saeczi

(Small Area Estimation for Continuous Zero Inflated data)

Overview

saeczi is an R package that implements a small area estimator that uses a two-stage modeling approach for zero-inflated response variables. In particular, we are working with variables that follow a semi-continuous distribution with a mixture of zeroes and positive continuously distributed values. An example can be seen below.

saeczi first fits a linear mixed model to the non-zero portion of the response and then a generalized linear mixed model with binomial response to classify the probability of zero for a given data point. In estimation these models are each applied to new data points and combined to compute a final prediction.

The package can also generate MSE estimates using a parametric bootstrap approach described in Chandra and Sud (2012) either in parallel or sequentially.

Installation

Install the latest CRAN release with:

install.packages("saeczi")

You can also install the developmental version of saeczi from GitHub with:

# install.packages("pak")
pak::pkg_install("harvard-ufds/saeczi")

Usage

We’ll use the internal package data to show an example of how to use saeczi. The two data sets contained within the package contain example forestry data collected by the Forestry Inventory and Analysis (FIA) research program.

• saeczi::samp: Example FIA plot-level sample data for each county in Oregon.
• saeczi::pop: Example FIA pixel level population auxiliary data for each county in Oregon.

The main response variable included in samp is above ground live biomass and our small areas in this case are the counties in Oregon. To keep things simple we will use tree canopy cover (tcc16) and elevation (elev) as our predictors in both of the models. We can use saeczi to get estimates for the mean biomass in each county as well as the corresponding bootstrapped (B = 500) MSE estimate as follows.

library(saeczi)
data(pop)
data(samp)

result <- saeczi(samp_dat = samp,
                 pop_dat = pop, 
                 lin_formula =  DRYBIO_AG_TPA_live_ADJ ~ tcc16 + elev,
                 log_formula = DRYBIO_AG_TPA_live_ADJ ~ tcc16,
                 domain_level = "COUNTYFIPS",
                 mse_est = TRUE,
                 B = 1000L)

Return

The function returns the following objects:

Name	Description
call	The original function call
res	A data.frame containing the estimates
lin_mod	The linear model object of class merMod used to compute the estimates
log_mod	The logistic model object of class merMod used to compute the estimates

As there are 36 total counties in Oregon, we will just look at the first few rows of the results:

result$res |> head()
#>   COUNTYFIPS        mse       est
#> 1      41001   38.30647  14.57288
#> 2      41003  122.90662 103.33016
#> 3      41005 1069.30963  86.08616
#> 4      41007 4691.01214  78.79615
#> 5      41009  356.53805  73.98920
#> 6      41011  273.34697  90.44174

Parallelization

saeczi supports parallelization through the future package to speed up the bootstrapping process, but requires a small amount of additional work on the part of the user. It is not enough just to specify parallel = TRUE in the function signature as a future::plan must also be specified.

Below is an example that uses multisession’ future resolution with 6 threads:

future::plan("multisession", workers = 6)
result_par <- saeczi(samp_dat = samp,
                     pop_dat = pop, 
                     lin_formula =  DRYBIO_AG_TPA_live_ADJ ~ tcc16 + elev,
                     log_formula = DRYBIO_AG_TPA_live_ADJ ~ tcc16,
                     domain_level = "COUNTYFIPS",
                     mse_est = TRUE,
                     parallel = TRUE,
                     B = 1000L)