AMELIA II: A Package for Missing Data

Transcription

1 AMELIA II: A Package for Missing Data James Honaker Gary King Matthew Blackwell July 24, 2009

2 I want to convince you of three things.

3 I want to convince you of three things. 1 Missing data is a problem for statistical analysis.

4 I want to convince you of three things. 1 Missing data is a problem for statistical analysis. 2 Multiple imputation is a method that drastically improves the analysis of incomplete data.

5 I want to convince you of three things. 1 Missing data is a problem for statistical analysis. 2 Multiple imputation is a method that drastically improves the analysis of incomplete data. 3 Our software, Amelia, is a simple yet powerful way to implement this method.

6 the problem: missing data a solution our approach

7 year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso Burkina Faso Burkina Faso Burkina Faso

8 year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso

9 > NA + 34 [1] NA

10 year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso

11 Listwise Deletion year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso

12 Listwise Deletion year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso Burkina Faso

13 Listwise Deletion Solves <the problem>?

14 Listwise Deletion Solves <the problem>? Yes.

15 Listwise Deletion Solves <the problem>? Yes. Creates new problems?

16 Listwise Deletion Solves <the problem>? Yes. Creates new problems? Yes.

17 New Problems

18 New Problems BIAS The cases you throw out are systematically different than the ones that you leave in.

19 New Problems BIAS The cases you throw out are systematically different than the ones that you leave in. INEFFICIENCY Tossing out observed information with the missing values.

20 Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso

21 Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso

22 Mean Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 Xin Xtrade Burkina Faso Burkina Faso 435 Xin Burkina Faso

23 Mean Imputation Solves <the problem>?

24 Mean Imputation Solves <the problem>? Yes.

25 Mean Imputation Solves <the problem>? Yes. Creates new problems?

26 Mean Imputation Solves <the problem>? Yes. Creates new problems? Yes.

27 New Problems

28 New Problems BIAS Ignores correlations between variables.

29 New Problems BIAS Ignores correlations between variables. OVERCONFIDENCE Treating imputations as observed data.

30 The problem, revised How do we fill in the data in an way that both preserves the relationships in the observed data and incorporates the uncertainty of imputation?

31 the problem a solution: multiple imputation our approach

32 The Multiple Imputation Scheme

33 The Multiple Imputation Scheme incomplete data

34 The Multiple Imputation Scheme incomplete data imputation imputed datasets

35 The Multiple Imputation Scheme incomplete data imputation imputed datasets analysis separate results

36 The Multiple Imputation Scheme incomplete data imputation imputed datasets analysis separate results combination final results

37 Multiple Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso

38 Multiple Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso

39 Multiple Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso

40 Multiple Imputation year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 x a x b Burkina Faso Burkina Faso 435 x c Burkina Faso

41 Multiple Imputation

42 Multiple Imputation REGRESSION To preserve the relationships in the data.

43 Multiple Imputation REGRESSION To preserve the relationships in the data. SIMULATION To reflect the uncertainty of our imputation.

44 How to impute y = X β + ε REGRESSION

45 How to impute X mis i = X obs i β + ε REGRESSION

46 How to impute X mis i = X obs i β + ε REGRESSION β N(β, var( β)) SIMULATION ε N(0, σ 2 X mis )

47 How to impute X mis i = X obs i β + ε EM β N(β, var( β)) SIMULATION ε N(0, σ 2 X mis )

48 How to impute X mis i = X obs i β + ε EM β N(β, var( β)) BOOTSTRAP ε N(0, σ 2 X mis )

49 the problem a solution our approach: Amelia features diagnostics

50 The Amelia Scheme

51 The Amelia Scheme incomplete data

52 The Amelia Scheme incomplete data bootstrap bootstrapped data

53 The Amelia Scheme incomplete data bootstrap bootstrapped data EM imputed datasets

54 The Amelia Scheme incomplete data bootstrap bootstrapped data EM imputed datasets analysis

55 The Amelia Scheme incomplete data bootstrap bootstrapped data EM imputed datasets analysis combination final results

56 the problem a solution our approach: Amelia features diagnostics

57 Simplicity a.out <- amelia(data)

58 A GUI

59 Transformations GDP log(gdp) Frequency Frequency a.out <- amelia(africa, logs = "gdp")

60 Polynomials of Time year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso f(t) = t + t 2 + t 3

61 Polynomials of Time year country GDP infl trade population Burkina Faso Burkina Faso Burkina Faso 393 NA NA Burkina Faso Burkina Faso 435 NA Burkina Faso f(t) = t + t 2 + t 3 data yesterday imputation tomorrow

62 Easily passed to other platforms for analysis ## Pass to Zelig library(zelig) a.out <- amelia(africa) z.out <- zelig(infl ~ gdp, data = a.out$imputations, model = ls) ## Write to Stata files write.amelia(a.out, stem = "outdata", format = "dta")

63 Error Checking > a.out <- amelia(africa) Amelia Error Code: 37 The variable(s) country are "factors". You may have wanted to set this as a ID variable to remove it from the imputation model or as an ordinal or nominal variable to be imputed. Please set it as either and try again.

64 the problem a solution our approach: Amelia features diagnostics

65 Missingness Maps Burkina Faso Missingness Map Missing Observed Burundi Cameroon Congo Senegal Zambia trade gdp_pc population civlib infl country year > missmap(africa, tsvar = "year", csvar = "country")

66 Overimputation Observed versus Imputed Values Imputed values Observed values > overimpute(a.out, var = trade)

67 Time-Series Cross-Sectional Plots Burundi trade Time > tscsplot(a.out, var = "trade", cs = "Burundi")

68 the problem: missing data a solution: multiple imputation our approach: Amelia

69 thank you. Learn more about Amelia: