1. Adapting to missing data
Missing Values
Adapting to missing data

2. Sources of Missing Data
People refuse to answer a question
Responses are indistinct or ambiguous
Numeric data are obviously wrong
Broken objects cannot be measured
Equipment failure or malfunction
Detailed analysis of subsample

3. Assumptions 1 Missing Completely at Random Missing at Random
probability of data missing on X is unrelated to the value of X or to values on other variables in data set
Missing at Random
the probability of missing data on X is unrelated to the value of X after controlling for other variables in the analysis

4. Assumptions 2 Ignorable Nonignorable
MAR plus parameters governing missing data process unrelated to parameters being estimated
Nonignorable
If not MAR, missing data mechanism must be modeled to get good estimates of parameters

5. Methods Listwise Deletion Pairwise Deletion Dummy Variable Adjustment
Imputation

6. Listwise Deletion 1 Delete any samples with missing data
Can be used for any statistical analysis
No special computational methods
If data are MCAR (esp if random sample of full data set), they are an unbiased estimate of the full data set

7. Listwise Delete 2
If data are MAR, can produce biased estimates if missing values in independent variables are dependent on dependent variable
Main issue is the loss of observations and the increase in standard errors (meaning a decrease in the power of the test)

8. Listwise Deletion 3
In anthropology listwise deletion often includes removal of variables (columns) as well as cases (rows)
Finding an optimal complete data set involves removing variables with many missing variables and then rows still having missing variables

9. Pairwise Deletion 1
Compute means using available data and covariances using cases with observations for the pair being computed
Uses more of the data
If MCAR, reasonably unbiased estimates, but if MAR, estimates may be seriously biased

10. Pairwise Deletion 2 Covariance/Correlation matrix may be singular
Less of an issue with distance matrices

11. Dummy Variable
Create variable to flag observations missing on a particular variable
Used in regression analysis but provides biased estimators

12. Imputation Replace missing values with an estimate:
Mean for that variable – biased estimates of variances and covariances
Multiple regression to predict value – complicated with multiple variables containing missing values, but can still lead to underestimated standard errors

13. Maximum Likelihood
Try to reconstruct the complete data set by selecting values that would maximize the probability of observing the actually observed data
Categorical and continuous data
Expectation-maximization algorithm gives estimates of means and covariances

14. Expectation Maximization
Iterative steps of expectation and maximization to produce estimates that converge on the ML estimates
These estimates will generally underestimate the standard errors in regression and other statistical models

15. Multiple Imputation 1
Has the same optimal properties of ML but several advantages
Can be used with any kind of data and any kind of statistical model
But produces multiple estimates which must be combined
Random component used to give unbiased estimates

16. Multiple Imputation 2
Multivariate normal model (relatively resistant to deviations)
Each variable represented as a linear function of the other variables
Methods
Data Augmentation, package norm
Sampling Importance/Resampling, package amelia

17. Multiple Imputation 3 Categorical data, multinomial model, package cat
Categorical and interval/ratio data, package mix
Also can use multivariate normal models with dummy variables

18. Multiple Imputation 4
Predictive mean matching – use regression to predict values for a particular variable. Find complete cases that have predictions similar to the case with a missing value on that variable and randomly one of the actual values, package Hmisc, function aregImpute

19. Analysis
The analysis is run on each imputed data set and the estimates (e.g. regression coefficients are combined)
Packages such as zelig provide ways of combining the datasets for generalized linear models

20. Missing Data with R 1 NA is used to identify a missing value
is.na() is used to test for a missing value: is.na(c(1:4, NA, 6:10))
na.omit(dataframe) will delete all cases with missing data (Rcmdr: Data | Active Data set| Remove cases with missing values

21. Missing Data with R 2
Some functions have an na.rm= option. True means remove cases with missing values, False means do not remove them so that the function returns NA if there are missing values.

22. Missing Data in R 3
Other functions (e.g. lm, princomp, glm) have an na.action= option that must can be set to one of the following options: na.fail, na.omit, na.exclude to remove cases (omit, exclude) or have the analysis fail

23. Missing Data in R 4
Other functions (e.g. cor, cov, var) have a use= option:
everything (NA’s propagate)
all.obs (NA causes error)
complete.obs (delete cases with NA’s)
na.or.complete (delete cases with NA’s)
pairwise.complete.obs (complete pairs of observations)

24. Example 1
ErnestWitte data set has missing values among the 242 cases and 38 variables
Using R to remove all cases with missing values reduces the number of cases to 52!
If we don’t need all of the variables we can retain more cases

25. Example 2 Total NA’s in ErnestWitte (815)
sum(is.na(ErnestWitte))
Check missing values by variable:
sort(apply(ErnestWitte, 2, function(x) sum(is.na(x))), decreasing=TRUE)
Looking has 171, SkullPos 126, Depos 112
Removing these gives 112 cases

26. Multiple Imputation with R
A wide variety of options:
Packages norm, cat, mix
Package amelia
Package mi (relatively new, but flexible)