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Adjusting for Unequal Selection Probability in Multilevel Models: A Comparison of Software Packages. by Kim Chantala C. M. Suchindran Dan Blanchette. Overview. Compare capabilities of multilevel modeling software packages for analyzing data collected with a complex sampling plan

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adjusting for unequal selection probability in multilevel models a comparison of software packages

Adjusting for Unequal Selection Probability in Multilevel Models: A Comparison of Software Packages

by

Kim Chantala

C. M. Suchindran

Dan Blanchette

overview
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
slide6

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

slide7

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).

slide8

Some MLM Software Packages Requires Special Weights* Constructed for Each Level:

*Method of weight construction from Pfeffermann (1998)

slide9

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)

slide10

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.
slide12

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

slide13

Effect of Sampling Weights on Estimates

When sampling weights were omitted from analyses, all software packages gave nearly the same results.

slide15

Parameter Estimate Profile for Analysis Using Sampling Weights

g01

g00

s2d0

s2

sd0,d1

g10

s2d1

g11

slide16

Predictions from Analysis Using Sampling Weights

Solid lines (RC_S=1): schools with recreation centers

Dashed lines (RC_S=0): schools without recreation centers

slide17

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.
slide18

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.