What Is The Most Effective Method To Handle Missing Values In A Longitudinal Dataset Of Student Math Scores, Where The Missingness Is Suspected To Be Non-ignorable And Related To The Student's Prior Math Ability, And How Can I Implement This Method In R To Minimize Bias In My Analysis Of The Relationship Between Math Scores And Socio-economic Status?

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Handling non-ignorable missing data in a longitudinal dataset of student math scores requires a thoughtful approach to minimize bias when analyzing the relationship between math scores and socio-economic status. Here's a structured plan to address this issue using a Bayesian method in R:

1. Understand the Missing Data Mechanism

  • Non-Ignorable Missingness (MNAR): The missing values are related to prior math ability, suggesting that students with lower prior ability are more likely to have missing scores.

2. Choose an Appropriate Method

  • Bayesian Modeling: This approach allows explicit modeling of both the analysis and the missing data mechanism, making it suitable for non-ignorable missingness.

3. Prepare the Data

  • Structure the dataset in a long format, with each row representing a measurement occasion for a student.
  • Include variables: math scores, socio-economic status, prior math ability, and an indicator for missingness.

4. Specify the Bayesian Model

  • Analysis Model: Relates math scores to socio-economic status, including random effects for students and time to account for longitudinal structure.
  • Missingness Model: Includes prior math ability as a predictor to model the probability of missing scores.

5. Implement the Model in R

  • Use packages like brms or rstanarm for Bayesian modeling.
  • Example code structure using brms:
    library(brms)

    fit <- brm(
math_score ~ ses + (1|student) + (1|time),
data = df,
missing = ~ prior_ability,
prior = c(prior(normal(0, 1), class = "b")),
chains = 2,
cores = 2,
iter = 2000,
warmup = 1000
)

6. Model Diagnostics and Convergence

  • Check trace plots and R-hat values to ensure convergence.
  • Adjust iterations or thin chains if necessary to improve computational efficiency.

7. Extract and Interpret Results

  • Focus on the posterior distribution of coefficients related to socio-economic status.
  • Use summarised posterior estimates (e.g., mean, credible intervals) to draw conclusions.

8. Sensitivity Analysis

  • Test the robustness of findings by varying priors or model specifications.

9. Address Potential Challenges

  • Monitor for computational demands and convergence issues, adjusting model parameters as needed.

By following this structured approach, you can effectively handle non-ignorable missing data and draw reliable conclusions about the relationship between math scores and socio-economic status.