`select_sample` Issues With `n` Variable: Expected Hits

by Alex Johnson 56 views

Introduction

This article delves into a peculiar issue encountered while using the select_sample function from the SampleSelectR package in R. Specifically, we'll explore how the presence of a variable named n within the data frame can lead to unexpected behavior and discrepancies in the calculated ExpectedHits. This issue was brought to light in the ExpectedHitsDiscussion category and warrants a closer examination to understand the underlying mechanisms and potential workarounds. We'll walk through a reproducible example, dissect the code, and provide insights into the methods that output selection probabilities and expected hits, along with the calculation of expected hits itself.

Reproducible Example

To illustrate the issue, let's start with a reproducible example using the dplyr and SampleSelectR packages. This code snippet sets up a scenario where the presence of an n variable in the data frame influences the outcome of select_sample. It's crucial to understand this example thoroughly, as it forms the basis for our discussion and analysis.

library(dplyr)
library(SampleSelectR)
set.seed(8675309)

county_2023_slim_n <- county_2023 |>
  select(GEOID, Region, Pop_Tot) |>
  mutate(
    n=50,
    ExpHits_man=10*Pop_Tot/sum(Pop_Tot),
    .by="Region"
  )

sampsizes <- county_2023_slim_n |>
  distinct(Region) |>
  mutate(sample_size=10)

samp1 <- county_2023_slim_n |>
  select_sample("sys_pps", n=sampsizes, strata="Region", mos="Pop_Tot", outall = TRUE)

samp2 <- county_2023_slim_n |>
  select(-n) |>
  select_sample("sys_pps", n=sampsizes, strata="Region", mos="Pop_Tot", outall = TRUE)

waldo::compare(
  samp1 |> select(-c(SelectionIndicator, SamplingWeight, NumberHits, n)),
  samp2 |> select(-c(SelectionIndicator, SamplingWeight, NumberHits))
)

Code Breakdown

  1. Loading Libraries: We begin by loading the necessary libraries: dplyr for data manipulation and SampleSelectR for the sampling functions.
  2. Setting Seed: set.seed(8675309) ensures reproducibility of the random sampling process. This is crucial for consistent results when running the code multiple times.
  3. Creating the Data Frame county_2023_slim_n: This is where the issue begins to materialize. We create a data frame named county_2023_slim_n by:
    • Selecting GEOID, Region, and Pop_Tot columns from the original county_2023 data frame.
    • Mutating the data frame to add a column named n with a constant value of 50 for each row. This is the problematic variable we'll be discussing.
    • Calculating ExpHits_man (manually calculated Expected Hits) based on population proportions within each region.
  4. Creating sampsizes: This data frame defines the sample sizes for each region. It extracts distinct regions and sets the sample_size to 10 for each.
  5. Sampling with select_sample (samp1): This is the first call to the select_sample function. Notice that we are passing n = sampsizes which is the correct way of specifying sample sizes by strata. The crucial point here is that the data frame county_2023_slim_n includes the variable n. This is where the interference occurs.
  6. Sampling with select_sample (samp2): In this second call, we explicitly remove the n variable from the data frame using select(-n) before calling select_sample. This is done to demonstrate the impact of the n variable's presence. Again, we are passing n = sampsizes which is the correct way of specifying sample sizes by strata.
  7. Comparing Results: The waldo::compare function is used to compare the results of the two sampling calls (samp1 and samp2), focusing on the ExpectedHits column. This comparison highlights the discrepancies caused by the presence of the n variable in the first sampling operation.

Observed Discrepancy

The output of waldo::compare clearly shows a significant difference in the ExpectedHits values between samp1 and samp2. The ExpectedHits in samp1 are consistently higher than those in samp2. This suggests that the presence of the n variable in the data frame interferes with the calculation of ExpectedHits within the select_sample function, leading to inflated values.

Understanding Expected Hits and Selection Probabilities

Before diving deeper into the cause of this issue, it's essential to understand how ExpectedHits and selection probabilities are calculated within the context of sampling. ExpectedHits, in the context of sampling, represents the anticipated number of times a unit (e.g., a county in our example) would be selected if the sampling process were repeated many times. Selection probability, on the other hand, is the probability that a particular unit will be included in a single sample.

Methods Outputting Selection Probability

The SampleSelectR package offers various sampling methods, and many of them implicitly or explicitly calculate selection probabilities. For instance, in Probability Proportional to Size (PPS) sampling methods like the systematic PPS (sys_pps) used in our example, the selection probability of a unit is proportional to its size (e.g., population). In simpler random sampling methods, the selection probability is often uniform across all units within a stratum.

Methods Outputting Expected Hits

ExpectedHits are often a byproduct of the sampling process, especially in PPS sampling. While not all methods directly output ExpectedHits, they can be derived from the selection probabilities. The select_sample function in SampleSelectR calculates and outputs ExpectedHits for several methods. The methods that explicitly calculate and output ExpectedHits typically involve PPS sampling or variations thereof.

