Single Imputation Methods

Question 1

Describe complete case analysis (note not an imputation method)

Answer 1

• excludes data for any case that has one or more missing value
• data treated as if cases with missing values simply aren’t there

Question 2

When is CCA good?

Answer 2

Can produce unbiased estimates of regression coefficients provided missingness is a function of a prediction variable and not a response variable

Question 3

Describe available case analysis (note not an imputation method)

Answer 3

• (X1, X2) data matrix where only X2 is subject to missingness
• all cases would be used for mean and variance of X1, but only complete cases contribute to estimates for X2 and covariance of X1 and X2

Question 4

Problems with ACA?

Answer 4

• not clear which sample size should be used to calculate standard errors
• estimates can be biased if data not MCAR

Question 5

What is the main issue with single imputation methods?

Answer 5

Standard errors of estimates tend to be too low, hence single imputation is not recommended

Question 6

Describe mean imputation

Answer 6

• each missing value is imputed by overall mean of observed values for that variable
• can use mode for categorical data

Question 7

Why is mean imputation worse than CCA?

Answer 7

Reduces variability of the data

Question 8

Describe conditional mean imputation

Answer 8

• replaces missing value with a predicted conditional mean from a regression equation
• first step is to fit a regression model, where the variable with the missing values is regressed on the observed ones, then find predictions for missing values

Question 9

Issue with conditional mean imputation?

Answer 9

There is no random error

Question 10

Describe stochastic regression imputation

Answer 10

• regression model gets added error term, which is a random value from N(0 , σhat^2)

Question 11

Does stochastic regression imputation fix the issue of attenuating standard errors?

Answer 11

No

Question 12

Describe hot deck imputation

Answer 12

• imputes values from “similar” individuals
• replaces the missing value with a random draw from a subsample of individuals that have similar values on a set of matching variables

Question 13

What is the issue with hot deck imputation

Answer 13

Can produce substantially biased estimates of correlations and regression coefficients, and under estimates standard errors

Question 14

Describe last observation carried forward

Answer 14

• in longitudinal studies, imputes missing value with its value at a previous time point
• assumes that values do not change after the last observed measurement or during the intermittent period where scores are missing

Question 15

Issues with last observation carried forward?

Answer 15

May produce biased results even when MCAR

Question 16

Describe iterative regression imputation

Answer 16

1. impute all missing values in Y1, Y2, …, Yk with some crude imputation method
2. impute Y1 given Y2, …, Yk and Yobs using stochastic regression imputation
3. impute Y2 given Y1, Y3, …, Yk and Yobs using newly imputed values for Y1
4. ….
5. impute Yk given Y1, …, Y(k-1) and Yobs using newly imputed values for Y1, …, Y(k-1)
6. loop until convergence

Question 17

When does iterative regression imputation work?

Answer 17

only <5% missing values