The R-package `forestinventory`

adresses the current interest of combining existing forest inventory data, which are derived by field surveys, with additional information sources such as remote sensing data. The major benefit of these so-called *multisource inventory methods* is the potential increase of estimation precision without an increase in the number of expensive field surveys. Additionally, it also allows for deriving estimates of sufficient accuracy for spatial units where terrestrial information is scarcely available if not absent.

The aim of `forestinventory`

is to facilitate the application of multiphase forest inventories by providing an extensive set of functions for global and small-area estimation procedures. The implementation includes all estimators for simple and cluster sampling published by Daniel Mandallaz between 2007 and 2014, providing point estimates, their external- and design-based variances as well as confidence intervals. The procedures have also been optimized for the use of remote sensing data as auxiliary information.

We look at the example dataset `grisons`

which comes with our package:

```
library(forestinventory)
?grisons
```

As the help tells us, `grisons`

contains the data of a twophase inventory: We are provided with LiDAR canopy height metrics at 306 inventory locations, and at 67 subsamples we have the terrestrially measured timber volume values. We now want to estimate the timber volume in m^{3}/ha within four subdomains A, B, C and D (*small areas*).

If we only use the terrestrial information within the small areas, we call the `onephase`

-function:

```
op <- onephase(formula = tvol~1,
data = grisons,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
area = list(sa.col = "smallarea", areas = c("A", "B", "C", "D")))
summary(op)
#>
#> One-phase estimation
#>
#> Call:
#> onephase(formula = tvol ~ 1, data = grisons, phase_id = list(phase.col = "phase_id_2p",
#> terrgrid.id = 2), area = list(sa.col = "smallarea", areas = c("A",
#> "B", "C", "D")))
#>
#> Method used:
#> One-phase estimator
#>
#> Estimation results:
#> area estimate variance n2
#> A 410.4047 1987.117 19
#> B 461.4429 3175.068 17
#> C 318.0091 1180.853 15
#> D 396.8496 2290.652 16
```

We now try to increase the precision of our estimates by applying a *twophase estimation method*, where we use the large sample of LiDAR-metrics and a linear regression model to specify the relationship between the remote sensing derived predictor variables and the terrestrial timber volume:

```
sae.2p.uv<- 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))
summary(sae.2p.uv)
#>
#> Two-phase small area estimation
#>
#> Call:
#> 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))
#>
#> Method used:
#> Extended pseudosynthetic small area estimator
#>
#> Regression Model:
#> tvol ~ mean + stddev + max + q75 + smallarea
#>
#> Estimation results:
#> area estimate ext_variance g_variance n1 n2 n1G n2G r.squared
#> A 391.1605 995.5602 1016.956 306 67 94 19 0.6526503
#> B 419.6746 1214.6053 1019.270 306 67 81 17 0.6428854
#> C 328.0117 916.2266 1035.091 306 67 66 15 0.6430018
#> D 371.0596 1272.7056 1112.735 306 67 65 16 0.6556178
```

We now want to compare the results and performances of the onephase and twophase method. For such issues, the package provides the `estTable()`

function that concatenates the results from the different methods in one `list`

:

```
sae.table<- estTable(est.list = list(op, sae.2p.uv), sae = TRUE)
data.frame(sae.table[c(1:6,9)])
#> area domain method estimator vartype estimate error
#> 1 A global onephase onephase variance 410.4047 10.86
#> 2 A smallarea twophase psynth extended ext_variance 391.1605 8.07
#> 3 A smallarea twophase psynth extended g_variance 391.1605 8.15
#> 4 B global onephase onephase variance 461.4429 12.21
#> 5 B smallarea twophase psynth extended ext_variance 419.6746 8.30
#> 6 B smallarea twophase psynth extended g_variance 419.6746 7.61
#> 7 C global onephase onephase variance 318.0091 10.81
#> 8 C smallarea twophase psynth extended ext_variance 328.0117 9.23
#> 9 C smallarea twophase psynth extended g_variance 328.0117 9.81
#> 10 D global onephase onephase variance 396.8496 12.06
#> 11 D smallarea twophase psynth extended ext_variance 371.0596 9.61
#> 12 D smallarea twophase psynth extended g_variance 371.0596 8.99
```

We can already see that the estimation errors of the twophase estimation are up to 5% smaller than the onephase errors.

The function `mphase.gain()`

can now be used to further compare the performance of the methods:

```
mphase.gain(sae.table)
#> area var_onephase var_multiphase method estimator gain rel.eff
#> 1 A 1987.117 1016.956 twophase psynth extended 48.8 1.953986
#> 2 B 3175.068 1019.270 twophase psynth extended 67.9 3.115041
#> 3 C 1180.853 1035.091 twophase psynth extended 12.3 1.140821
#> 4 D 2290.652 1112.735 twophase psynth extended 51.4 2.058579
```

The column `gain`

tells us that the twophase estimation procedure here leads to a 67.9 % reduction in variance compared to the one- phase procedure“. The column `rel.eff`

speciﬁes the relative efﬁciency that can be interpreted as the relative sample size of the one-phase estimator needed to achieve the variance of the multi-phase (here twophase) estimator. For small area”B" we can thus see that we would have to increase the terrestrial sample size by factor 3 in the one-phase approach in order to get the same estimation precision as the twophase extended psynth estimator.

So in our short example, we were able to considerably improve the estimation precision when combining the terrestrial data with the remote sensing data. The package `forestinventory`

offers further estimators that can be applied to a wide range of multiphase inventory scenarios.

The package can be installed from CRAN:

`install.packages("forestinventory")`