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Introduction to Multiple Imputation. CFDR Workshop Series Spring 2008. 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. Missing data mechanisms.

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## Introduction to Multiple Imputation

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**Introduction to Multiple Imputation**CFDR Workshop Series Spring 2008**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**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**What is Multiple Imputation?**• Imputation • Make M=3 to 10 copies of incomplete data set filling in with conditionally random values • Analyses • Of each data set separately • Pooling • Point estimates. Average across M analyses • Standard errors. Combine variances .**Three steps**• Imputation • Make M=2 to 10 copies of incomplete data set filling in with conditionally random values • Analyses • Of each data set separately • Pooling • Point estimates. Average across M analyses • Standard errors. Combine variances .**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.**Stata Example**• ICE to impute • Regression commandsmay 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**Step 1: Proc MI**• Typical syntax: proc mi data=mi_example out=outmi seed=1234; var Oxygen RunTime RunPulse; run;**Step 2: Run Models**procreg 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**Parameter Estimates & Covariance Matrices**procprint data=outreg(obs=8); var _Imputation_ _Type_ _Name_ Intercept RunTime RunPulse; run;**Step 3. Proc Mianalyze**procmianalyze data=outreg; modeleffects Intercept RunTime RunPulse; run;**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.**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.**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.**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.**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?**Thanks**Next up: “COLLATERAL CONSEQUENCES OF VIOLENCE IN DISADVANTAGED NEIGHBORHOODS” Dr. David HardingWednesday, February 13,Noon - 1:00 pm Accessing and Analyzing Add Health DataInstructor: Dr. Meredith PorterMonday, February 25, 12:00-1:00 pm

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