A Multiple Imputation Score Test for Model Modification in Structural Equation Models

Structural equation modeling (SEM) applications routinely employ a trilogy of significance tests that includes the likelihood ratio test, Wald test, and score test or modification index. Researchers use these tests to assess global model fit, evaluate whether individual estimates differ from zero, and identify potential sources of local misfit, respectively. This full cadre of significance testing options is not yet available for multiply imputed data sets, as methodologists have yet to develop a general score test for this context. Thus, the goal of this article is to outline a new score test for multiply imputed data. Consistent with its complete-data counterpart, this imputation-based score test provides an estimate of the familiar expected parameter change statistic. The new procedure is available in the R package semTools and naturally suited for identifying local misfit in SEM applications (i.e., a model modification index). The article uses a simulation study to assess the performance (Type I error rate, power) of the proposed score test relative to the score test produced by full information maximum likelihood (FIML) estimation. Due to the two-stage nature of multiple imputation, the score test exhibited slightly lower power than the corresponding FIML statistic in some situations but was generally well calibrated

The development of delinquency during adolescence: a comparison of missing data techniques

Reinecke J, Weins C. The development of delinquency during adolescence: a comparison of missing data techniques. Quality & Quantity. 2013;47(6):3319-3334.Conclusions on the development of delinquent behaviour during the life-course can only be made with longitudinal data, which is regularly gained by repeated interviews of the same respondents. Missing data are a problem for the analysis of delinquent behaviour during the life-course shown with data from an adolescents’ four-wave panel. In this article two alternative techniques to cope with missing data are used: full information maximum likelihood estimation and multiple imputation. Both methods allow one to consider all available data (including adolescents with missing information on some variables) in order to estimate the development of delinquency. We demonstrate that self-reported delinquency is systematically underestimated with listwise deletion (LD) of missing data. Further, LD results in false conclusions on gender and school specific differences of the age–crime relationship. In the final discussion some hints are given for further methods to deal with bias in panel data affected by the missing process

Including auxiliary item information in longitudinal data analyses improved handling missing questionnaire outcome data

Objectives Previous studies show that missing values in multi-item questionnaires can best be handled at item score level. The aim of this study was to demonstrate two novel methods for dealing with incomplete item scores in outcome variables in longitudinal studies. The performance of these methods was previously examined in a simulation study. The two methods incorporate item information at the background when simultaneously the study outcomes are estimated. Study Design and Setting The investigated methods include the item scores or a summary of a parcel of available item scores as auxiliary variables while using the total score of the multi-item questionnaire as the main focus of the analysis in a latent growth model. That way the items help estimating the incomplete information of the total scores. The methods are demonstrated in two empirical data sets. Results Including the item information results in more precise outcomes in terms of regression coefficient estimates and standard errors, compared with not including item information in the analysis. Conclusion The inclusion of a parcel summary is an efficient method that does not overcomplicate longitudinal growth estimates. Therefore, it is recommended in situations where multi-item questionnaires are used as outcome measure in longitudinal clinical studies with incomplete scores because of missing item scores

Analyzing Incomplete Item Scores in Longitudinal Data by Including Item Score Information as Auxiliary Variables

The aim of this study is to investigate a novel method for dealing with incomplete scale scores in longitudinal data that result from missing item responses. This method includes item information as auxiliary variables, which is advantageous because it incorporates the observed item-level data while maintaining the scale scores as the focus of the analysis. These auxiliary variables do not change the analysis model, but improve missing data handling. The investigated novel method uses the item scores or some summary of a parcel of item scores as auxiliary variables, while treating the scale scores missing in a latent growth model. The performance of these methods was examined in several simulated longitudinal data conditions and analyzed through bias, mean square error, and coverage. Results show that including the item information as auxiliary variables results in rather dramatic power gains compared with analyses without auxiliary variables under varying conditions