The effect of imputed values on the distribution of the goodness-of-fit chi-square statistic

Abstract

A method used to compensate for nonresponse is to impute missing values; that is, to replace each missing value with a respondent value selected from all observed values or from a subset of observed values. The imputation procedure used in this paper selects imputed values from the respondent data using simple random sampling with replacement within homogeneous subsets and replaces the missing values with these values to complete the data set. The empirical distribution of the goodness-of-fit chi-square statistic computed from the `completed' data set is compared to its asymptotic distribution and to the distribution of the traditional chi-square test statistic applied to the completed data set by ignoring the imputation.At nominal levels of five and ten percent, the asymptotic distribution of the goodness-of-fit chi-square statistic computed from the completed data set is shown to have a good empirical behavior at moderate sample sizes. When the imputed values are treated as actual responses and the imputation is ignored, the empirical levels of significance are much larger than the nominal levels.