Description Usage Arguments Value Author(s) See Also Examples

For a given model object the function computes a linear function of the parameters and the corresponding standard errors, p-values and confidence intervals.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
ci.lin( obj,
ctr.mat = NULL,
subset = NULL,
subint = NULL,
xvars = NULL,
diffs = FALSE,
fnam = !diffs,
vcov = FALSE,
alpha = 0.05,
df = Inf,
Exp = FALSE,
sample = FALSE )
ci.exp( ..., Exp = TRUE, pval = FALSE )
Wald( obj, H0=0, ... )
ci.mat( alpha = 0.05, df = Inf )
ci.pred( obj, newdata,
Exp = NULL,
alpha = 0.05 )
ci.ratio( r1, r2,
se1 = NULL,
se2 = NULL,
log.tr = !is.null(se1) & !is.null(se2),
alpha = 0.05,
pval = FALSE )
``` |

`obj` |
A model object (in general of class |

`ctr.mat` |
Matrix, data frame or list (of two data frames). If it is a matrix, it should be a contrast matrix to be multiplied to the parameter vector, i.e. the desired linear function of the parameters. If it is a data.frame it should have columns corresponding to a prediction frame, see details. If it is a list, it must contain two data frames that are (possibly
partial) prediction frames for |

`xvars` |
Character vector. If variables in the model are omitted
from data frames supplied in a list to |

`subset` |
The subset of the parameters to be used. If given as a
character vector, the elements are in turn matched against the
parameter names (using |

`subint` |
Character. |

`diffs` |
If TRUE, all differences between parameters
in the subset are computed. |

`fnam` |
Should the common part of the parameter names be included
with the annotation of contrasts? Ignored if |

`vcov` |
Should the covariance matrix of the set of parameters be
returned? If this is set, |

`alpha` |
Significance level for the confidence intervals. |

`df` |
Integer. Number of degrees of freedom in the t-distribution used to compute the quantiles used to construct the confidence intervals. |

`Exp` |
For |

`sample` |
Logical or numerical. If |

`pval` |
Logical. Should a column of P-values be included with the
estimates and confidence intervals output by |

`H0` |
Numeric. The null values for the selected/transformed parameters to be tested by a Wald test. Must have the same length as the selected parameter vector. |

`...` |
Parameters passed on to |

`newdata` |
Data frame of covariates where prediction is made. |

`r1,r2` |
Estimates of rates in two independent groups, with confidence intervals. |

`se1,se2` |
Standard errors of log-rates in the two groups. If
given, it is assumed that |

`log.tr` |
Logical, if true, it is assumed that |

`ci.lin`

returns a matrix with number of rows and row names as
`ctr.mat`

. The columns are Estimate, Std.Err, z, P, 2.5% and
97.5% (or according to the value of `alpha`

). If
`vcov=TRUE`

a list of length 2 with components `coef`

(a
vector), the desired functional of the parameters and `vcov`

(a
square matrix), the variance covariance matrix of this, is returned
but not printed. If `Exp==TRUE`

the confidence intervals for the
parameters are replaced with three columns: exp(estimate,c.i.).

`ci.exp`

returns only the exponentiated parameter estimates with
confidence intervals. It is merely a wrapper for `ci.lin`

,
fishing out the last 3 columns from `ci.lin(...,Exp=TRUE)`

. If
you just want the estimates and confidence limits, but not
exponentiated, use `ci.exp(...,Exp=FALSE)`

.

If `ctr.mat`

is a data frame, the model matrix corresponding to
this is constructed and supplied, so the default behaviour will be to
produce the same as `ci.pred`

, apparently superfluous. The purpose
of this is to allow the use of the arguments `vcov`

that produces
the variance-covariance matrix of the predictions, and `sample`

that produces a sample of predictions using sampling from the
multivariate normal with mean equal to parameters and variance equal
to the hessian.

