Missing data is a problem that occurs frequently in many scientific areas. The most sophisticated method for dealing with this problem is multiple imputation. Contrary to other methods, like listwise deletion, this method does not throw away information, and partly repairs the problem of systematic dropout. Although from a theoretical point of view multiple imputation is considered to be the optimal method, many applied researchers are reluctant to use it because of persistent misconceptions about this method. Instead of providing an(other) overview of missing data methods, or extensively explaining how multiple imputation works, this article aims specifically at rebutting these misconceptions, and provides applied researchers with practical arguments supporting them in the use of multiple imputation.

Azathioprine and 6-mercaptopurine were considered effective in approximately 40% of IBD patients after 5 years of treatment. A quarter of the patients discontinued thiopurines within 3 months, mostly due to adverse events. A high 6-MMP concentration or 6-MMP/6-TGN ratio was associated with therapeutic failure. If thiopurine use was successfully initiated in the first months, its use was usually extended over many years, as long-term use was associated with continuation of therapy.

We propose using latent class analysis as an alternative to loglinear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike loglinear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihoodWe would like to thank Paul Allison and Jay Magidson, as well as the editor and the three anonymous reviewers, for their comments, which very much helped to improve this article. We would also like to thank Greg Richards for providing the data of the ATLAS Cultural Tourism Research Project, 2003. *Tilburg University † Leiden University 369 370 VERMUNT, VAN GINKEL, VAN DER ARK, AND SIJTSMA estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

As a procedure for handling missing data, Multiple imputation consists of estimating the missing data multiple times to create several complete versions of an incomplete data set. All these data sets are analyzed by the same statistical procedure, and the results are pooled for interpretation. So far, no explicit rules for pooling F-tests of (repeated-measures) analysis of variance have been defined. In this paper we outline the appropriate procedure for the results of analysis of variance for multiply imputed data sets. It involves both reformulation of the ANOVA model as a regression model using effect coding of the predictors and applying already existing combination rules for regression models. The proposed procedure is illustrated using three example data sets. The pooled results of these three examples provide plausible F- and p-values.

BackgroundDespite the disabling nature of eating disorders (EDs), many individuals with ED symptoms do not receive appropriate mental health care. Internet-based interventions have potential to reduce the unmet needs by providing easily accessible health care services.ObjectiveThis study aimed to investigate the effectiveness of an Internet-based intervention for individuals with ED symptoms, called “Featback.” In addition, the added value of different intensities of therapist support was investigated.MethodsParticipants (N=354) were aged 16 years or older with self-reported ED symptoms, including symptoms of anorexia nervosa, bulimia nervosa, and binge eating disorder. Participants were recruited via the website of Featback and the website of a Dutch pro-recovery–focused e-community for young women with ED problems. Participants were randomized to: (1) Featback, consisting of psychoeducation and a fully automated self-monitoring and feedback system, (2) Featback supplemented with low-intensity (weekly) digital therapist support, (3) Featback supplemented with high-intensity (3 times a week) digital therapist support, and (4) a waiting list control condition. Internet-administered self-report questionnaires were completed at baseline, post-intervention (ie, 8 weeks after baseline), and at 3- and 6-month follow-up. The primary outcome measure was ED psychopathology. Secondary outcome measures were symptoms of depression and anxiety, perseverative thinking, and ED-related quality of life. Statistical analyses were conducted according to an intent-to-treat approach using linear mixed models.ResultsThe 3 Featback conditions were superior to a waiting list in reducing bulimic psychopathology (d=−0.16, 95% confidence interval (CI)=−0.31 to −0.01), symptoms of depression and anxiety (d=−0.28, 95% CI=−0.45 to −0.11), and perseverative thinking (d=−0.28, 95% CI=−0.45 to −0.11). No added value of therapist support was found in terms of symptom reduction although participants who received therapist support were significantly more satisfied with the intervention than those who did not receive supplemental therapist support. No significant differences between the Featback conditions supplemented with low- and high-intensity therapist support were found regarding the effectiveness and satisfaction with the intervention.ConclusionsThe fully automated Internet-based self-monitoring and feedback intervention Featback was effective in reducing ED and comorbid psychopathology. Supplemental therapist support enhanced satisfaction with the intervention but did not increase its effectiveness. Automated interventions such as Featback can provide widely disseminable and easily accessible care. Such interventions could be incorporated within a stepped-care approach in the treatment of EDs and help to bridge the gap between mental disorders and mental health care services.Trial RegistrationNetherlands Trial Registry: NTR3646; http://www.trialregister.nl/trialreg/admin/ rctview.asp?TC=3646 (Archived by WebCite at http://www.webcitation.org...

A well-known problem in the analysis of test and questionnaire data is that some item scores may be missing. Advanced methods for the imputation of missing data are available, such as multiple imputation under the multivariate normal model and imputation under the saturated logistic model (Schafer, 1997). Accompanying software was made available by, for example, Schafer (1998a, 1998b) and in SOLAS (2001) and S-Plus 6 for Windows (2001). However, these methods and software may be too complicated for a typical psychological researcher, and for the imputation of his or her missing data, he or she depends on the help of a trained statistician. If available, this statistician may not always have enough time or may not be an experienced software user, so the researcher may decide to simply delete all incomplete observations. To help researchers impute scores using simple methods, two SPSS subroutines were written. The aim of these subroutines is that researchers can apply them easily within SPSS and without experienced help. The subroutine "tw" performs two-way imputation, and the subroutine "rf" performs responsefunction imputation. Two-way imputation and response-function imputation are described by Sijtsma and Van der Ark (2003). Simulation studies by Van der Ark and Sijtsma (in press) indicate that these imputation methods work rather well when applied to an approximately unidimensional set of items (i.e., the items measure the same construct). The subroutines allow the researcher to transform an SPSS data file with missing values (an incomplete data file) into an SPSS data file without missing values (a completed data file). The researcher can use the completed data file for further analysis. To run the subroutines, one must select the variables containing the missing scores that need to be imputed, and some optional arguments also can be specified. For two-way imputation, the most important optional argument pertains to changing or removing the random error that is added to the imputed values by default. For response-function imputation, the most important optional argument pertains to changing the minimum group size used for estimating the response function (see Sijtsma & Van der Ark, 2003).

The performance of five simple multiple imputation methods for dealing with missing data were compared. In addition, random imputation and multivariate normal imputation were used as lower and upper benchmark, respectively. Test data were simulated and item scores were deleted such that they were either missing completely at random, missing at random, or not missing at random. Cronbach's alpha, Loevinger's scalability coefficient H, and the item cluster solution from Mokken scale analysis of the complete data were compared with the corresponding results based on the data including imputed scores. The multiple-imputation methods, two-way with normally distributed errors, corrected item-mean substitution with normally distributed errors, and response function, produced discrepancies in Cronbach's coefficient alpha, Loevinger's coefficient H, and the cluster solution from Mokken scale analysis, that were smaller than the discrepancies in upper benchmark multivariate normal imputation.

The focus of this study was the incidence of different kinds of missing-data problems in personality research and the handling of these problems. Missing-data problems were reported in approximately half of more than 800 articles published in three leading personality journals. In these articles, unit nonresponse, attrition, and planned missingness were distinguished but missing item scores in trait measurement were reported most frequently. Listwise deletion was the most frequently used method for handling all missing-data problems. Listwise deletion is known to reduce the accuracy of parameter estimates and the power of statistical tests and often to produce biased statistical analysis results. This study proposes a simple alternative method for handling missing item scores, known as two-way imputation, which leaves the sample size intact and has been shown to produce almost unbiased results based on multi-item questionnaire data.