Multidimensional Control Totals for Poststratified Weights

Transcription

1 Multidimensional Control Totals for Poststratified Weights Darryl V. Creel and Mansour Fahimi Joint Statistical Meetings Minneapolis, MN August 7-11, 2005 RTI International is a trade name of Research Triangle Institute 6110 Executive Blvd. Suite 900 Rocville, Maryland, USA Phone dcreel@rti.org

2 Outline for Weighting Adjustments Motivation Implementation Bacground Information for Education Study Issues and Solutions Impact

3 Motivation: Account for Nonresponse Minimize Nonresponse Item Nonresponse Imputation Unit Nonresponse Weighting Adjustments

4 Motivation: Potential Bias from Nonresponse N B( y ) M ( y y R R M N ), NM is the number of nonrespondents in the population, N is the number of observations in the population, y R y M is the mean of the respondents in the population, and is the mean of the nonrespondents in the population.

5 Motivation: Account for Under or Over Coverage Poststratification is used to account for potential bias due to under or over coverage. Use of external population counts.

6 Response Propensity ( φ) Weighting Adjustments Assume Missing at Random (MAR) Weighting Class and Poststratification Raing Logistic Regression and Generalized Exponential Modeling

7 Weighting Class w * i = w φˆ C i = w i j E R w w j

8 Poststratification w * i = w i N R C w

9 Raing or Raing Ratio T Rh = K n h, = 1 i = 1 w hi T C = H n h, h = 1 i= 1 w hi

10 Logistic Regression Model φˆ i = 1+ e αˆ 1 ˆ + βi xi

11 Logistic Regression Model Form Groups for Other Methods Directly 1 βˆ ix * αˆ w = w = w (1 + e i i ˆ i φ i + i )

12 Generalized Exponential Model (GEM) Folsom and Singh, 2000 Methodology for Nonresponse Adjustments, Poststratification, and Extreme Weight Values Weighting Adjustments Adhere to Control Totals and Bounds on Adjustment Factors Simultaneously (Weight Calibration) Enhancement of Deville and Sarndal s (1992) Logit Type Method

13 Deville and Sarndal Logit Type Method a ( λ) where l( u 1) + u(1 l)exp( Ax λ) =, ( u 1) + (1 l)exp( Ax λ) u l l < 1 < u and A =. ( u 1)(1 l) As l 0 and u, a ( λ ) exp( x λ ).

14 GEM Generalization. ) )( (, ) )exp( ( ) ( ) )exp( ( ) ( ) ( l c c u l u A and u c where l x A l c c u x A l c u c u l a = < < + + = λ λ λ ). exp( 1 ) (, 2,, 1 λ λ x a and u c Asl +

15 GEM: Flexibility Identify Extreme Weights Bounds on Adjustment Factors Incorporate Control Totals Used for All Weighting Adjustments, Except Multiplicity

16 2004 National Study of Postsecondary Faculty (NSOPF: 04) Two Stage Sample Design First Stage: Institutions Second Stage: Faculty Members at Sampled Institutions Weights Faculty Weight Product of Institution and Individual Weights Separate Institution Weight

17 2004 National Study of Postsecondary Faculty Initial Faculty Weight Institution Faculty Weight Faculty Member Sampling Weight Weighting Adjustments Multiplicity Unnown Eligibility Nonresponse Poststratification

18 Issue One: Identifying Respondents Rules for Classifying Partial Respondents as Complete or Nonrespondent Two Qestionnaires Institution Faculty Member

19 Issue Two: Control Totals for Total Faculty Internal Institution Questionnaire Faculty Member Questionnaire External Winter Employee by Assigned Position Survey (EAP:03) Source Used for Control Totals

20 Issue Two: Control Totals for Total Faculty EAP:03 Instructional Faculty NSOPF:04 Instructional Faculty and Non-faculty Who Provide Instruction Poststratified NSOPF:04 Instructional Faculty to EAP:03 Instructional Faculty NSOPF:04 Non-faculty Who Provide Instruction Removed Prior to Poststratification Added Bac After Poststratification

21 Issue Three: Cell Collapsing Poststratification Joint Distribution of Employment Status and Institution Type Joint Distribution of Race/Ethnicity, Gender, and Institution Type Replicate Weights Dropped Three-way Interaction Separately Race/Ethnicity and Gender with Institution Type

22 Impact: Design Effect for Unequal Weighting 1 + (( cv( w)) 2 = n n n i= 1 i= 1 w w i 2 i 2

23 Impact: Design Effect for Unequal Weighting Table 1. Analysis Weight Information Stratum Count Minimum Median Mean Maximum Coefficient Weight Weight Weight Weight Of Variation UWE Overall

24 Impact: Distribution of Weights Distribution of the Weights in Stratum Seven

25 Impact: External Validity of Estimates Computed Estimates of Key Outcome Measures Checed Estimates Against Available Prior Estimates

26 Summary Motivation Implementation Bacground Information for an Education Study Issues and Solutions Impact

27 Web Site