival |
| License: | GPL-2 | GPL-3 |
| Config/testthat/edition: | 3 |
| RoxygenNote: | 7.3.2 |
| Encoding: | UTF-8 |
| NeedsCompilation: | no |
| Packaged: | 2025-01-24 19:51:56 UTC; david |
| Author: | David Firth  [aut,
cre] |
| Repository: | CRAN |
| Date/Publication: | 2025-01-24 21:20:02 UTC |
Print with Line Indentation
Description
Same as print, but adds a specified amount of white space at
the start of each printed line
Usage
indentPrint(object, indent = 4, ...)
Arguments
object |
any printable object |
indent |
a non-negative integer, the number of spaces to insert |
... |
other arguments to pass to |
Value
object is returned invisibly
Author(s)
David Firth, d.firth@warwick.ac.uk
Examples
indentPrint("this indented by 10 spaces", indent=10)
Plot method for objects of class qv
Description
Provides visualization of estimated contrasts using intervals based on quasi standard errors.
Usage
## S3 method for class 'qv'
plot(
x,
intervalWidth = 2,
ylab = "estimate",
xlab = "",
ylim = NULL,
main = "Intervals based on quasi standard errors",
levelNames = NULL,
...
)
Arguments
x |
an object of class |
intervalWidth |
the half-width, in quasi standard errors, of the plotted intervals |
ylab |
as for |
xlab |
as for |
ylim |
as for |
main |
as for |
levelNames |
labels to be used on the x axis for the levels of the factor whose effect is plotted |
... |
other arguments understood by |
Details
If levelNames is unspecified, the row names of x$qvframe will
be used.
Value
invisible(x)
Author(s)
David Firth, d.firth@warwick.ac.uk
References
Easton, D. F, Peto, J. and Babiker, A. G. A. G. (1991) Floating absolute risk: an alternative to relative risk in survival and case-control analysis avoiding an arbitrary reference group. Statistics in Medicine 10, 1025–1035. doi:10.1002/sim.4780100703
Firth, D. (2000) Quasi-variances in Xlisp-Stat and on the web. Journal of Statistical Software 5.4, 1–13. doi:10.18637/jss.v005.i04
Firth, D. (2003) Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1–18. doi:10.1111/j.0081-1750.2003.t01-1-00125.x
Firth, D. and Mezezes, R. X. de (2004) Quasi-variances. Biometrika 91, 65–80. doi:10.1093/biomet/91.1.65
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Menezes, R. X. (1999) More useful standard errors for group and factor effects in generalized linear models. D.Phil. Thesis, Department of Statistics, University of Oxford.
See Also
Examples
## Overdispersed Poisson loglinear model for ship damage data
## from McCullagh and Nelder (1989), Sec 6.3.2
library(MASS)
data(ships)
ships$year <- as.factor(ships$year)
ships$period <- as.factor(ships$period)
shipmodel <- glm(formula = incidents ~ type + year + period,
family = quasipoisson,
data = ships, subset = (service > 0), offset = log(service))
qvs <- qvcalc(shipmodel, "type")
summary(qvs, digits = 4)
plot(qvs, col = c(rep("red", 4), "blue"))
## if we want to plot in decreasing order (of estimates):
est <- qvs$qvframe$estimate
qvs2 <- qvs
qvs2$qvframe <- qvs$qvframe[order(est, decreasing = TRUE), , drop = FALSE]
plot(qvs2)
Quasi Variances for Model Coefficients
Description
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).
Usage
qvcalc(object, ...)
## Default S3 method:
qvcalc(
object,
factorname = NULL,
coef.indices = NULL,
labels = NULL,
dispersion = NULL,
estimates = NULL,
modelcall = NULL,
...
)
## S3 method for class 'coxph'
qvcalc(object, factorname = NULL, coef.indices = NULL, ...)
## S3 method for class 'itempar'
qvcalc(object, ...)
## S3 method for class 'lm'
qvcalc(object, factorname = NULL, coef.indices = NULL, dispersion = NULL, ...)
## S3 method for class 'survreg'
qvcalc(object, factorname = NULL, coef.indices = NULL, ...)
Arguments
object |
For |
... |
other arguments to pass to |
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 |
Details
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.
Value
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
|
Author(s)
David Firth, d.firth@warwick.ac.uk
References
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. doi:10.1002/sim.4780100703
Firth, D. (2000) Quasi-variances in Xlisp-Stat and on the web. Journal of Statistical Software 5.4, 1–13. doi:10.18637/jss.v005.i04
Firth, D. (2003) Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1–18. doi:10.1111/j.0081-1750.2003.t01-1-00125.x
Firth, D. and de Mezezes, R. X. (2004) Quasi-variances. Biometrika 91, 65–80. doi:10.1093/biomet/91.1.65
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.
See Also
Examples
## 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.
## End(Not run)
Accuracy of a Quasi-variance Approximation
Description
Computes the worst relative error, among all contrasts, for the standard error as derived from a set of quasi variances. For details of the method see Menezes (1999) or Firth and Menezes (2004).
Usage
worstErrors(qv.object)
Arguments
qv.object |
An object of class |
Value
A numeric vector of length 2, the worst negative relative error and the worst positive relative error.
Author(s)
David Firth, d.firth@warwick.ac.uk
References
Firth, D. and Mezezes, R. X. de (2004) Quasi-variances. Biometrika 91, 69–80. doi:10.1093/biomet/91.1.65
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.
See Also
Examples
## 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)
worstErrors(shiptype.qvs)