twophase: twophase
In forestinventory: Design-Based Global and Small-Area Estimations for Multiphase Forest Inventories
Description
Usage
Arguments
Details
Value
Note
References
Examples
Description
twophase is used to calculate estimations based on double sampling under the
model-assisted Monte Carlo approach. A first phase of auxiliary information
(e.g. taken from remote sensing data) is used to generate model predictions based on multiple linear
regression using the method of ordinary least squares. A subsample of the first phase comprises
the second phase which contains terrestrial observations (i.e. the local densities
of the ground truth) that is used to correct for bias in the design-based sense.
The estimation method is available for simple and cluster sampling and includes
the special case where the first phase is based on an exhaustive sample (i.e. a census).
Small-area applications are supported for synthetic estimation as well as two varieties
of bias-corrected estimators: the traditional small-area estimator and an asymptotically
equivalent version derived under Mandallaz' extended model approach.
Usage
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Arguments
formula
an object of class "formula" as would be used in the function lm
data
a data frame containing all variables contained in formula and a column indexing
phase membership. Additional columns designating small-area membership, cluster ID and
boundary weights should also be contained in the data frame if they are
requested in the function.
phase_id
an object of class "list" containing two elements:
-
phase.col: the column name in data that specifies the
phase membership of each observation
-
terrgrid.id: the indicator identifying the terrestrial
(a.k.a. "ground truth") phase for that column
(must be of type "numeric")
cluster
(Optional) Specifies the column name in data
containing the cluster ID. Only used in case of
cluster sampling.
small_area
(Optional) a list that if containing three elements:
-
sa.col: the column name in data containing
domain identification
-
areas: vector of desired small-area domain identifiers
-
unbiased: an object of type "logical"
that when FALSE designates that the estimator is allowed to be
biased (i.e. the synthetic estimator) and when TRUE forces
it to be design-unbiased. See 'Details'.
Note: If small_area is left unchanged then twophase defaults to global estimation.
boundary_weights
(Optional) Specifies the column name in data
containing the weights for boundary adjustment. See 'Details'
exhaustive
(Optional) For global estimation, a vector of true auxiliary means corresponding to
an exhaustive first phase.
The vector must be input in the same order that lm processes a formula object
and include the intercept term.
For small area estimation, exhaustive is a data.frame containing column names
(colnames) for every variable appearing in the parameter formula including
the variable "Intercept".Rownames (row.names) have to be used and must correspond
to the names of the small areas. See 'Details'.
progressbar
(Optional) an object a type "logical" that when TRUE prints
the progress of the calculation in the console (recommended for large amount of small areas). Defaults to FALSE.
psmall
(Optional) an object a type "logical" used for small area estimations
that only works when unbiased in the parameter small_area is set to TRUE. See 'Details'.
Details
If estimations for multiple small-area domains should be computed, the domains have to be
defined within a character vector using c(). Using small_area(..., unbiased=FALSE)
calculates design-based estimates with the synthetic estimator and may be design-biased if
the model is biased in that small area. The default, small_area(..., unbiased=TRUE), allows for a residual
correction by one of two asymptotically equivalent methods to create design-unbiased estimates:
Mandallaz' extended model approach calculates the residual correction by extending the
model formula with an indicator variable in the small area. It is the default method
psmall=FALSE.
the traditional small area estimator calculates the residual correction by taking the
synthetic estimator and adding the mean residual observed in the small area. It is activated
when psmall=TRUE.
Missing values (NA) in the auxiliary variables (i.e. at least one auxiliary variable cannot be observed at
an inventory location) are automatically removed from the dataset before the estimations are computed.
Note that missingness in the auxiliary variables is only allowed if we assume that they are missing at random,
since the unbiasedness of the estimates is based on the sampling design.
The boundary weight adjustment is pertinent for auxiliary information derived from remote sensing and
is equal to the percentage of forested area (e.g. as defined by a forest mask) in the interpretation area.
