Growth curve modeling (GCM) is a statistical approach to studying changes in variables over time. When working with survey data that involves complex sampling designs, such as stratification, clustering, or weighting, it’s important to incorporate the survey design into your analysis to avoid biased estimates. This can be done using the survey package in R, which provides tools for analyzing complex survey data. Below is a step-by-step guide on performing growth curve modeling with svy in R.
1. Install and Load Required Packages
Ensure you have the necessary packages installed.
2. Prepare the Data
The dataset should include:
- A response variable measured at multiple time points.
- Predictor variables (e.g., demographics, intervention status).
- Survey design information (weights, strata, cluster IDs).
Example of a dataset structure:
| ID | Time | Outcome | Weight | Strata | Cluster |
|---|---|---|---|---|---|
| 101 | 1 | 5.2 | 1.5 | 1 | A |
| 101 | 2 | 6.3 | 1.5 | 1 | A |
| 102 | 1 | 4.8 | 1.2 | 2 | B |
3. Define the Survey Design
Use the svydesign() function to define the survey design.
4. Reshape Data for Growth Curve Modeling
Ensure the data is in long format, where each row represents one time point for a given individual. Use the reshape() function or tidyr::pivot_longer() for reshaping.
5. Specify the Growth Curve Model
Growth curve models typically include random effects for individuals and fixed effects for predictors. In survey data, this requires using svyglm() for fixed effects or advanced custom functions for mixed models.
For more complex random effects (e.g., slopes), you’ll need to use tools like lmer() from the lme4 package, but these do not natively support survey weights. One approach is to incorporate weights as fixed effects or pseudo-likelihood approximations.
6. Check Model Fit
Assess model fit using residual diagnostics and goodness-of-fit statistics. For survey-weighted models, standard metrics like AIC or BIC may not be applicable.
7. Interpret the Results
Once the model is fitted, interpret the coefficients to understand the relationship between predictors and the outcome over time. For example:
- The fixed effect of
Timeindicates the average rate of change in the outcome. - Random effects capture individual-level deviations from the average trajectory.
8. Optional: Visualize Growth Curves
Visualization helps in interpreting the growth trajectories.
Challenges and Considerations
- Mixed Effects with Survey Weights: Mixed-effects models (
lmer()) don’t natively support survey weights. Use approximate methods or resample data. - Complex Survey Design: Ensure you correctly specify clusters and strata to account for design effects.
- Software Limitations: Advanced survey-weighted growth modeling may require specialized software like Mplus or SAS.
