Multiple Imputation Using Gaussian Copulas

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper, we present a simple-to-use method for generating multiple imputations using a Gaussian copula. The Gaussian copula for multiple imputation (Hoff, 2007) allows scholars to attain estimation results that have good coverage and small bias. The use of copulas to model the dependence among variables will enable researchers to construct valid joint distributions of the data, even without knowledge of the actual underlying marginal distributions. Multiple imputations are then generated by drawing observations from the resulting posterior joint distribution and replacing the missing values. Using simulated and observational data from published social science research, we compare imputation via Gaussian copulas with two other widely used imputation methods: MICE and Amelia II. Our results suggest that the Gaussian copula approach has a slightly smaller bias, higher coverage rates, and narrower confidence intervals compared to the other methods. This is especially true when the variables with missing data are not normally distributed. These results, combined with theoretical guarantees and ease-of-use suggest that the approach examined provides an attractive alternative for applied researchers undertaking multiple imputations

Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques

Ordinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests (Δχ2) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of (Δχ2) tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results

Microdata Imputations and Macrodata Implications: Evidence from the Ifo Business Survey

A widespread method for now- and forecasting economic macro level parameters such as GDP growth rates are survey-based indicators which contain early information in contrast to official data. But surveys are commonly affected by nonresponding units which can produce biases if these missing values can not be regarded as missing at random. As many papers examined the effect of nonresponse in individual or household surveys, only less is known in the case of business surveys. So, literature leaves a gap on this issue. For this reason, we analyse and impute the missing observations in the Ifo Business Survey, a large business survey in Germany. The most prominent result of this survey is the Ifo Business Climate Index, a leading indicator for the German business cycle. To reflect the underlying latent data generating process, we compare different imputation approaches for longitudinal data. After this, the microdata are aggregated and the results are compared with the original indicators to evaluate their implications on the macro level. Finally, we show that the bias is minimal and ignorable