Survey Package in R

The “survey” package in R is a powerful tool for analyzing complex survey data. It provides functions and methods for handling survey design features, such as stratification, clustering, and weighting. This package is particularly useful when working with data collected from complex survey designs, like those from large-scale social surveys or health studies. Below, I’ll provide a brief explanation of survey analysis theory and examples using the “survey” package.

Survey Analysis Theory

In R Programming Language the survey package has some features that are discussed below.

• Survey Sampling: Survey data is often collected by sampling from a population. Survey sampling can involve various methods, including simple random sampling, stratified sampling, and cluster sampling. The “survey” package allows you to account for these sampling methods.
• Stratification: Stratification is the process of dividing the population into subgroups or strata based on certain characteristics. Stratum-specific estimates are often computed to improve precision.
• Clustering: In cluster sampling, the population is divided into clusters, and a sample of clusters is selected. Within each selected cluster, all individuals are often included in the sample.
• Weighting: Survey weights are applied to correct for unequal probabilities of selection and nonresponse. Weighting ensures that the sample is representative of the population.
• Survey Design Object (svydesign): The survey design object is the core of the “survey” package. It represents the survey’s sampling design, including stratification, clustering, sampling weights, and other relevant information. You create it using the svydesign function, specifying the survey’s strata, clusters, sampling weights, and nesting if applicable.
• Descriptive Statistics: The “survey” package provides functions to calculate weighted descriptive statistics. Weighted estimates account for the complex survey design and nonresponse. Functions like svytotal, svymean, svyvar, and svyquantile can be used to calculate sums, means, variances, and quantiles, respectively.
• Survey Tables: The svytable function creates contingency tables for categorical variables. It allows you to analyze the distribution of categories within different strata and clusters, taking into account survey weights.
• Regression Analysis: The package supports complex survey regression models. The svyglm function is used for generalized linear models (e.g., linear, logistic, and Poisson regression), and the svycoxph function for survival analysis. These functions account for survey design features.
• Complex Survey Analysis:The svycontrast function is used to compare survey-weighted means or proportions between different subgroups while adjusting for survey design features.

Applications of survey package

The package “survey” in R is widely used because it helps to analyze complex data collected from surveys. When it comes to handling all the complicated parts of surveys like stratification, clustering, and unequal probabilities of selection, “survey” does it all. However, there are some things you should know about it.

• Learning Curve: People who aren’t familiar with survey sampling concepts will find using the “survey” package difficult. One has to have a good understanding of survey design and analysis techniques, which might be a lot for beginners.
• Large Data Sets: For very large survey datasets, the “survey” package may not be efficient in terms of memory and computation time. Many computational resources might be needed when processing large datasets.
• Limited Machine Learning Integration: Since the main focus of this package is on traditional methods for analyzing surveys. If you want to integrate machine learning techniques with complex survey data, you may need to custom code the necessary features that’ll allow seamless integration.
• Limited Graphics Support: While you can make basic survey-weighted graphs and plots with the “survey” package, other specialized data visualization packages like ggplot2 give more freedom when making visualizations.

Example 1: Loading and Handling Survey Data

R

# Load the "survey" package
library(survey)

# Load a sample survey dataset included with the package
data(api)

# Create a survey design object
api_design <- svydesign(id = ~1, strata = ~stype, weights = ~pw, data = apistrat,
                        fpc = ~fpc)

# Calculate weighted descriptive statistics
# Calculate the weighted mean of enrollment
svymean(~enroll, design = api_design)

Output:

         mean     SE
enroll 595.28 18.509

library(survey): This line loads the “survey” package, which is essential for handling complex survey data and conducting survey analysis.

• data(api): This line loads a sample survey dataset called “api” included with the package. This dataset contains information about California school districts and is used for demonstration purposes.
• api_design <- svydesign(…): Here, we create a survey design object called .
• svymean(…): This function calculates the weighted mean. The argument ~enroll specifies the variable for which you want to calculate the mean, which is “enroll” in this case.

design = api_design: The design argument specifies the survey design object that we created earlier, api_design. This design object is used to apply the survey weights and account for the survey’s complex design features.

R

# Create a survey table
svytable(~stype + meals, design = api_design)

Output:

