1. Presenter: Ting-Ting Chung July 11, 2017
Multiple Imputation
Presenter: Ting-Ting Chung
July 11, 2017

2. Introduction
Missing data is a pervasive and persistent problem in many data sets
Representative?
Deliberately results in missing data (questions asked only of women), refusal to answer (sensitive questions), insufficient knowledge (month of first words spoken), and attrition due to death or loss of contact with respondents in longitudinal surveys

3. Introduction
Analysts often make assumptions about the nature of missing data including categorizations
Missing at Random (MAR)
The probability of missing data on Y is unrelated to the value of Y after controlling for other variables in the analysis (say X)
Missing Completely at Random (MCAR)
Suppose variable Y has some missing values. We will say that these values are MCAR if the probability of missing data on Y is unrelated to the value of Y itself or to the values of any other variable in the data set. However, it does allow for the possibility that “missingness” on Y is related to the “missingness” on some other variable X
Not Missing at Random (NMAR)
Missing values do depend on unobserved values

4. Type of missing
We can distinguish between two main patterns of missingness
Missing monotone
missing data is a pattern in which the missing data exists at the end (reading from left to right) of the data record with no gaps between full and missing data
Missing arbitrarily
missing data pattern that has missingness interspersed among full data

5. Methods for handling missing data
Conventional methods
Listwise deletion (or complete case analysis)
If a case has missing data for any of the variables, then simply exclude that case from the analysis
Imputation methods
Substitute each missing value for a reasonable guess, and then carry out the analysis as if there were not missing values
Advanced Methods
Multiple Imputation
It replaces each missing item with two or more acceptable values, representing a distribution of possibilities
Maximum Likelihood
Bayesian simulation methods
Hot deck imputation methods

6. Steps of Multiple Imputation
Running an imputation model defined by the chosen variables to create imputed data sets. In other words, the missing values are filled in m times to generate m complete data sets. m=20 is considered good enough. Correct model choices require considering:
Firstly, we should identify which are the variables with missing values
Secondly, we should compute the proportion of missing values for each variable
Thirdly, we should assess whether different missing value patterns exist in the data, and try to understand the nature of the missing values
The m complete data sets are analyzed by using standard procedures
The parameter estimates from each imputed data set are combined to get a final set of parameter estimates

8. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
Step 1. proc mi data=one nimpute=0 ; var hhinc age sex ed4cat region weight ; run ; PROC MI with a NIMPUTE=0 option to initially examine the existing missing data pattern
shows that 1.79% of the n of 5692 have missing data on the WEIGHT variable

9. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
Step 2.
proc mi data=one nimpute=5 out=outimputex2 seed=20102 ;
class region ed4cat sex ;
monotone regression ;
var hhinc age region sex ed4cat weight ;
run ;
The MONOTONE REGRESSION statement requests the use of the regression method for imputation of the continuous variable WEIGHT. The regression method is recommended for imputation of a continuous variable with a monotone missing data pattern and categorical covariates contributing to the imputation step

10. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
RE >0.9good

11. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
Step 3. proc surveyreg data=outimputex2 ; strata sestrat ; cluster seclustr ; weight ncsrwtlg ; class region sex ed4cat ; domain _imputation_ ; model weight=hhinc age region sex ed4cat / solution ; ods output ParameterEstimates=outregex2 (where=(_imputation_ ne . )); run ;

13. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
Step 4. proc mianalyze parms=outregex2; modeleffects intercept hhinc age region1 region2 region3 sex1 ed4cat1 ed4cat2 ed4cat3 ; run;

15. Example MONOTONE REGRESSION IMPUTATION WITH MISSING DATA ON CONTINUOUS VARIABLE AND CATEGORICAL COVARIATES
Table 2.5 includes the synthesized output for the 5 imputed data sets with the complex sample adjusted standard errors (Step 2 using PROC SURVEYREG) and the variance further adjusted by PROC MIANALYZE. The parameter estimates and other statistics are mean values from the 5 imputed values and are now adjusted correctly to account for the multiple imputation and the complex survey features.

16. Example 2 proc mianalyze parms=lgparms proc logistic data=OutFish;
covb=lgcovb;
modeleffects Intercept Length;
run;
proc mi data=Fish seed= out=OutFish;
class Species;
monotone reg(Height Width/ details)
logistic( Species= Length Height Width Height*Width/ details);
var Length Height Width Species;
run;
proc logistic data=OutFish;
class Species;
model Species= Length / covb;
by _Imputation_;
ods output ParameterEstimates=lgparms CovB=lgcovb;
run;