Exhaustive estimation refers to when the true means of certain auxiliary variables are known
and an exhaustive first phase (i.e. a census). For global estimation, the vector must be input
in the same order that lm processes a formula object including the intercept term whose
true mean will always be one. For small area estimation, exhaustive is a data.frame containing column names for every variable appearing in
the parameter formula including the variable "Intercept". The observations of the data.frame
must represent the true auxiliary means in the same order as was presented in areas from the
parameter small_area. See 'Examples'.
Value
twophase returns an object of class "twophase".
An object of class "twophase" returns a list of the following components:
input
a list containing the function's inputs
estimation
a data frame containing the following components:
-
area: the domain (only present if argument areas has been used)
-
estimate: the point estimate
-
ext_variance: the external variance of the point estimate that doesn't account for
fitting the model from the current inventory
-
g_variance: the internal (g-weight) variance that accounts for
fitting the model from the current inventory
-
n1 the first phase sample size of plots
-
n2 the second phase (i.e. terrestrial) sample size of plots
-
n1G the first phase sample size in the small area
-
n2G the second phase (i.e. terrestrial) sample size in the small area
-
r.squared the R squared of the linear model
samplesizes
a data.frame summarizing all samplesizes: in case of cluster sampling both,
the number of individual plots and the number of clusters is reported.
coefficients
the linear model coefficients
cov_coef
the design-based covariance matrix of the model coefficients
Z_bar_1G
the estimated auxiliary means of formula based on the first phase.
If the first phase is exhaustive, these are the true auxiliary means specified in the input-argument exhaustive.
cov_Z_bar_1G
the covariance matrix of Z_bar_1G
Rc_x_hat_G
the small-area residuals at either the plot level or cluster level depending on the call
Rc_x_hat
the residuals at either the plot level or cluster level depending on the call
Yx_s2G
the local densities in the small area
Mx_s2G
the cluster weights in the small area
mean_Rc_x_hat_G
the mean residual (weighted mean in the case of cluster sampling) in the small area
mean_Rc_x_hat
the mean residual (weighted mean in the case of cluster sampling)
warn.messages
logical indicating if warning messages were issued
Note
In the special case of cluster sampling, the reported sample sizes in estimation are the number of clusters.
The samplesize-object also provides the respective number of single plot units for cluster sampling.
The reported r.squared describe the model fit of the applied linear regression
model (i.e. on plot-level, not on cluster 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. (2007). Sampling techniques for forest inventories. Chapter 4. CRC Press.
Mandallaz, D. (2013). Design-based properties of some small-area estimators in forest inventory with two-phase sampling. Can. J. For. Res. 43: 441-449
Mandallaz, D. and Hill, A. and Massey, A. (2016). Design-based properties of some small-area estimators in forest inventory with two-phase sampling. ETH Zurich, Department of Environmental Systems Science,Tech. rep. Available from http://e-collection.library.ethz.ch.
Examples
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## load datasets:
data(grisons)
data(zberg)
# ------------------------------------------------#
# ----------- GLOBAL ESTIMATION ------------------#
#----
## 1) -- Design-based estimation with non-exhaustive auxiliary information
#----
# 1.1) non-cluster-sampling:
summary(twophase(formula = tvol ~mean + stddev + max + q75,
data = grisons,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2)))
# 1.2) cluster-sampling (see eqns. [57] and [58] in Mandallaz, Hill, Massey 2016):
summary(twophase(formula = basal ~ stade + couver + melange,
data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster"))
# 1.3) example for boundary weight adjustment (non-cluster example):
summary(twophase(formula=tvol ~ mean + stddev + max + q75,
data=grisons,
phase_id=list(phase.col = "phase_id_2p", terrgrid.id = 2),
boundary_weights = "boundary_weights"))
#----
## 2) -- Design-based estimation with exhaustive auxiliary information
#----
# establish order for vector of true auxiliary means:
colnames(lm(formula = tvol ~ mean + stddev + max + q75, data = grisons, x = TRUE)$x)
true.means <- c(1, 11.39, 8.84, 32.68, 18.03)
# 2.1) non-cluster-sampling:
summary(twophase(formula = tvol ~ mean + stddev + max + q75,
