HOW TO DEAL WITH MISSING DATA:

INTRODUCTION

LI QI

UNC CHARLOTTE

GENERAL STEPS FOR ANALYSIS WITH MISSING DATA

1. Identify patterns/reasons for missing and recode correctly

2. Decide on best method of analysis

3. Make an inference about some aspect (parameter) of the distribution of the “full” data when some of the data are missing

STEP 1: UNDERSTAND YOUR DATA

Attrition due to social/natural processes

Eg: School graduation, dropout, death…

Skip pattern in survey

Eg: Certain questions only asked to respondents who indicate

they are married

Intentional missing as part of data collection process Respondent refusal/Non-response

Observations are not sampled with the same frequency. 

UNDERSTAND YOUR DATA (CONT.)

Are certain groups more likely to have missing values?

Example: Respondents in service occupations less likely to report income

Are certain responses more likely to be missing?

Example: Respondents with high income less likely to report income

MISSING DATA MECHANISM

MCAR (missing completely at random): The probability of missingness is independent of the data.

If the data are MCAR, then the complete-case estimator is unbiased and consistent, as our intuition would suggest.

In fact, there is no way that we can distinguish whether the missing data were MCAR or not from the observed data.--Identifiability problem

MISSING DATA MECHANISM (CONT.)

MAR (missing at random): The probability of missingness depends only on the observed data.

The MAR assumption allows the dependence between missingness δ and the variable Y.

P(δ=1|Y,W)=f(W);

Example: Respondents in service occupations less likely to report income

NMAR (nonmissing at random): The probability of missingness may also depend on the unobservable part of the data.

Difficult to deal with

MISSING DATA MECHANISM (CONT.)

STEP 2: DEAL WITH MISSING DATA

Use what you know about why data is missing. Decide on the best analysis strategy to yield the best estimates.

TRADITIONAL APPROACHES

Deletion Methods

Listwise deletion, pairwise deletion

Single imputation methods

Mean/Mode substitution

Regression substitution

ADVANCED METHODS

Maximum Likelihood method (ML)

Weighing method (IPW)

Multiple imputation method (MI)

MODEL-BASED METHODS: ML

Identify the set of parameter values that produces the highest log-likelihood.

Advantages: Use both complete cases and incomplete cases; Enjoy the optimality properties afforded to an MLE.

Disadvantages: We need correctly specify the two parametric models; Difficult to compute.

INVERSE PROBABILITY WEIGHTING

Little and Rubin (1987) proposed this method for missing data problems in survey.

INVERSE PROBABILITY WEIGHTING

Idea: A subject with weight of 4 has a probability of observation of 0.25 (or 1/pi= 0.25). As a result, data from this subject should count once for herself and 3 times for those subjects missing.

INVERSE PROBABILITY WEIGHTING (CONT.)

Advantages: Full likelihood is not necessary; use GEE. Could be applied widely in different models.

Disadvantages: The selection probability model is not correctly specified, then IPW estimator would be biased. If the true selection probability is very small, then it could be very .

INVERSE PROBABILITY WEIGHTING (CONT.)

Robins, Rotnitzky and Zhao (1994) discussed the idea of adding an augmentation term to a simple weighted estimation equation.

INVERSE PROBABILITY WEIGHTING (CONT.)

SAS: The GEE and CAUSALTRT Procedures

R: The ipw and CausalGAM package

SINGLE IMPUTATION

Since some of the Y are missing, a natural strategy is to impute or “estimate” a value for such missing data and then estimate the parameter of interest behaving as if the imputed values were the true values.

SINGLE IMPUTATION (CONT.)

For monotone missing data patterns

Regression Method

Propensity Score Method

For arbitrary missing data patterns

MCMC method

All these options are available in SAS MI procedure.

MULTIPLE IMPUTATION (MI)

Single imputation does not refect the uncertainty about the predictions of the unknown missing values, and the resulting estimated variances of the parameter estimates will be biased toward zero.

Multiple imputation does not attempt to estimate each missing value through simulated values but rather to represent a random sample of the missing values.

MI PROCEDURE

Multiple imputation inference involves three distinct phases:

The missing data are filled in m times to generate m complete data sets.

The m complete data sets are analyzed by using standard procedures.

The results from the m complete data sets are combined for the inference.

MULTIPLE IMPUTATION PROCESS

MULTIPLE IMPUTATION (CONT.)

SAS

PROC MI

R

mi package

TIME SERIES DATA

Idea: aggregation and interpolation

SAS: PROC EXPAND  

http://support.sas.com/rnd/app/examples/ets/missval

Missing Spatial Data

Thank you!