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Adjusting for Unequal Selection Probability in Multilevel Models

This study compares different software packages for multilevel modeling, focusing on their capabilities in analyzing complex survey data. It discusses the characteristics of survey data that can affect estimates and provides methods to construct sampling weights for estimating multilevel models. Results from estimating a two-level model using different software packages are contrasted.

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Adjusting for Unequal Selection Probability in Multilevel Models

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  1. Adjusting for Unequal Selection Probability in Multilevel Models: A Comparison of Software Packages by Kim Chantala C. M. Suchindran Dan Blanchette

  2. Overview • Compare capabilities of multilevel modeling software packages for analyzing data collected with a complex sampling plan • Describe characteristics of survey data that can influence estimates • Construct sampling weights for estimating multilevel models • Contrast results from estimating a two-level model with different software packages

  3. Comparison of Software Packages: General Information

  4. Comparison of Software Packages: Implementation of Sampling Weights

  5. Comparison of Software Packages: MLM Analyses with Sampling Weights

  6. Survey Data Characteristics: Design of Add Health • 80 High Schools selected with probability proportional to size from list of 26,666 schools sorted by: • Enrollment Size • Region of Country • School Type • Location • Percent White 52 High Schools did not include a 7th or 8th grade Feeder school selected with probability proportional to percentage of each high schools’ entering class that came from feeder school. 52 Feeder Schools 80 High Schools 18,924 Students selected from 132 schools for Wave I In-Home Interview All Students from 16 Schools Disabled Sample • Genetic Samples • Twins • Full siblings • Half siblings • Unrelated in Same HH • Ethnic Samples • High SES Black • Cuban • Puerto Rican • Chinese Core Sample

  7. Constructing Multilevel WeightsWeight Components Needed to Construct Sampling Weights for Two-Level Analysis using the Add Health Data: * Stata programs for constructing sampling weights for estimating two-level models can be downloaded from our website (http://www.cpc.unc.edu/restools/data_analysis/ml_sampling_weights) after August 1, 2005. These programs have implemented methods from Pfefferman (1998) and Asparouhov (2004).

  8. Some MLM Software Packages Requires Special Weights* Constructed for Each Level: *Method of weight construction from Pfeffermann (1998)

  9. Other MLM Software Packages require one Weight* that combines the weights from each level in a particular way: *Method of weight construction from Asparouhov (2004)

  10. Illustrative Example • Research Question: How is the effect of hours watching TV on BMI of students in a school influenced by the availability of a school recreation center? • Data from the National Longitudinal Study of Adolescent Health (Add Health) • Contrast the results from MPLUS, MIXED, LISREL, MLWIN, and GLAMM • Weights for MPLUS & MIXED will be constructed with the Asparouhov (2004) method; weights for LISREL, MLWIN, and GLAMM will be constructed with the Pfeffermann (1998) method.

  11. Data in example

  12. Two-level Model • Student-level model (Within or Level 1): BMIPCTij = {0j + 1j(HR_WATCHij)} + eij where: E(eij) = 0, Var(eij) = σ2 • School-level Model (Between or Level 2): 0j = 00 + 01(RC_S)j + 0j 1j = 10 + 11(RC_S)j + 1j where: E(0j ) = E(1j ) = 0 Var (0j ) = σ20, Var(1j) = σ21, Cov(0j, 1j ) = σ0,1

  13. Effect of Sampling Weights on Estimates When sampling weights were omitted from analyses, all software packages gave nearly the same results.

  14. Analysis Results from Different Packages

  15. Parameter Estimate Profile for Analysis Using Sampling Weights g01 g00 s2d0 s2 sd0,d1 g10 s2d1 g11

  16. Predictions from Analysis Using Sampling Weights Solid lines (RC_S=1): schools with recreation centers Dashed lines (RC_S=0): schools without recreation centers

  17. Conclusion • Use of sampling weights to adjust for non-response and the design characteristics of complex survey data has recently been incorporated in software used for estimating multilevel models. • This provides analysts with a simple method for obtaining unbiased estimates from complex survey data. • When sampling weights are used, results from these packages can vary. If weights are ignored, these packages produce the same results. • Simulation studies need to be conducted to determine why these packages produce different results when sampling weights are used. • Models with non-normal outcomes need to be examined.

  18. References • Asparouhov, T. (2004). Weighting for Unequal Probability of Selection in Multilevel Modeling, Mplus Web Notes No. 8 available from http://www.statmodel.com/ • Grilli, L., and Pratesi, M. Weighted Estimation in Multilevel Ordinal and Binary Models in the Presence of Informative Sampling Designs. Survey Methodology, June 2004, Volume 30, pp 93-103 • Pfeffermann, D., Skinner, C. J., Holmes D. J, and H. Goldstein, Rasbash, J., (1998). Weighting for Unequal Selection Probabilities in Multilevel Models. JRSS, Series B, 60, 123-40.

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