Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples
View source: R/family.categorical.R
Fits a stopping ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
1 2 |
link |
Link function applied to the M
stopping ratio probabilities.
See |
parallel |
A logical, or formula specifying which terms have equal/unequal coefficients. |
reverse |
Logical.
By default, the stopping ratios used are
eta_j = logit(P[Y=j|Y>=j])
for j=1,…,M.
If |
zero |
Can be an integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,...,M}. The default value means none are modelled as intercept-only terms. |
whitespace |
See |
In this help file the response Y is assumed to be a factor with ordered values 1,2,…,M+1, so that M is the number of linear/additive predictors eta_j.
There are a number of definitions for the continuation ratio
in the literature. To make life easier, in the VGAM package,
we use continuation ratios (see cratio
)
and stopping ratios.
Continuation ratios deal with quantities such as
logitlink(P[Y>j|Y>=j])
.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
rrvglm
and vgam
.
No check is made to verify that the response is ordinal if the
response is a matrix;
see ordered
.
The response should be either a matrix of counts (with row sums that
are all positive), or a factor. In both cases, the y
slot
returned by vglm
/vgam
/rrvglm
is the matrix
of counts.
For a nominal (unordered) factor response, the multinomial
logit model (multinomial
) is more appropriate.
Here is an example of the usage of the parallel
argument.
If there are covariates x1
, x2
and x3
, then
parallel = TRUE ~ x1 + x2 -1
and
parallel = FALSE ~ x3
are equivalent. This would constrain
the regression coefficients for x1
and x2
to be
equal; those of the intercepts and x3
would be different.
Thomas W. Yee
Agresti, A. (2013). Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.
Simonoff, J. S. (2003). Analyzing Categorical Data, New York, USA: Springer-Verlag.
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Yee, T. W. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1–34. https://www.jstatsoft.org/v32/i10/.
cratio
,
acat
,
cumulative
,
multinomial
,
margeff
,
pneumo
,
logitlink
,
probitlink
,
clogloglink
,
cauchitlink
.
1 2 3 4 5 6 7 |
Loading required package: stats4
Loading required package: splines
Call:
vglm(formula = cbind(normal, mild, severe) ~ let, family = sratio(parallel = TRUE),
data = pneumo)
Coefficients:
(Intercept):1 (Intercept):2 let
8.733797 8.051302 -2.321359
Degrees of Freedom: 16 Total; 13 Residual
Residual deviance: 7.626763
Log-likelihood: -26.39023
logitlink(P[Y=1|Y>=1]) logitlink(P[Y=2|Y>=2])
(Intercept) 8.733797 8.051302
let -2.321359 -2.321359
$`(Intercept)`
[,1] [,2]
[1,] 1 0
[2,] 0 1
$let
[,1]
[1,] 1
[2,] 1
logitlink(P[Y=1|Y>=1]) logitlink(P[Y=2|Y>=2])
1 4.6531774 3.9706824
2 2.4474398 1.7649448
3 1.6117442 0.9292491
4 1.0403809 0.3578859
5 0.5822388 -0.1002563
6 0.1997827 -0.4827124
7 -0.1538548 -0.8363499
8 -0.4160301 -1.0985252
P[Y=1|Y>=1] P[Y=2|Y>=2]
1 0.9905587 0.9814886
2 0.9203740 0.8538279
3 0.8336534 0.7169229
4 0.7389235 0.5885286
5 0.6415824 0.4749569
6 0.5497802 0.3816118
7 0.4616120 0.3023041
8 0.3974671 0.2500163
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