Introduction to Multiple Imputation CFDR Workshop Series Spring 2008

2 Outline Missing data mechanisms What is Multiple Imputation? SAS Proc MI, Proc MIANALYZE Stata ICE, MICOMBINE SAS IVEware What’s the diff? Problems with categorical imputation

3 Missing data mechanisms Missing Completely At Random (MCAR) –The probability of missingness doesn't depend on anything. Missing At Random (MAR) –The probability of missingness does not depend on the unobserved value of the missing variable, but it can depend on any of the other variables in your dataset Not Missing at Random (NMAR) –The probability of missingness depends on the unobserved value of the missing variable itself

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5 What is Multiple Imputation? 1.Imputation Make M=3 to 10 copies of incomplete data set filling in with conditionally random values 2.Analyses Of each data set separately 3.Pooling Point estimates. Average across M analyses Standard errors. Combine variances.

6 1. Imputation: Multiple Copies of Dataset

7 Three steps 1.Imputation Make M=2 to 10 copies of incomplete data set filling in with conditionally random values 2.Analyses Of each data set separately 3.Pooling Point estimates. Average across M analyses Standard errors. Combine variances.

8 What is MI? STATA –based on each conditional density –chained equations SAS –joint distribution of all the variables –assumed multivariate normal distribution SAS IVEware –same as Stata, more options.

9 Stata Example ICE to impute –Regression commands may be logistic, mlogit, ologit, or regress. MICOMBINE to analyze and combine the results. –Supported regression cmds are clogit, cnreg, glm, logistic, logit, mlogit, ologit, oprobit, poisson, probit, qreg, regress, rreg, stcox, streg, or xtgee. Easy to use, nice documentation

10 SAS example

11 Step 1: Proc MI Typical syntax: proc mi data=mi_example out=outmi seed=1234; var Oxygen RunTime RunPulse; run;

12 Step 2: Run Models proc reg data=outmi outest=outreg covout noprint; model Oxygen = RunTime RUnPulse; by _Imputation_; run; Note that the regression output is stored as dataset “outreg” Proc’s= Reg, Logistic, Genmod, Mixed, GLM

13 Parameter Estimates & Covariance Matrices proc print data=outreg(obs=8); var _Imputation_ _Type_ _Name_ Intercept RunTime RunPulse; run;

14 Step 3. Proc Mianalyze proc mianalyze data=outreg; modeleffects Intercept RunTime RunPulse; run;

15 Irritating Parameter Est. & Covariance Matrices Syntax depends on what procedure you used in previous step: proc mianalyze data=parmcov; (or) proc mianalyze parms=parmsdat covb=covbdat; (or) proc mianalyze parms=parmsdat xpxi=xpxidat; PROC’s: reg, genmod, logit, mixed, glm.

16 SAS IVEware: 4 Components 1. IMPUTE -- nice options. 2. DESCRIBE estimates the population means, proportions, subgroup differences, contrasts and linear combinations of means and proportions. A Taylor Series approach is used to obtain variance estimates appropriate for a user specified complex sample design. 3. REGRESS fits linear, logistic, polytomous, Poisson, Tobit and proportional hazard regression models for data resulting from a complex sample design. 4. SASMOD allows users to take into account complex sample design features when analyzing data with several SAS procedures. SAS PROCS can be called:CALIS, CATMOD, GENMOD, LIFEREG, MIXED, NLIN, PHREG, and PROBIT.

17 IVEware Impute IMPUTE assumes the variables in the data set are one of the following five types: (1) continuous (2) binary (3) categorical (polytomous with more than two categories) (4) counts (5) mixed The types of regression models used are linear, logistic, Poisson, generalized logit or mixed logistic/linear, depending on the type of variable being imputed.

18 SAS IVEware: 4 Components 1. IMPUTE -- nice options. 2. DESCRIBE estimates the population means, proportions, subgroup differences, contrasts and linear combinations of means and proportions. A Taylor Series approach is used to obtain variance estimates appropriate for a user specified complex sample design. 3. REGRESS fits linear, logistic, polytomous, Poisson, Tobit and proportional hazard regression models for data resulting from a complex sample design. 4. SASMOD allows users to take into account complex sample design features when analyzing data with several SAS procedures. SAS PROCS can be called:CALIS, CATMOD, GENMOD, LIFEREG, MIXED, NLIN, PHREG, and PROBIT.

19 A Few Issues Do I impute the dependent variable? Which model has more information? The imputation model or the analyst model? How many imputations do I need to do? Can I impute in one language and analyze in another? How do I get summary statistics such as R squared? Can I do this in SPSS? Where do I go with questions?

20 Thanks Next up: “COLLATERAL CONSEQUENCES OF VIOLENCE IN DISADVANTAGED NEIGHBORHOODS” Dr. David Harding Wednesday, February 13, Noon - 1:00 pm Accessing and Analyzing Add Health Data Instructor: Dr. Meredith Porter Monday, February 25, 12:00-1:00 pm