data = grisons,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
exhaustive = true.means))
# 2.2) cluster-sampling:
summary(twophase(formula = stem ~ stade + couver + melange,
data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
exhaustive = c(1, 0.10, 0.7, 0.10, 0.6, 0.8)))
# ----------------------------------------------------#
# ----------- SMALL AREA ESTIMATION ------------------#
#----
## 1) -- Design-based estimation with non-exhaustive auxiliary information
#----
# 1.1) Mandallaz's extended pseudo small area estimator (see eqns. [35] and [36] in Mandallaz 2013):
summary(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(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = TRUE)))
# 1.2) pseudo small area estimator (see eqns. [25] and [26] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
psmall = TRUE))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = TRUE),
psmall = TRUE))
# 1.3) pseudosynthetic small area estimator (see eqns. [35] and [36] in Mandallaz 2013):
summary(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("B", "A"),
unbiased = FALSE)))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = FALSE)))
#----
## 2) -- Design-based estimation with exhaustive auxiliary information
#----
# establish order for vector of true auxiliary means:
colnames(lm(formula = tvol ~ mean + stddev + max + q75, data = grisons, x = TRUE)$x)
colnames(lm(formula = basal ~ stade + couver + melange, data = zberg, x = TRUE)$x)
# true auxiliary means taken from Mandallaz et al. (2013):
truemeans.G <- data.frame(Intercept = rep(1, 4),
mean = c(12.85, 12.21, 9.33, 10.45),
stddev = c(9.31, 9.47, 7.90, 8.36),
max = c(34.92, 35.36, 28.81, 30.22),
q75 = c(19.77, 19.16, 15.40, 16.91))
rownames(truemeans.G) <- c("A", "B", "C", "D")
# true auxiliary means taken from Mandallaz (1991):
truemeans.G.clust <- data.frame(Intercept = 1,
stade400 = 0.175,
stade500 = 0.429,
stade600 = 0.321,
couver2 = 0.791,
melange2 = 0.809)
rownames(truemeans.G.clust) <- c("1")
# 2.1) Mandallaz's extended small area estimator (see eqns. [31] and [33] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
exhaustive = truemeans.G))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallold", areas = c("1"),
unbiased = TRUE),
exhaustive = truemeans.G.clust))
# 2.2) small area estimator (see eqns. [20] and [21] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
exhaustive = truemeans.G, psmall = TRUE))
summary(twophase(formula = basal ~ stade + couver + melange, data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col ="ismallold", areas = c("1"),
unbiased = TRUE),
psmall = TRUE,
exhaustive = truemeans.G.clust))
# 2.3) synthetic small area estimator (see eqns. [18] and [19] in Mandallaz 2013):
summary(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"),
unbiased = FALSE),
exhaustive = truemeans.G))
summary(twophase(formula = basal ~ stade + couver + melange, data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallold", areas = c("1"),
unbiased = FALSE),
exhaustive = truemeans.G.clust))
forestinventory documentation built on Jan. 13, 2021, 9:11 p.m.
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Description Usage Arguments Details Value Note References Examples
Description
twophase is used to calculate estimations based on double sampling under the
model-assisted Monte Carlo approach. A first phase of auxiliary information
(e.g. taken from remote sensing data) is used to generate model predictions based on multiple linear
regression using the method of ordinary least squares. A subsample of the first phase comprises
the second phase which contains terrestrial observations (i.e. the local densities
of the ground truth) that is used to correct for bias in the design-based sense.
The estimation method is available for simple and cluster sampling and includes
the special case where the first phase is based on an exhaustive sample (i.e. a census).
Small-area applications are supported for synthetic estimation as well as two varieties
of bias-corrected estimators: the traditional small-area estimator and an asymptotically
equivalent version derived under Mandallaz' extended model approach.
Usage
1 2 3 4 5 6 7 8 9 10 11 |
Arguments
formula |
an object of class " |
data |
a data frame containing all variables contained in |
phase_id |
an object of class "
|
cluster |
(Optional) Specifies the column name in |
small_area |
(Optional) a list that if containing three elements:
Note: If |
boundary_weights |
(Optional) Specifies the column name in |
exhaustive |
(Optional) For global estimation, a vector of true auxiliary means corresponding to
an exhaustive first phase.
