Tools for the simulation of data in the context of small area estimation. Combine all steps of your simulation - from data generation over drawing samples to model fitting - in one object. This enables easy modification and combination of different scenarios. You can store your results in a folder or start the simulation in parallel.
Two external resources may be of interest in addition to this vignette:
An initial Example
Consider a linear mixed model. It contains two components. A fixed effects part, and an error component. The error component can be split into a random effects part and a model error.
library(saeSim)
setup <- sim_base() %>%
sim_gen_x() %>%
sim_gen_e() %>%
sim_gen_v() %>%
sim_resp_eq(y = 100 + 2 * x + v + e) %>%
sim_simName("Doku")
setup
## # Description: data.frame [10,000 × 6]
## idD idU x e v y
## * <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 -2.51 -3.22 0.235 92.0
## 2 1 2 0.735 -4.23 0.235 97.5
## 3 1 3 -3.34 -4.14 0.235 89.4
## 4 1 4 6.38 -4.74 0.235 108.
## 5 1 5 1.32 -2.00 0.235 101.
## 6 1 6 -3.28 -2.10 0.235 91.6
## # … with 9,994 more rows
sim_base() is responsible to supply a data.frame to which variables can be
added. The default is to create a data.frame with indicator variables idD
and idU (2-level-model), which uniquely identify observations. ‘D’ stands for
the domain, i.e. the grouping variable. ‘U’ stands for unit and is the
identifier of single observations within domains. sim_resp will add a variable
y as response.
The setup itself does not contain the simulated data but the functions to
process the data. To start a simulation use the function sim. It will return a
list containing data.frames as elements:
dataList <- sim(setup, R = 10)
You can coerce a simulation setup to a data.frame with as.data.frame.
simData <- sim_base() %>%
sim_gen_x() %>%
sim_gen_e() %>%
as.data.frame
simData
Naming and structure
Components in a simulation setup should be added using the pipe operator %>%
from magrittr. A component defines ‘when’ a specific function will be applied in
a chain of functions. To add a component you can use one of: sim_gen,
sim_resp, sim_comp_pop, sim_sample, sim_comp_sample, sim_agg and
sim_comp_agg. They all expect a simulation setup as first argument and a
function as second and will take care of the order in which the functions are
called. The reason for this is the following:
setup <- sim_base() %>%
sim_gen_x() %>%
sim_gen_e() %>%
sim_resp_eq(y = 100 + 2 * x + e)
setup1 <- setup %>% sim_sample(sample_fraction(0.05))
setup2 <- setup %>% sim_sample(sample_number(5))
You can define a rudimentary scenario and only have to explain how scenarios
differ. You do not have to redefine them. setup1 and setup2 only differ in
the way samples are drawn. sim_sample will take care, that the sampling will
take place at the appropriate place in the chain of functions no matter how
setup was composed.
If you can’t remember all function names, use auto-complete. All functions to
add components start with sim_. And all functions meant to be used in a given
phase will start with the corresponding prefix, i.e. if you set the sampling
scheme you use sim_sample – all functions to control sampling have the prefix
sample.
Exploring the setup
You will want to check your results regularly when working with sim_setup
objects. Some methods are supplied to do that:
show- this is theprintmethod for S4-Classes. You don’t have to callshowexplicitly. You may have noticed that only a few lines of data are printed to the console if you evaluate a simulation setup.showwill print theheadof the resulting data of one simulation run.plot- for visualizing the dataautoplot- Will imitatesmoothScatterwith ggplot2
setup <- sim_base_lmm()
plot(setup)
autoplot(setup)
autoplot(setup, "e")
autoplot(setup %>% sim_gen_vc())
sim_gen
Semi-custom data
saeSim has an interface to standard random number generators in R. If things get more complex you can always define new generator functions.
base_id(2, 3) %>%
sim_gen(gen_generic(rnorm, mean = 5, sd = 10, name = "x", groupVars = "idD"))
## # Description: data.frame [6 × 3]
## idD idU x
## <int> <int> <dbl>
## 1 1 1 -3.48
## 2 1 2 -3.48
## 3 1 3 -3.48
## 4 2 1 13.2
## 5 2 2 13.2
## 6 2 3 13.2
You can supply any random number generator to gen_generic and since we are in
small area estimation you have an optional group variable to generate
‘area-level’ variables. Some short cuts for data generation are sim_gen_x,
sim_gen_v and sim_gen_e which add normally distributed variables named ‘x’,
‘e’ and ‘v’ respectively. Also there are some function with the prefix ‘gen’
which will be extended in the future.