If `ctr.mat`

is a list of two data frames, the difference of the
predictions from using the first versus the last as newdata arguments
to predict is computed. Columns that are identical in the two data
frames can be omitted (see below), but names of numerical variables
omitted must be supplied in a character vector `xvars`

. Factors
omitted need not be named. If the second data frame has only one row,
this is replicated to match the number of rows in the first. The
facility is primarily aimed at teasing out RRs that are non-linear
functions of a quantitative variable without setting up contrast
matrices using the same code as in the model. Note however if splines
are used with computed knots stored in a vector such as
`Ns(x,knots=kk)`

then the `kk`

must be available in the
(global) environment; it will not be found inside the model object. In
practical terms it means that if you save model objects for later
prediction you should save the knots used in the spline setups too.

Finally, only arguments `Exp`

, `vcov`

, `alpha`

and
`sample`

from `ci.lin`

are honored when `ctr.mat`

is a
data frame or a list of two data frames.

You can leave out variables (columns) from the two data frames that
would be constant and identical, basically variables not relevant for
the calculation of the contrast. In many cases `ci.lin`

(really
`Epi:::ci.dfr`

) can figure out the names of the omitted columns,
but occasionally you will have to supply the names of the omitted
variables in the `xvars`

argument. Factors omitted need not be
listed in `xvars`

, though no harm is done doing so.

`Wald`

computes a Wald test for a subset of (possibly linear
combinations of) parameters being equal to the vector of null
values as given by `H0`

. The selection of the subset of
parameters is the same as for `ci.lin`

. Using the `ctr.mat`

argument makes it possible to do a Wald test for equality of
parameters. `Wald`

returns a named numerical vector of length 3,
with names `Chisq`

, `d.f.`

and `P`

.

`ci.mat`

returns a 2 by 3 matrix with rows `c(1,0,0)`

and
`c(0,-1,1)*1.96`

, devised to post-multiply to a p by 2 matrix with
columns of estimates and standard errors, so as to produce a p by 3 matrix
of estimates and confidence limits. Used internally in `ci.lin`

and
`ci.cum`

.
The 1.96 is replaced by the appropriate quantile from the normal or
t-distribution when arguments `alpha`

and/or `df`

are given.

`ci.pred`

returns a 3-column matrix with estimates and upper and
lower confidence intervals as columns. This is just a convenience
wrapper for `predict.glm(obj,se.fit=TRUE)`

which returns a rather
unhandy structure. The prediction with c.i. is made in the `link`

scale, and by default transformed by the inverse link, since the most
common use for this is for multiplicative Poisson or binomial models
with either log or logit link.

`ci.ratio`

returns the rate-ratio of two independent set of
rates given with confidence intervals or s.e.s. If `se1`

and
`se2`

are given and `log.tr=FALSE`

it is assumed that
`r1`

and `r2`

are rates and `se1`

and `se2`

are
standard errors of the log-rates.