Calculation of Expected Hits

The basic principle behind calculating ExpectedHits is:

ExpectedHits = n * Selection Probability

Where:

  • n is the sample size (or the number of draws in sampling with replacement).
  • Selection Probability is the probability that the unit will be selected in a single draw.

In PPS sampling, the selection probability for a unit i within a stratum is approximately:

Selection Probability_i ≈ (Size_i / TotalSize_stratum) * n_stratum

Where:

  • Size_i is the size of unit i (e.g., population of a county).
  • TotalSize_stratum is the total size of the stratum (e.g., total population of the region).
  • n_stratum is the sample size for the stratum.

Therefore, the ExpectedHits for unit i can be expressed as:

ExpectedHits_i ≈ n * (Size_i / TotalSize_stratum) * n_stratum

This formula highlights that ExpectedHits are directly proportional to the unit's size and the stratum sample size. However, it's also crucial to note that the n in this formula refers to the number of draws not a variable in the input frame.

Root Cause Analysis: The n Variable Conflict

The core issue lies in the ambiguity created by having a variable named n within the input data frame and using the n parameter in the select_sample function to specify sample sizes. The select_sample function likely encounters the n variable in the data frame and, under certain circumstances, might incorrectly use its values in the ExpectedHits calculation instead of the intended sample sizes passed through the n parameter. This is a classic example of a naming conflict leading to unexpected behavior.

In our reproducible example, the county_2023_slim_n data frame includes a column named n with a constant value of 50. When select_sample is called with this data frame, it appears that the function sometimes uses this constant value (50) in the ExpectedHits calculation, leading to inflated values. When the n variable is removed (in samp2), the function correctly uses the sample sizes specified in the sampsizes data frame, resulting in accurate ExpectedHits.

This highlights the importance of avoiding variable names that might conflict with function parameters or internal variables within a package. Clear and distinct naming conventions are crucial for writing robust and maintainable code.

Implications and Recommendations

The implications of this issue are significant, especially in survey sampling and statistical analysis where accurate ExpectedHits are critical for weighting and variance estimation. If ExpectedHits are miscalculated, it can lead to biased estimates and incorrect inferences.

To mitigate this issue, we strongly recommend the following:

  1. Avoid Naming Conflicts: Do not use variable names that coincide with function parameters or reserved names within the packages you are using. In this case, avoid using n as a variable name if you are using select_sample with the n parameter for sample sizes.
  2. Inspect Intermediate Results: When working with complex sampling procedures, it's always a good practice to inspect intermediate results, such as selection probabilities and ExpectedHits, to ensure they are within expected ranges. This can help identify issues early on.
  3. Consult Package Documentation: Carefully read the documentation for the SampleSelectR package (and any other statistical package) to understand the expected input formats and potential pitfalls. The documentation often provides valuable insights into function behavior and parameter usage.
  4. Report Issues: If you encounter unexpected behavior or potential bugs in a package, report the issue to the package maintainers. This helps improve the package and prevents others from encountering the same problems.

Methods that Output Selection Probability and Expected Hits

The SampleSelectR package includes a variety of methods for sample selection, each with its own approach to calculating selection probabilities and ExpectedHits. Let's discuss some of the key methods:

  1. Systematic PPS Sampling (sys_pps): This method, used in our example, selects units systematically with probabilities proportional to their size. It involves calculating a sampling interval based on the total size and sample size within each stratum. The selection probability for each unit is approximately proportional to its size, and ExpectedHits are derived from these probabilities. This is the method most affected by the n variable issue.
  2. Probability Proportional to Size with Replacement (pps_wr): In PPS sampling with replacement, units are selected with probabilities proportional to their size, but units can be selected multiple times. Selection probabilities are calculated based on the size measure, and ExpectedHits represent the expected number of times each unit will be selected.
  3. Stratified Random Sampling: This family of methods (including simple random sampling within strata) typically involves uniform selection probabilities within each stratum. ExpectedHits can be calculated based on the stratum sample sizes and the number of units in each stratum.
  4. Other Methods: SampleSelectR offers other methods like sequential PPS sampling and various non-PPS methods. Each method has its own formulas for calculating selection probabilities and, consequently, ExpectedHits.

It's crucial to consult the SampleSelectR documentation for the specific formulas and algorithms used in each method.

Conclusion

In conclusion, the interference of a variable named n with the select_sample function's calculation of ExpectedHits underscores the importance of careful variable naming and a thorough understanding of the tools we use. By avoiding naming conflicts, inspecting intermediate results, and consulting package documentation, we can prevent such issues and ensure the accuracy of our sampling procedures. This exploration not only sheds light on a specific bug but also reinforces best practices in statistical programming.

For further information on survey sampling methodologies and best practices, consider exploring resources from reputable organizations such as the American Statistical Association. They offer a wealth of information and guidance on statistical methods and their applications.