The vector must be input in the same order that |
progressbar |
(Optional) an object a type " |
psmall |
(Optional) an object a type " |
Details
If estimations for multiple small-area domains should be computed, the domains have to be
defined within a character vector using c(). Using small_area(..., unbiased=FALSE)
calculates design-based estimates with the synthetic estimator and may be design-biased if
the model is biased in that small area. The default, small_area(..., unbiased=TRUE), allows for a residual
correction by one of two asymptotically equivalent methods to create design-unbiased estimates:
Mandallaz' extended model approach calculates the residual correction by extending the model formula with an indicator variable in the small area. It is the default method
psmall=FALSE.the traditional small area estimator calculates the residual correction by taking the synthetic estimator and adding the mean residual observed in the small area. It is activated when
psmall=TRUE.
Missing values (NA) in the auxiliary variables (i.e. at least one auxiliary variable cannot be observed at
an inventory location) are automatically removed from the dataset before the estimations are computed.
Note that missingness in the auxiliary variables is only allowed if we assume that they are missing at random,
since the unbiasedness of the estimates is based on the sampling design.
The boundary weight adjustment is pertinent for auxiliary information derived from remote sensing and is equal to the percentage of forested area (e.g. as defined by a forest mask) in the interpretation area.
Exhaustive estimation refers to when the true means of certain auxiliary variables are known
and an exhaustive first phase (i.e. a census). For global estimation, the vector must be input
in the same order that lm processes a formula object including the intercept term whose
true mean will always be one. For small area estimation, exhaustive is a data.frame containing column names for every variable appearing in
the parameter formula including the variable "Intercept". The observations of the data.frame
must represent the true auxiliary means in the same order as was presented in areas from the
parameter small_area. See 'Examples'.
Value
twophase returns an object of class "twophase".
An object of class "twophase" returns a list of the following components:
input |
a |
estimation |
a data frame containing the following components:
|
samplesizes |
a |
coefficients |
the linear model coefficients |
cov_coef |
the design-based covariance matrix of the model coefficients |
Z_bar_1G |
the estimated auxiliary means of |
cov_Z_bar_1G |
the covariance matrix of |
Rc_x_hat_G |
the small-area residuals at either the plot level or cluster level depending on the call |
Rc_x_hat |
the residuals at either the plot level or cluster level depending on the call |
Yx_s2G |
the local densities in the small area |
Mx_s2G |
the cluster weights in the small area |
mean_Rc_x_hat_G |
the mean residual (weighted mean in the case of cluster sampling) in the small area |
mean_Rc_x_hat |
the mean residual (weighted mean in the case of cluster sampling) |
warn.messages |
logical indicating if warning messages were issued |
Note
In the special case of cluster sampling, the reported sample sizes in estimation are the number of clusters.
The samplesize-object also provides the respective number of single plot units for cluster sampling.
The reported r.squared describe the model fit of the applied linear regression
model (i.e. on plot-level, not on cluster 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. (2007). Sampling techniques for forest inventories. Chapter 4. CRC Press.
