Carcass persistence is modeled as survival function where the
one or both parameter(s) can depend on any number of covariates. Format
and usage parallel that of common R functions such as lm,
glm, and gam. However, the input data (data) are
structured differently to accommodate the survival model approach (see
"Details"), and model formulas may be entered for both l
("location") and s ("scale").
cpm(formula_l, formula_s = NULL, data, left, right, dist = "weibull",
allCombos = FALSE, sizeCol = NULL, CL = 0.9, quiet = FALSE)cpm0(formula_l, formula_s = NULL, data = NULL, left = NULL,
right = NULL, dist = "weibull", CL = 0.9, quiet = FALSE)
cpmSet(formula_l, formula_s = NULL, data, left, right,
dist = c("exponential", "weibull", "lognormal", "loglogistic"),
CL = 0.9, quiet = FALSE)
cpmSize(formula_l, formula_s = NULL, data, left, right,
dist = c("exponential", "weibull", "lognormal", "loglogistic"),
sizeCol = NULL, allCombos = FALSE, CL = 0.9, quiet = FALSE)
Formula for location; an object of class
"formula" (or one that can be coerced to that class):
a symbolic description of the model to be fitted. Details of model
specification are given under "Details".
Formula for scale; an object of class
"formula" (or one that can be coerced to that class):
a symbolic description of the model to be fitted. Details of model
specification are given under "Details".
Data frame with results from carcass persistence trials and any
covariates included in formula_l or formula_s (required).
Name of columns in data where the time of last present
observation is stored.
Name of columns in data where the time of first absent
observation is stored.
Distribution name ("exponential", "weibull", "loglogistic", or "lognormal")
logical. If allCombos = FALSE, then the single model
expressed by formula_l and formula_s is fit using a call to
cpm0. If allCombos = TRUE, a full set of cpm
submodels derived from combinations of the given covariates for p
and k is fit. For example, submodels of formula_l = p ~ A * B
would be p ~ A * B, p ~ A + B, p ~ A, p ~ B,
and p ~ 1. Models for each pairing of a p submodel with a
k submodel are fit via cpmSet, which fits each model
combination using successive calls to cpm0, which fits a
single model.
character string. The name of the column in data that
gives the size class of the carcasses in the field trials. If
sizeCol = NULL, then models are not segregated by size. If a
sizeCol is provided, then separate models are fit for the data
subsetted by sizeCol.
confidence level
Logical indicator of whether or not to print messsages
an object of an object of class cpm, cpmSet,
cpmSize, or cpmSetSize.
cpm0()returns a cpm object, which is a description
of a single, fitted pk model. Due to the large number and complexity of
components of acpm model, only a subset of them is printed
automatically; the rest can be viewed/accessed via the $ operator
if desired. These are described in detail in the 'cpm Components'
section.
cpmSet()returns a list of cpm objects, one for each
of the submodels, as described with parameter allCombos = TRUE.
cpmSize()returns a list of cpmSet objects (one for
each 'size') if allCombos = T, or a list of cpm objects (one
for each 'size') if allCombos = T
cpmreturns a cpm, cpmSet, cpmSize, or
cpmSetSize object:
cpm object if allCombos = FALSE, sizeCol = NULL
cpmSet object if allCombos = TRUE, sizeCol = NULL
cpmSize object if allCombos = FALSE, sizeCol != NULL
cpmSetSize object if allCombos = TRUE, sizeCol != NULL
The following components of a cpm object are displayed automatically:
callthe function call to fit the model
formula_lthe model formula for the p parameter
formula_sthe model formula for the k parameter
distributiondistribution used
predictorslist of covariates of l and/or s
AICcthe AIC value as corrected for small sample size
convergenceconvergence status of the numerical optimization
to find the maximum likelihood estimates of p and k. A
value of 0 indicates that the model was fit successfully. For
help in deciphering other values, see optim.
cell_lssummary statistics for estimated cellwise
l and s, including the medians and upper & lower bounds
on CIs for each parameter, indexed by cell (or combination of
covariate levels).
cell_absummary statistics for estimated cellwise
pda and pdb, including the medians and upper & lower
bounds on CIs for each parameter, indexed by cell (or combination of
covariate levels).
cell_descDescriptive statistics for estimated cellwise median persistence time and rI for search intervals of 1, 3, 7 14, and 28 days, where rI is the probability of that carcass that arrives at a uniform random time in within a search interval of I days persists until the first search after arrival.
The following components are not printed automatically but can be accessed
via the $ operator:
datathe data used to fit the model
betahat_lparameter estimates for the terms in the
regression model for for l
betahat_sparameter estimates for the terms in the
regression model for for s. If dist = "exponential", s
is set at 1 and not calculated.
varbetathe variance-covariance matrix of the estimators
for c(betahat_l, betahat_s.
cellMM_la cellwise model (design) matrix for covariate
structure of l_formula
cellMM_sa cellwise model(design) matrix for covariate
structure of s_formula
levels_lall levels of each covariate of l
levels_sall levels of each covariate of s
nbeta_lnumber of parameters fit for l
nbeta_snumber of parameters fit for s
cellscell structure of the cp-model, i.e., combinations of
all levels for each covariate of p and k. For example, if
covar1 has levels "a", "b", and "c", and
covar2 has levels "X" and "Y", then the cells
would consist of a.X, a.Y, b.X, b.Y,
c.X, and c.Y.
ncelltotal number of cells
predictors_llist of covariates of l
predictors_slist of covariates of s
observationsobservations used to fit the model
carcCellsthe cell to which each carcass belongs
AICthe AIC value for the fitted model
CLthe input CL
cpmSize may also be used to fit a single model for each size class if
allCombos = FALSE. To do so, formula_l, formula_s, and
dist be named lists with names matching the sizes listed in
unique(data[, sizeCol]). The return value is then a list of
cpm objects, one for each size.
The probability of a carcass persisting to a particular time is
dictated by the specific distribution chosen and its underlying location
(l) and scale (s) parameters (for all models except the exponential,
which only has a location parameter). Both l and s may
depend on covariates such as ground cover, season, species, etc., and a
separate model format (formula_l and formula_s) may be
entered for each. The models are entered as they would be in the familiar
lm or glm functions in R. For example, l might vary
with A, B, and C, while k varies only with
A. A user might then enter p ~ A + B + C for formula_l
and k ~ A for formula_s. Other R conventions for defining
formulas may also be used, with A:B for the interaction between
covariates A and B and A * B as short-hand for A + B + A:B.
Carcass persistence data must be entered in a data frame with data
in each row giving the fate of a single carcass in the trials. There
must be a column for each of the last time the carcass was observed
present and the first time the carcass was observed absent (or NA if the
carcass was always present). Additional columns with values for
categorical covariates (e.g., visibility = E, M, or D) may also be
included.
# NOT RUN {
head(data(wind_RP))
mod1 <- cpm(formula_l = l ~ Season, formula_s = s ~ 1, data = wind_RP$CP,
left = "LastPresent", right = "FirstAbsent")
class(mod1)
mod2 <- cpm(formula_l = l ~ Season, formula_s = s ~ 1, data = wind_RP$CP,
left = "LastPresent", right = "FirstAbsent", allCombos = TRUE)
class(mod2)
names(mod2)
class(mod2[[1]])
mod3 <- cpm(formula_l = l ~ Season, formula_s = s ~ 1, data = wind_RP$CP,
left = "LastPresent", right = "FirstAbsent",
allCombos = TRUE, sizeCol = "Size")
class(mod3)
names(mod3)
class(mod3[[1]])
class(mod3[[1]][[1]])
# }
Run the code above in your browser using DataCamp Workspace