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Missing values that are missing not at random (MNAR) can result from a variety of missingness processes. However, two fundamental subtypes of MNAR values can be obtained from the definition of the MNAR mechanism itself. The distinction between them deserves consideration because they have characteristic differences in how they distort relationships in the data. This has implications for the validity of statistical results and generalizability of methodological findings that are based on data (empirical or generated) with MNAR values. However, these MNAR subtypes have largely gone unnoticed by the literature. As few studies have considered both subtypes, their relevance to methodological and substantive research has been overlooked. This article systematically introduces the two MNAR subtypes and gives them descriptive names. A case study demonstrates they are mechanically distinct from each other and from other missing-data mechanisms. Applied examples are given to help researchers conceptually identify MNAR subtypes in real data. Methods are provided to generate missing values from both subtypes in simulation studies. Simulation studies for regression and growth curve modeling contexts show MNAR subtypes consistently differ in the severity of their impact on statistical inference. This behavior is examined in light of how relationships in the data become characteristically distorted. The contents of this article are intended to provide a foundation and tools for organized consideration of MNAR subtypes.

Background Comorbid disease in cancer patients can substantially impact medical care, emotional distress, and mortality. However, there is a paucity of research on how coping may affect the relationship between comorbidity and emotional distress. Purpose The current study investigated whether the relations between comorbidity and emotional distress and between functional impairment and emotional distress were mediated by three types of coping: action planning (AP), support/advice seeking (SAS), and disengagement (DD). Methods Four hundred and eighty-three persons with cancer completed a measure of functional impairment (Sickness Impact Profile), the Checklist of Comorbid Conditions, the Brief COPE, the Hospital Anxiety and Depression Scale, the Quality of Life Assessment for Cancer Survivors (Negative Feelings Scale), and the Distress Screening Schedule (Emotional Distress Scale). The latter three measures were used to form a latent construct representing the outcome, emotional distress. Results Model comparison analysis indicated that the model with DD as a mediator had a better fit than models containing AP and SAS. DD mediated the relationship between functional impairment and emotional distress, so that engaging in DD was associated with greater distress. In addition, comorbidity and functional impairment were directly and positively related to emotional distress, but the relation between comorbidity and distress was not mediated by coping type. Conclusions Both comorbidity and functional impairment may be associated with distress, but disengagement coping only mediated the relation involving functional impairment and was positively associated with distress. Future studies can investigate whether teaching active coping or adaptive coping (e.g., through mindfulness exercises) can decrease distress in cancer patients, despite functional impairments.

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Data in social sciences are typically non-normally distributed and characterized by heavy tails. However, most widely used methods in social sciences are still based on the analyses of sample means and sample covariances. While these conventional methods continue to be used to address new substantive issues, conclusions reached can be inaccurate or misleading. Although there is no 'best method' in practice, robust methods that consider the distribution of the data can perform substantially better than the conventional methods. This article gives an overview of robust procedures, emphasizing a few that have been repeatedly shown to work well for models that are widely used in social and behavioural sciences. Real data examples show how to use the robust methods for latent variable models and for moderated mediation analysis when a regression model contains categorical covariates and product terms. Results and logical analyses indicate that robust methods yield more efficient parameter estimates, more reliable model evaluation, more reliable model/data diagnostics, and more trustworthy conclusions when conducting replication studies. R and SAS programs are provided for routine applications of the recommended robust method.