Bendix Carstensen, BendixCarstensen.com & Michael Hills

See also `ci.cum`

for a function computing
cumulative sums of (functions of) parameter estimates. The example
code for `matshade`

has an application of predicting a
rate-ratio using a list of two prediction frame in the `ctr.mat`

argument.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | ```
# Bogus data:
f <- factor( sample( letters[1:5], 200, replace=TRUE ) )
g <- factor( sample( letters[1:3], 200, replace=TRUE ) )
x <- rnorm( 200 )
y <- 7 + as.integer( f ) * 3 + 2 * x + 1.7 * rnorm( 200 )
# Fit a simple model:
mm <- lm( y ~ x + f + g )
ci.lin( mm )
ci.lin( mm, subset=3:6, diff=TRUE, fnam=FALSE )
ci.lin( mm, subset=3:6, diff=TRUE, fnam=TRUE )
ci.lin( mm, subset="f", diff=TRUE, fnam="f levels:" )
print( ci.lin( mm, subset="g", diff=TRUE, fnam="gee!:", vcov=TRUE ) )
# Use character defined subset to get ALL contrasts:
ci.lin( mm, subset="f", diff=TRUE )
# Suppose the x-effect differs across levels of g:
mi <- update( mm, . ~ . + g:x )
ci.lin( mi )
# RR a vs. b by x:
nda <- data.frame( x=-3:3, g="a", f="b" )
ndb <- data.frame( x=-3:3, g="b", f="b" )
#
ci.lin( mi, list(nda,ndb) )
# Same result if f column is omitted because "f" columns are identical
ci.lin( mi, list(nda[,-3],ndb[,-3]) )
# However, Crashes if knots in spline is supplied, and non-factor omitted
xk <- -1:1
xi <- c(-0.5,0.5)
ww <- rnorm(200)
mi <- update( mm, . ~ . -x +ww + Ns(x,knots=xk) + g:Ns(x,knots=xi) )
# Will crash
try( cbind( nda$x, ci.lin( mi, list(nda,ndb) ) ) )
# Must specify num vars (not factors) omitted from nda, ndb
cbind( nda$x, ci.lin( mi, list(nda,ndb), xvars="ww" ) )
# A Wald test of whether the g-parameters are 0
Wald( mm, subset="g" )
# Wald test of whether the three first f-parameters are equal:
( CM <- rbind( c(1,-1,0,0), c(1,0,-1,0)) )
Wald( mm, subset="f", ctr.mat=CM )
# or alternatively
( CM <- rbind( c(1,-1,0,0), c(0,1,-1,0)) )
Wald( mm, subset="f", ctr.mat=CM )
# Confidence intervals for ratio of rates
# Rates and ci supplied, but only the range (lower and upper ci) is used
ci.ratio( cbind(10,8,12.5), cbind(5,4,6.25) )
ci.ratio( cbind(8,12.5), cbind(4,6.25) )
# Beware of the offset when making predictions with ci.pred and ci.exp
## Not run:
library( mgcv )
data( mortDK )
m.arg <- glm( dt ~ age , offset=log(risk) , family=poisson, data=mortDK )
m.form <- glm( dt ~ age + offset(log(risk)), family=poisson, data=mortDK )
a.arg <- gam( dt ~ age , offset=log(risk) , family=poisson, data=mortDK )
a.form <- gam( dt ~ age + offset(log(risk)), family=poisson, data=mortDK )
nd <- data.frame( age=60:65, risk=100 )
round( ci.pred( m.arg , nd ), 4 )
round( ci.pred( m.form, nd ), 4 )
round( ci.exp ( m.arg , nd ), 4 )
round( ci.exp ( m.form, nd ), 4 )
round( ci.pred( a.arg , nd ), 4 )
round( ci.pred( a.form, nd ), 4 )
round( ci.exp ( a.arg , nd ), 4 )
round( ci.exp ( a.form, nd ), 4 )
nd <- data.frame( age=60:65 )
try( ci.pred( m.arg , nd ) )
try( ci.pred( m.form, nd ) )
try( ci.exp ( m.arg , nd ) )
try( ci.exp ( m.form, nd ) )
try( ci.pred( a.arg , nd ) )
try( ci.pred( a.form, nd ) )
try( ci.exp ( a.arg , nd ) )
try( ci.exp ( a.form, nd ) )
## End(Not run)
# The offset may be given as an argument (offset=log(risk))
# or as a term (+offset(log)), and depending on whether we are using a
# glm or a gam Poisson model and whether we use ci.pred or ci.exp to
# predict rates the offset is either used or ignored and either
# required or not; the state of affairs can be summarized as:
#
# offset
# -------------------------------------
# usage required?
# ------------------ ---------------
# function model argument term argument term
# ---------------------------------------------------------
# ci.pred glm used used yes yes
# gam ignored used no yes
#
# ci.exp glm ignored ignored no yes
# gam ignored ignored no yes
# ---------------------------------------------------------
``` |

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