library(saeSim)
setup <- sim_base() %>%
sim_gen_x() %>% # Variable 'x'
sim_gen_e() %>% # Variable 'e'
sim_gen_v() %>% # Variable 'v' as a random-effect
sim_gen(gen_v_sar(name = "vSp")) %>% # random-effect following a SAR(1)
sim_resp_eq(y = 100 + x + v + vSp + e) # Computing 'y'
setup
## # Description: data.frame [10,000 × 7]
## idD idU x e v vSp y
## * <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 -3.26 -5.80 -1.29 0.00300 89.7
## 2 1 2 4.26 4.77 -1.29 0.00300 108.
## 3 1 3 -3.07 1.02 -1.29 0.00300 96.7
## 4 1 4 5.21 2.32 -1.29 0.00300 106.
## 5 1 5 1.91 8.53 -1.29 0.00300 109.
## 6 1 6 -2.66 3.76 -1.29 0.00300 99.8
## # … with 9,994 more rows
Contaminated data
For contaminated data you can use the same generator functions, however, instead
of using sim_gen you use sim_gen_cont which will have some extra arguments
to control the contamination. To extend the above setup with a contaminated
spatially correlated error component you can add the following:
contSetup <- setup %>%
sim_gen_cont(
gen_v_sar(sd = 40, name = "vSp"), # defining the model
nCont = 0.05, # 5 per cent outliers
type = "area", # whole areas are outliers, i.e. all obs within
areaVar = "idD", # var name to identify domain
fixed = TRUE # if in each iteration the same area is an outlier
)
Note that the generator is the same but with a higher standard deviation. The
argument nCont controls how much observations are contaminated. Values < 1 are
interpreted as probability. A single number as the number of contaminated units
(can be areas or observations in each area or observations). When given with
length(nCont) > 1 it will be interpreted as number of contaminated
observations in each area. Use the following example to see how these things
play together:
base_id(3, 4) %>%
sim_gen_x() %>%
sim_gen_e() %>%
sim_gen_ec(mean = 0, sd = 150, name = "eCont", nCont = c(1, 2, 3)) %>%
as.data.frame
## idD idU x e eCont idC
## 1 1 1 2.1238928 2.85552209 0.00000 FALSE
## 2 1 2 1.8224797 -3.70320125 0.00000 FALSE
## 3 1 3 -0.7466757 -4.63509843 0.00000 FALSE
## 4 1 4 0.2864107 -0.51238608 174.16195 TRUE
## 5 2 1 -4.1711873 -1.64389880 0.00000 FALSE
## 6 2 2 -0.9948926 2.68706944 0.00000 FALSE
## 7 2 3 -4.4030395 0.08884468 131.30190 TRUE
## 8 2 4 1.4103819 0.77040266 -111.81580 TRUE
## 9 3 1 -0.3921937 0.88877112 0.00000 FALSE
## 10 3 2 -5.7884702 -1.54674283 47.70671 TRUE
## 11 3 3 -4.8635870 1.35621664 -306.40766 TRUE
## 12 3 4 -5.7893455 4.26584633 305.57991 TRUE
sim_comp
Here follow some examples how to add components for computation to a
sim_setup. Three points can be accessed with
sim_comp_pop- add a computation before samplingsim_comp_sample- add a computation after samplingsim_comp_agg- add a computation after aggregation
base_id(2, 3) %>%
sim_gen_x() %>%
sim_gen_e() %>%
sim_gen_ec() %>%
sim_resp_eq(y = 100 + x + e) %>%
# the mean in each domain:
sim_comp_pop(comp_var(popMean = mean(y)), by = "idD")
## # Description: data.frame [6 × 7]
## idD idU x e idC y popMean
## * <int> <int> <dbl> <dbl> <lgl> <dbl> <dbl>
## 1 1 1 0.575 6.62 FALSE 107. 108.
## 2 1 2 3.77 0.226 FALSE 104. 108.
## 3 1 3 12.6 1.07 FALSE 114. 108.
## 4 2 1 6.64 5.01 FALSE 112. 106.
## 5 2 2 -0.842 3.41 FALSE 103. 106.
## 6 2 3 4.50 0.359 FALSE 105. 106.
The function comp_var is a wrapper around dplyr::mutate so you can add
simple data manipulations. The argument by is a little extension and lets you
define operations in the scope of groups identified by a variable in the data.
In this case the mean of the variable ‘y’ is computed for every group identified
with the variable ‘idD’. This is done before sampling, hence the prefix ‘pop’
for population.
Add custom computation functions
By adding computation functions you can extend the functionality to wrap your whole simulation. This will separate the utility of this package from only generating data.
comp_linearPredictor <- function(dat) {
dat$linearPredictor <- lm(y ~ x, dat) %>% predict
dat
}
sim_base_lm() %>%
sim_comp_pop(comp_linearPredictor)
## # Description: data.frame [10,000 × 6]
## idD idU x e y linearPredictor
## <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 -8.50 -0.637 90.9 91.6
## 2 1 2 -0.732 3.09 102. 99.3
## 3 1 3 1.11 6.99 108. 101.
## 4 1 4 3.82 4.38 108. 104.
## 5 1 5 0.615 -0.191 100. 101.
## 6 1 6 0.382 -3.60 96.8 100.
## # … with 9,994 more rows
Or, should this be desirable, directly produce a list of lm objects or add
them as attribute to the data. The intended way of writing functions is that
they will return the modified data of class ‘data.frame’.