     meals
stype      0      1      2      3      4      5      6      7      8      9     10
    E   0.00  44.21   0.00   0.00  88.42   0.00  88.42 132.63   0.00  44.21  88.42
    H  15.10  45.30   0.00  15.10   0.00  30.20  15.10   0.00  30.20  30.20   0.00
    M   0.00   0.00  20.36   0.00  40.72   0.00  20.36   0.00   0.00   0.00   0.00
     meals
stype     11     12     13     14     15     17     18     19     20     21     23
    E  44.21   0.00  44.21 132.63  44.21   0.00  44.21   0.00  88.42   0.00   0.00
    H   0.00  15.10  15.10   0.00  15.10   0.00  15.10  30.20  45.30  30.20  60.40
    M   0.00   0.00  40.72   0.00   0.00  20.36  20.36  20.36   0.00  20.36   0.00
     meals
stype     24     25     26     28     29     31     32     33     34     35     36
    E  88.42 132.63  44.21  44.21   0.00  44.21   0.00  88.42  88.42  44.21  88.42
    H   0.00   0.00   0.00  15.10  15.10  30.20   0.00  15.10  15.10  15.10  30.20
    M  81.44   0.00   0.00   0.00  20.36  20.36  20.36  20.36   0.00   0.00  40.72
     meals
stype     37     38     39     40     41     42     43     44     45     46     47
    E   0.00 132.63  88.42  44.21  44.21  88.42  44.21   0.00 132.63  44.21  44.21
    H  15.10  15.10  15.10   0.00   0.00   0.00   0.00  15.10   0.00   0.00  15.10
    M   0.00  20.36   0.00   0.00   0.00   0.00   0.00  20.36  20.36  20.36  40.72
     meals
stype     48     49     50     51     52     54     56     57     58     59     60
    E  44.21  44.21   0.00  88.42   0.00  88.42  44.21   0.00  44.21   0.00   0.00
    H   0.00   0.00  15.10  15.10   0.00   0.00   0.00   0.00   0.00   0.00   0.00
    M   0.00   0.00   0.00  20.36  40.72  20.36  20.36  20.36   0.00  20.36  40.72
     meals
stype     61     63     64     66     67     69     71     72     73     74     75
    E  44.21   0.00  44.21   0.00  88.42 132.63  44.21  88.42   0.00 132.63 132.63
    H   0.00  15.10   0.00  15.10   0.00   0.00   0.00  15.10   0.00   0.00   0.00
    M   0.00   0.00  40.72  40.72  20.36  20.36   0.00  20.36  20.36   0.00  20.36
     meals
stype     76     77     78     79     80     82     83     85     86     88     89
    E  88.42  44.21  88.42   0.00  44.21  44.21 132.63   0.00   0.00  44.21   0.00
    H   0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00  15.10   0.00  15.10
    M   0.00  20.36  20.36  20.36   0.00   0.00   0.00  20.36   0.00   0.00   0.00
     meals
stype     91     92     93     95     96     97     98     99    100
    E   0.00  44.21  44.21  88.42  44.21  44.21 221.05  44.21 132.63
    H   0.00   0.00   0.00   0.00   0.00   0.00  15.10   0.00  15.10
    M  20.36   0.00   0.00   0.00   0.00   0.00   0.00  20.36   0.00

svytable(…): This function is used to create a survey table. It helps you understand the distribution and relationship between variables in your complex survey data.

~stype + meals: This specifies the variables you want to cross-tabulate in the survey table. In this example, you are creating a table to explore the relationship between the “stype” variable (school type) and the “meals” variable (percentage of students eligible for free meals).

R

# Fit a weighted linear regression model
model <- svyglm(api00 ~ meals + mobility, design = api_design)

# Summarize the regression results
summary(model)

Output:

Call:
svyglm(formula = api00 ~ meals + mobility, design = api_design)
Survey design:
svydesign(id = ~1, strata = ~stype, weights = ~pw, data = apistrat, 
    fpc = ~fpc)
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 821.2318     9.9265  82.731   <2e-16 ***
meals        -3.4068     0.1717 -19.847   <2e-16 ***
mobility      0.3105     0.3887   0.799    0.425    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for gaussian family taken to be 5217.241)
Number of Fisher Scoring iterations: 2

svyglm(…): This function fits a weighted linear regression model to your complex survey data. In this case, you are trying to predict the variable “api00” (academic performance) based on the predictors “meals” (percentage of students eligible for free meals) and “mobility” (percentage of students who changed schools).

• api00 ~ meals + mobility: Here, you specify the regression formula. You want to model “api00” as a linear function of “meals” and “mobility.”
• design = api_design: The design argument specifies the survey design object, api_design. This ensures that the model accounts for the survey weights and complex survey design features.
• summary(model): This line generates a summary of the regression model. It includes information such as coefficients, standard errors, p-values, and goodness-of-fit statistics.

The summary of the model provides insights into the relationships between the predictor variables (meals and mobility) and the response variable (api00) while considering the complex survey design and weights. It helps you interpret the results of the regression analysis and draw conclusions about the predictors’ impact on the academic performance variable.

Make Predictions

To make predictions using a fitted model, you can use the predict.survey.design function. Here’s an example of how to make predictions.

R

# Predict the outcome variable (api00) using the model
predictions <- predict(model, newdata = apistrat)

# Print the first few predictions
head(predictions)

# Create a data frame with the new input data
new_data <- data.frame(meals = 2.5, mobility = 0.8)
# Make predictions using the fitted model
predictions <- predict(model, newdata = new_data)

# Print the predictions
print("Predicted API00:")
print(predictions)

Output:

       1        2        3        4        5        6 
712.2228 495.4380 608.4748 542.5033 742.2811 801.1104 
    link    SE
1 812.96 9.504

In this code, we are using the predict function with our fitted model (model) and specifying the dataset (apistrat) for which we want to make predictions. we can use the head function to view the first few predicted values.

Create Visualizations

We can create various visualizations to understand the results of your survey analysis. Let’s create a scatterplot of the actual vs. predicted values.

R

# Load the "ggplot2" library for visualization
library(ggplot2)

# Combine the actual and predicted values into a data frame
prediction_data <- data.frame(Actual = apistrat$api00, Predicted = predictions)

# Create a scatterplot of actual vs. predicted values
ggplot(prediction_data, aes(x = Actual, y = Predicted.link)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "blue") +
  labs(x = "Actual API00", y = "Predicted API00", title = "Actual vs. Predicted Values")

Output:

survey package in R

First fits a weighted linear regression model to survey data, predicting “api00” based on “meals” and “mobility.” Predictions are made and compared to actual values. The scatterplot shows how closely predictions align with actual values, aiding in assessing the model’s performance. If data points closely follow the blue line, it suggests accurate predictions; scattered points indicate potential inaccuracies. This visual assessment helps evaluate the model’s effectiveness and areas needing improvement.