Goodness-Of-Fit Chi-Square Statistics Using Imputed Data (Missing Data, Survey Samples).

Abstract

A method to compensate for nonresponse in survey data is to complete the data set by using respondent data to replace all nonresponses; this procedure is called imputation. Due to the re-use of the respondent data, the distribution theory of statistics computed from an imputed data set is more complex than that of the same statistics when there are no missing data. The effect of imputation on statistics used in the analysis of categorical data is investigated in this thesis. The asymptotic distribution for proportions is derived under a model that incorporates r and omness due to response, to simple r and om sampling and to the imputation procedure. Proportions computed from an imputed data set are shown to be unbiased estimates of the population probabilities; their covariance matrix depends on on the overall response rate, imputation class parameters and response rates, and the imputation procedure used. Proportions estimated from an imputed data set can be closer to the population probabilities than those estimated from the respondent data. The asymptotic distribution of the chi-square statistic computed from the imputed data set is determined by the distribution of a quadratic form of normal variates and , in special cases, simplifies to the chi-squared distribution. A test for goodness-of-fit based on these results is proposed and alternative tests are considered that are easier to use. The empirical properties of these tests are examined for three imputation procedures at moderate samples by means of simulation using as criteria the mean of the imputed chi-square statistics, the estimated tail probabilities and the empirical cumulative distribution function. For two imputation procedures, the proposed test for goodness-of-fit using the estimated distribution function of the imputed chi-square statistic appears to be unbiased when the sample size is greater than 2000. For the third procedure, the proposed test for goodness-of-fit is biased since the estimate of the distribution function is biased. When the sample size is smaller, the estimated tail probabilities tend to overestimate the nominal level of the test.