Observed data

−4 −2 0 2 4

Imputed data−−Missing completely at random

−4 −2 0 2 4

Imputed data−−Fitted normal model

−4 −2 0 2 4

−4 −2 0 2 4 −4 −2 0 2 4

−4 −2 0 2 4 −4 −2 0 2 4

Imputed data−−Various assumptions

Easier Said Than Done: Open Problems inMultilevel Regression and Poststratification

Andrew Gelman

Department of Statistics and Department of Political ScienceColumbia University, New York

Conference in honor of Rod Little, 31 Oct 2015

From Wikipedia:

Survey response rates are going through the floor!R

espo

nse

rate

1940 1960 1980 2000

0%20

%40

%60

%80

%10

0%

Year

Survey response rates are going through the floor!R

espo

nse

rate

1940 1960 1980 2000

0%20

%40

%60

%80

%10

0%

Year

The poststratification identity

θ =

∑Jj=1 Njθj∑Jj=1 Nj

The poststratified estimate

θ̂ =

∑Jj=1 Nj θ̂j∑Jj=1 Nj

Xbox estimates, adjusting for demographics:

Xbox estimates, adjusting for demographics and partisanship:

Why multilevel regression?

Open problems in MRP

I Deep interactionsI Non-census variablesI Survey weightsI Cluster samplingI Estimating regression coefficientsI Building trust in results