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Appendix D: Discriminant
Multiple Imputation
D I S C R I M I N A N T
M U L T I P L E
I M P U T A T I O N
Discriminant Multiple Imputation
This appendix describes the method used to impute binary and categorical variables for
Discriminant Multiple Imputation.
Discriminant Multiple Imputation is a model based method for binary or categorical variables.
The detailed imputation method is described in the following:
Let 1,…,s be the categories of the categorical imputation variable y. By applying Bayes’
Theorem, the statistical model of discriminant imputation is given by the following equation:
P( y = j | x ) =
φ (x | µ j ; Σ j )π j
s
å φ (x | µ
v =1
v
; Σv )π v
, j = 1, K, s In this equation P( y = j | x ) is the
probability that the imputation variable y is equal to its j-th category given the vector x of the
observed values of the covariates of y and :
φ (. | µ , Σ )
is the density of the multivariate normal distribution with mean µ and covariance matrix: Σ.
µj
and Σ j
are the conditional mean and covariance matrix of the covariates of y given that y is equal to its
j-th category, and π j is the apriori probability that y is equal to its j-th category.
The imputation scheme for discriminant multiple imputation is given by:
(i)
Let n j be the number of observed values of y equal to the j-th category of y and let
a j = 1 / 2 + n j , for j = 1, K, s ;
(ii)
Draw θ 1* , K ,θ *s from the standard Gamma distribution with parameters given by
a1 ,K, a s ;
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