compute.real: Compute estimates of real parameters

Description

Computes real estimates and var-cov from design matrix (design) and coefficients (beta) using specified link functions

Usage

compute.real(model, beta = NULL, design = NULL,
    data = NULL, se = TRUE, vcv = FALSE)

Arguments

model

MARK model object

beta

estimates of beta parameters for real parameter computation

design

design matrix for MARK model

data

dataframe with covariate values that are averaged for estimates

if TRUE returns std errors and confidence interval of real estimates

vcv

logical; if TRUE, sets se=TRUE and returns v-c matrix of real estimates

Value

A data frame (real) is returned if vcv=FALSE; otherwise, a list is returned also containing vcv.real:
realdata 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
vcv.realvariance-covariance matrix of real estimates

Details

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 confidence interval is computed for the link estimate (estimate +/- 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 real parameter. 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.

Examples

Run this code

# see examples in fill.covariates

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