sim_base_lm() %>%
sim_comp_pop(function(dat) lm(y ~ x, dat)) %>%
sim(R = 1)
## [[1]]
##
## Call:
## lm(formula = y ~ x, data = dat)
##
## Coefficients:
## (Intercept) x
## 100.0421 0.9872
comp_linearModelAsAttr <- function(dat) {
attr(dat, "linearModel") <- lm(y ~ x, dat)
dat
}
dat <- sim_base_lm() %>%
sim_comp_pop(comp_linearModelAsAttr) %>%
as.data.frame
attr(dat, "linearModel")
##
## Call:
## lm(formula = y ~ x, data = dat)
##
## Coefficients:
## (Intercept) x
## 100.017 1.032
If you use any kind of sampling, the ‘linearPredictor’ can be added after sampling. This is where small area models are supposed to be applied.
sim_base_lm() %>%
sim_sample() %>%
sim_comp_sample(comp_linearPredictor)
## # Description: data.frame [500 × 6]
## idD idU x e y linearPredictor
## * <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 98 5.47 -1.31 104. 106.
## 2 1 27 -0.462 8.40 108. 99.7
## 3 1 47 0.358 -2.91 97.4 101.
## 4 1 5 -6.90 3.15 96.2 93.1
## 5 1 35 2.40 -4.40 98.0 103.
## 6 2 50 -1.19 2.28 101. 98.9
## # … with 494 more rows
Should you want to apply area level models, use sim_comp_agg instead.
sim_base_lm() %>%
sim_sample() %>%
sim_agg() %>%
sim_comp_agg(comp_linearPredictor)
## # Description: data.frame [100 × 5]
## idD x e y linearPredictor
## * <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.202 2.20 102. 100.
## 2 2 0.103 -2.58 97.5 100.
## 3 3 -2.03 2.49 100. 97.9
## 4 4 1.52 -1.41 100. 101.
## 5 5 -0.649 0.413 99.8 99.3
## 6 6 -1.14 1.45 100. 98.8
## # … with 94 more rows
sim_sample
After the data generation you may want to draw a sample from the population. Use
the function sim_sample() to add a sampling component to your sim_setup.
sample_number- wrapper arounddplyr::sample_nsample_fraction- wrapper arounddplyr::sample_frac
base_id(3, 4) %>%
sim_gen_x() %>%
sim_sample(sample_number(1L))
## # Description: data.frame [1 × 3]
## idD idU x
## <int> <int> <dbl>
## 1 1 1 -7.73
base_id(3, 4) %>%
sim_gen_x() %>%
sim_sample(sample_number(1L, groupVars = "idD"))
## # Description: data.frame [3 × 3]
## idD idU x
## * <int> <int> <dbl>
## 1 1 2 0.299
## 2 2 4 1.63
## 3 3 4 -1.87
# simple random sampling:
sim_base_lm() %>% sim_sample(sample_number(size = 10L))
## # Description: data.frame [10 × 5]
## idD idU x e y
## <int> <int> <dbl> <dbl> <dbl>
## 1 37 63 -0.976 -2.66 96.4
## 2 59 79 -1.14 4.38 103.
## 3 7 19 4.97 -2.24 103.
## 4 28 36 2.00 4.49 106.
## 5 94 47 5.84 -2.69 103.
## 6 46 59 6.11 -3.75 102.
## # … with 4 more rows
sim_base_lm() %>% sim_sample(sample_fraction(size = 0.05))
## # Description: data.frame [500 × 5]
## idD idU x e y
## <int> <int> <dbl> <dbl> <dbl>
## 1 65 24 -0.538 2.33 102.
## 2 21 10 2.87 -4.87 98.0
## 3 95 71 -1.01 1.80 101.
## 4 7 49 4.77 -0.567 104.
## 5 93 68 7.60 1.86 109.
## 6 94 56 7.05 2.70 110.
## # … with 494 more rows
# srs in each domain/cluster
sim_base_lm() %>% sim_sample(sample_number(size = 10L, groupVars = "idD"))
## # Description: data.frame [1,000 × 5]
## idD idU x e y
## * <int> <int> <dbl> <dbl> <dbl>
## 1 1 26 -1.90 -1.80 96.3
## 2 1 49 9.35 3.79 113.
## 3 1 95 -6.71 5.98 99.3
## 4 1 41 1.57 -5.40 96.2
## 5 1 42 -8.54 -1.21 90.2
## 6 1 3 1.49 1.48 103.
## # … with 994 more rows
sim_base_lm() %>% sim_sample(sample_fraction(size = 0.05, groupVars = "idD"))
## # Description: data.frame [500 × 5]
## idD idU x e y
## * <int> <int> <dbl> <dbl> <dbl>
## 1 1 49 5.45 2.94 108.
## 2 1 12 0.0983 -2.76 97.3
## 3 1 19 -0.247 1.67 101.
## 4 1 5 -5.93 1.10 95.2
## 5 1 45 4.52 -8.22 96.3
## 6 2 32 0.0987 6.23 106.
## # … with 494 more rows