confint {forestinventory}

Calculates Confidence Intervals for Global and Small-Area Estimations

Description

Calculates Confidence Intervals for Global and Small-Area Estimations

Usage

## S3 method for class 'onephase'
confint(object, parm, level = 0.95, adjust.method = "none", ...)

## S3 method for class 'twophase'
confint(object, parm, level = 0.95, adjust.method = "none", ...)

## S3 method for class 'threephase'
confint(object, parm, level = 0.95, adjust.method = "none", ...)

Arguments

object

object of class onephase, twophase or threephase, containing estimation results of the respective estimation method.

parm

ignored.

level

the confidence level required.

adjust.method

correction method to obtain simultaneous confidence intervals for a set of estimates (thus restricted to objects of class "onephase", c("smallarea", "twophase") and c("smallarea", "threephase")). Available correction methods are c("none","bonferroni"). Defaults to "none".

...

additional arguments, so far ignored.

Details

Depending on the estimation method specified, confint() computes confidence intervals as follows:

onephase:

Two-sided confidence intervals are computed based on the t-distribution with n2 - 1 degrees of freedom, where n2 is the number of terrestrial data in the respective inventory domain.

twophase:

The calculation of the two-sided confidence intervals for global twophase estimates (objects of class global) are calculated based on the quantiles of the t-distribution with n2 - p degrees of freedom, where p is the number of parameters used in the regression model, and n2 is the number of terrestrial observations (i.e. local densities) in the inventory domain.

The calculation of the two-sided confidence intervals for smallarea twophase estimates (objects of class smallarea) are calculated based on the quantiles of the t-distribution with n2G - 1 degrees of freedom, where n2G is the number of terrestrial observations (i.e. local densities) in the smallarea.

threephase:

The calculation of the two-sided confidence intervals for global threephase estimates (objects of class global) are calculated based on the quantiles of the t-distribution with n2 - p degrees of freedom, where p is the number of parameters used in the full regression model, and n2 is the number of terrestrial observations (i.e. local densities) in the inventory domain (note: in notation used here n0, n1 and n2 correspond to the zero, first and second phase sample sizes respectively).

The calculation of the two-sided confidence intervals for smallarea theephase estimates (objects of class smallarea) are calculated based on the quantiles of the t-distribution with n2G - 1 degrees of freedom, where n2G is the number of terrestrial observations (i.e. local densities) in the smallarea.

Value

confint returns a list of the following 3 components:

ci

a data.frame containing the columns:

• area the domain, i.e. small area

• ci_lower_ext the lower confidence limit based on the external variance

• ci_upper_ext the upper confidence limit based on the external variance

• ci_lower_g the lower confidence limit based on the g-weight variance

• ci_upper_g the upper confidence limit based on the g-weight variance

level

the applied confidence level

adjust.method

the adjustment method applied to retrieve simultaneous confidence intervals

Note

In the special case of synthetic smallarea estimations, the two-sided confidence intervals are calculated based on the quantiles of the t-distribution with n2 - p degrees of freedom, i.e. based on the global sample size.

The confidence intervals for synthetic smallarea estimations do not account for the potential bias of a linear model that was fit in a large forest area and applied to a small area. Thus, the coverage rates for confidence intervals produced by synthetic estimators may be less than the nominal level of confidence.

In case of cluster-sampling, n2G is the number of terrestrial clusters (a cluster constitutes the sample unit). This is automatically considered by confint.

The adjustment methods passed to adjust.method are designed to achieve simultaneous confidence intervals by correcting the confidence level given by level. The use of this option is recommended if a set of estimates contained in a onephase- or smallarea-object should be compared by their confidence intervals. It ensures that the percentage of confidence intervals containing the true value will correspond to the nominal confidence level.

References

Hill, A., Massey, A. F. (2021). The R Package forestinventory: Design-Based Global and Small Area Estimations for Multiphase Forest Inventories. Journal of Statistical Software, 97(4), 1-40.

Mandallaz, D. (2013). Design-based properties of some small-area estimators in forest inventory with two-phase sampling. Canadian Journal of Forest Research, 43(5), 441-449.

Mandallaz, D., Breschan, J., & Hill, A. (2013). New regression estimators in forest inventories with two-phase sampling and partially exhaustive information: a design-based monte carlo approach with applications to small-area estimation. Canadian Journal of Forest Research, 43(11), 1023-1031.

Mandallaz, D. (2013). A three-phase sampling extension of the generalized regression estimator with partially exhaustive information. Canadian Journal of Forest Research, 44(4), 383-388.

Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B 57, 289-300.

Examples

## Calculate twophase estimations by extended pseudosynthetic estimator
#  for 4 small areas ("A", "B", "C", "D") using the grisons-dataset:
sae.est <- twophase(formula = tvol ~ mean + stddev + max + q75,
                    data = grisons,
                    phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
                    small_area = list(sa.col = "smallarea",
                                      areas = c("A", "B","C", "D"),
                                      unbiased = TRUE))

## calculate 95%-confidence intervals for each small area:
confint(sae.est)

## calculate simultaneous 95%-confidence intervals using 'bonferroni'-method:
confint(sae.est, adjust.method = "bonferroni")