Mandallaz, D. (2013). Design-based properties of some small-area estimators in forest inventory with two-phase sampling. Can. J. For. Res. 43: 441-449
Mandallaz, D. and Hill, A. and Massey, A. (2016). Design-based properties of some small-area estimators in forest inventory with two-phase sampling. ETH Zurich, Department of Environmental Systems Science,Tech. rep. Available from http://e-collection.library.ethz.ch.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 | ## load datasets:
data(grisons)
data(zberg)
# ------------------------------------------------#
# ----------- GLOBAL ESTIMATION ------------------#
#----
## 1) -- Design-based estimation with non-exhaustive auxiliary information
#----
# 1.1) non-cluster-sampling:
summary(twophase(formula = tvol ~mean + stddev + max + q75,
data = grisons,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2)))
# 1.2) cluster-sampling (see eqns. [57] and [58] in Mandallaz, Hill, Massey 2016):
summary(twophase(formula = basal ~ stade + couver + melange,
data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster"))
# 1.3) example for boundary weight adjustment (non-cluster example):
summary(twophase(formula=tvol ~ mean + stddev + max + q75,
data=grisons,
phase_id=list(phase.col = "phase_id_2p", terrgrid.id = 2),
boundary_weights = "boundary_weights"))
#----
## 2) -- Design-based estimation with exhaustive auxiliary information
#----
# establish order for vector of true auxiliary means:
colnames(lm(formula = tvol ~ mean + stddev + max + q75, data = grisons, x = TRUE)$x)
true.means <- c(1, 11.39, 8.84, 32.68, 18.03)
# 2.1) non-cluster-sampling:
summary(twophase(formula = tvol ~ mean + stddev + max + q75,
data = grisons,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
exhaustive = true.means))
# 2.2) cluster-sampling:
summary(twophase(formula = stem ~ stade + couver + melange,
data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
exhaustive = c(1, 0.10, 0.7, 0.10, 0.6, 0.8)))
# ----------------------------------------------------#
# ----------- SMALL AREA ESTIMATION ------------------#
#----
## 1) -- Design-based estimation with non-exhaustive auxiliary information
#----
# 1.1) Mandallaz's extended pseudo small area estimator (see eqns. [35] and [36] in Mandallaz 2013):
summary(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(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = TRUE)))
# 1.2) pseudo small area estimator (see eqns. [25] and [26] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
psmall = TRUE))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = TRUE),
psmall = TRUE))
# 1.3) pseudosynthetic small area estimator (see eqns. [35] and [36] in Mandallaz 2013):
summary(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("B", "A"),
unbiased = FALSE)))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallg23", areas = c("2", "3"),
unbiased = FALSE)))
#----
## 2) -- Design-based estimation with exhaustive auxiliary information
#----
# establish order for vector of true auxiliary means:
colnames(lm(formula = tvol ~ mean + stddev + max + q75, data = grisons, x = TRUE)$x)
colnames(lm(formula = basal ~ stade + couver + melange, data = zberg, x = TRUE)$x)
# true auxiliary means taken from Mandallaz et al. (2013):
truemeans.G <- data.frame(Intercept = rep(1, 4),
mean = c(12.85, 12.21, 9.33, 10.45),
stddev = c(9.31, 9.47, 7.90, 8.36),
max = c(34.92, 35.36, 28.81, 30.22),
q75 = c(19.77, 19.16, 15.40, 16.91))
rownames(truemeans.G) <- c("A", "B", "C", "D")
# true auxiliary means taken from Mandallaz (1991):
truemeans.G.clust <- data.frame(Intercept = 1,
stade400 = 0.175,
stade500 = 0.429,
stade600 = 0.321,
couver2 = 0.791,
melange2 = 0.809)
rownames(truemeans.G.clust) <- c("1")
# 2.1) Mandallaz's extended small area estimator (see eqns. [31] and [33] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
exhaustive = truemeans.G))
summary(twophase(formula = basal ~ stade + couver + melange, data=zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallold", areas = c("1"),
unbiased = TRUE),
exhaustive = truemeans.G.clust))
# 2.2) small area estimator (see eqns. [20] and [21] in Mandallaz 2013):
summary(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"),
unbiased = TRUE),
exhaustive = truemeans.G, psmall = TRUE))
summary(twophase(formula = basal ~ stade + couver + melange, data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col ="ismallold", areas = c("1"),
unbiased = TRUE),
psmall = TRUE,
exhaustive = truemeans.G.clust))
# 2.3) synthetic small area estimator (see eqns. [18] and [19] in Mandallaz 2013):
summary(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"),
unbiased = FALSE),
exhaustive = truemeans.G))
summary(twophase(formula = basal ~ stade + couver + melange, data = zberg,
phase_id = list(phase.col = "phase_id_2p", terrgrid.id = 2),
cluster = "cluster",
small_area = list(sa.col = "ismallold", areas = c("1"),
unbiased = FALSE),
exhaustive = truemeans.G.clust))
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