Enhancing Data Integration with Predictive Mean Matching

Data integration is an important process that helps combine information from different sources to get better insights. This is especially useful when dealing with different types of samples, like probability samples and Non-probability Samples. Probability samples are chosen randomly, making them more reliable for drawing conclusions about a larger population. On the other hand, non-probability samples are not selected randomly and may lead to biased results.

In this article, we focus on a technique called Predictive Mean Matching (PMM), which helps in filling in missing data and making estimates based on observed values. This method can be particularly useful when integrating data from different types of surveys or datasets.

#Importance of Data Integration

With the rise of big data and various data collection methods, integrating datasets has become crucial. Organizations often have access to vast amounts of administrative data, online surveys, and social media information. However, combining these different sources can be challenging due to the varied nature of the data.

When we talk about non-probability samples, we refer to data that may come from volunteer responses or social media surveys. These samples do not have a clear mechanism for how the data was gathered, making it difficult to use them reliably for estimating population characteristics. By integrating these with more reliable probability samples, we can improve the overall quality of the data analysis.

#Types of Inference Techniques

Several approaches are used to make inferences from non-probability samples. These techniques generally fall into three categories:

1. Inverse Probability Weighting (IPW): This method adjusts the results based on the probability of selection, trying to correct for the bias introduced by non-random sampling.

2. Prediction Estimators (PE): These estimators use predictions from models to estimate missing values or characteristics.

3. Doubly Robust Estimators (DR): These estimators combine both IPW and PE to improve reliability, offering some level of protection against mis-specification.

In our analysis, we focus on mass imputation (MI) estimators. MI estimators impute or fill in missing values based on observed data from both probability and non-probability samples.

#Mass Imputation and Predictive Mean Matching

Mass imputation involves predicting values for missing data points in a dataset. In this case, we specifically examine the predictive mean matching technique. PMM works by finding individuals in a dataset that are similar to those in another dataset, based on certain characteristics. Then, it uses the observed values from these similar individuals to estimate the missing values.

PMM can be implemented in two ways:

1. Predicted to Observed: Here, we match the predicted values from a model to observed values in the non-probability sample.

2. Predicted to Predicted: In this method, we match predicted values from both the probability and non-probability samples.

Both approaches aim to improve the estimates and reduce bias. The method chosen may depend on the available data and what is being estimated.

#Properties of PMM Estimators

We assess the consistency and variance of PMM estimators used in mass imputation. Consistency means that as we gather more data, the estimates will become more reliable and close to the true value. For PMM to be consistent, certain conditions must hold.

The estimators need to work well under different models, whether parametric (which assume a specific form for the function) or non-parametric (which do not make strict assumptions about the form). In practice, this flexibility allows researchers to choose models based on the nature of their data.

In addition to proving consistency, we also derive variance estimators. Variance indicates how much the estimates can fluctuate due to sampling. Having a good understanding of variance is crucial for constructing confidence intervals and making informed decisions based on the estimates.

#Simulation Studies

To assess the performance of PMM estimators, we conduct simulation studies. These studies involve generating datasets under controlled conditions to see how the estimators perform. We look at several aspects:

1. Bias: This is the difference between the expected estimate and the true value. We want our estimators to be as close to the true value as possible.

2. Standard Error (SE): This measures how much the estimates vary across different samples.

3. Relative Mean Square Error (RMSE): This combines bias and variance into a single measure, giving us an overall picture of estimator performance.

4. Coverage Rate (CR): This indicates how often the confidence intervals generated by the estimators contain the true value.

The results from our simulations show that the PMM estimators can handle various scenarios, including situations where the model specifications are not perfect. They often outperform other existing methods, particularly when dealing with non-linear data or complex relationships.

#Empirical Study: Job Vacancies in Poland

To illustrate the practical application of PMM estimators, we conduct an empirical study using data on job vacancies in Poland. We aim to estimate the proportion of job vacancies aimed at Ukrainian workers at a specific time.

We use two main data sources:

1. Job Vacancy Survey (JVS): This survey collects information from a range of companies, with a response rate of around 60%. The JVS captures details about companies, including their job openings.

2. Central Job Offers Database (CBOP): This is an administrative dataset that includes information on all vacancies submitted to public employment offices. It allows us to link data points and acquire auxiliary variables.

In our analysis, we utilize several estimators, including:

• Mass imputation estimators like MI-GLM, PMM A, and PMM B.
• Inverse probability weighting (IPW) estimators.
• Doubly robust (DR) estimators combining the above methods.

The results consistently show that mass imputation estimators yield similar point estimates for the proportion of job vacancies aimed at Ukrainians. However, they also indicate that the naive estimator produces lower estimates compared to the more robust methods.

#Conclusion

In summary, the integration of data from probability and non-probability samples can significantly improve estimates and insights obtained from different datasets. Predictive mean matching proves to be a valuable technique for handling missing data and ensuring more accurate results.

Our findings suggest that the flexibility of PMM estimators allows them to adapt well to various scenarios, including those involving non-linear relationships and model mis-specification. The empirical study reinforces these results, showcasing the effectiveness of PMM in real-world applications.

As we move forward, future research can focus on refining these methods and exploring additional applications across various fields. The insights gained can help organizations and researchers make informed decisions based on comprehensive data analyses.