Computes real estimates and var-cov from design matrix (design) and coefficients (beta) using specified link functions
compute.real(
model,
beta = NULL,
design = NULL,
data = NULL,
se = TRUE,
vcv = FALSE
)A data frame (real) is returned if vcv=FALSE;
otherwise, a list is returned also containing vcv.real:
data frame containing estimates, and if se=TRUE or vcv=TRUE it also contains standard errors and confidence intervals and notation of whether parameters are fixed or at a boundary
variance-covariance matrix of real estimates
MARK model object
estimates of beta parameters for real parameter computation
design matrix for MARK model
dataframe with covariate values that are averaged for estimates
if TRUE returns std errors and confidence interval of real estimates
logical; if TRUE, sets se=TRUE and returns v-c matrix of real estimates
Jeff Laake
The estimated real parameters can be derived from the estimated beta
parameters, a completed design matrix, and the link function specifications.
MARK produces estimates of the real parameters, se and confidence intervals
but there are at least 2 situations in which it is useful to be able to
compute them after running the analysis in MARK: 1) adjusting confidence
intervals for estimated over-dispersion, and 2) making estimates for
specific values of covariates. The first case is done in
get.real with a call to this function. It is done by
adjusting the estimated standard error of the beta parameters by multiplying
it by the square root of chat to adjust for over-dispersion. A
normal 95
+/- 1.96*se) and this is then back-transformed to the real parameters using
inverse.link with the appropriate inverse link function for
the parameter to construct a 95
There is one exception. For parameters using the mlogit
transformation, a logit transformation of each individual real Psi
and its se are used to derive the confidence interval. The estimated
standard error for the real parameter is also scaled by the square root of
the over-dispersion constant chat stored in model$chat. But,
the code actually computes the variance-covariance matrix rather than
relying on the values from the MARK output because real estimates will
depend on any individual covariate values used in the model which is the
second reason for this function.
New values of the real parameter estimates can easily be computed by simply
changing the values of the covariate values in the design matrix and
computing the inverse-link function using the beta parameter estimates. The
covariate values to be used can be specified in one of 2 ways. 1) Prior to
making a call to this function, use the functions
find.covariates to extract the rows of the design matrix with
covariate values and either fill in those values aautomatically with the
options provided by find.covariates or edit those values to be
the ones you want and then use fill.covariates to replace the
values into the design matrix and use it as the value for the argument
design, or 2) automate this step by specifying a value for the
argument data which is used to take averages of the covariate values
to fill in the covariate entries of the design matrix. In computing real
parameter estimates from individual covariate values it is important to
consider the scale of the individual covariates. By default, an analysis
with MARK will standardize covariates by subtracting the mean and dividing
by the standard deviation of the covariate value. However, in the
RMark library all calls to MARK.EXE do not standardize the covariates
and request real parameter estimates based on the mean covariate values.
This was done because there are many instances in which it is not wise to
use the standardization implemented in MARK and it is easy to perform any
standardization of the covariates with R commands prior to fitting the
models. Also, with pre-standardized covariates there is no confusion in
specifying covariate values for computation of real estimates. If the model
contains covariates and the argument design is not specified, the
design matrix is extracted from model and all individual covariate
values are assigned their mean value to be consistent with the default in
the MARK analysis.
If a value for beta is given, those values are used in place of the
estimates model$results$beta$estimate.
get.real,fill.covariates,find.covariates,inverse.link,deriv_inverse.link
# see examples in fill.covariates
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